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EMBRACING  THE  PRINCIPLES  OF  CONSTRUC- 
TION   AS    APPLIED    TO     PRACTICAL    DESIGN 


WITH  NUMEROUS  ILLUSTRATIONS  OF   TOPOGRAPHICAL, 

MECHANICAL,     ENGINEERING,     ARCHITECTURAL, 

PERSPECTIVE,   AND  FREE-HAND  DRAWING 


EDITED    BY 

W.    E.  WORTHEN,    C.  E. 


OF    1 

UN: 


NEW    YORK 
D.    APPLETON    AND    COMPANY 

1896 


COPYRIGHT,  1885,  1896, 
BY  D.  APPLETON  AND  COMPANY. 


PREFACE. 


"  AT  the  suggestion  of  the  publishers,  this  work  was  undertaken  to  form 
one  of  their  series  of  dictionaries  and  cyclopaedias.  In  this  view,  it  has 
been  the  intention  to  make  it  a  complete  course  of  instruction  and  book  of 
reference  to  the  mechanic,  architect,  and  engineer.  It  has  not,  therefore, 
been  confined  to  the  explanation  and  illustration  of  the  methods  of  projec- 
tion, and  the  delineation  of  objects  'which  might  serve  as  copies  to  the 
draughtsman,  matters  of  essential  importance  for  the  correct  and  intelligible 
representation  of  every  form ;  but  it  contains  the  means  of  determining  the 
amount  and  direction  of  strains  to  which  different  parts  of  a  machine  or 
structure  may  be  subjected,  and  the  rules  for  disposing  and  proportioning 
of  the  material  employed,  to  the  safe  and  permanent  resistance  of  those 
strains,  with  practical  applications  of  the  same.  Thus,  while  it  supplies 
numerous  illustrations  in  every  department  for  the  mere  copyist,  it  also 
affords  suggestions  and  aids  to  the  mechanic  in  the  execution  of  new 
designs.  And,  although  the  arranging  and  properly  proportioning  alone 
of  material  in  a  suitable  direction,  and  adequately  to  the  resistance  of  the 
strains  to  which  it  might  be  exposed,  would  produce  a  structure  sufficient 
in  point  of  strength  for  the  purposes  for  which  it  is  intended,  yet,  as  in 
many  cases  the  disposition  of  the  material  may  be  applied  not  only  practi- 
cally, but  also  artistically.  .  .  .  1857." 

"  There  are  no  changes  in  the  principles  of  projection  as  applied  to 
drawing,  and  no  marked  improvement  in  drawing-instruments ;  but  in  the 
present  practice  finished  drawings  in  shade  and  colour  are  exceptional.  It 
is  sufficient,  for  almost  every  purpose,  for  the  draughtsman  to  make  accu- 
rate projections  with  pencil  on  paper,  and  trace  them  afterward  on  cloth. 
The  pencil-drawings  can  be  readily  altered  or  amended,  and,  where  there 
are  many  repetitions  of  the  same  parts,  but  a  single  one  may  be  drawn. 
On  the  tracing  they  are  made  complete,  and  these  are  preserved  as  originals 
in  the  office,  while  sun-prints  of  them  are  used  for  details  of  construction 
in  the  shop,  or  distributed  as  circulars  among  customers. 

"  Of  late  years  the  science  of  '  graphics '  has  become  of  great  impor- 
tance, and  is  here  fully  illustrated  in  its  varied  applications,  showing  not 
only  this  method  of  recording  the  facts  of  the  statistician,  and  affording 
comparisons  of  circumstances  and  times,  the  growth  of  population,  the 

iii 


IV 


PREFACE. 


quantities  and  cost  of  agricultural  and  mechanical  production,  and  of  their 
transport,  movements  of  trade,  fluctuations  of  value,  the  atmospheric  con- 
ditions, death-rates,  etc.,  but  also  in  its  application  to  the  plotting  of 
formulae  for  their  ready  solution,  by  the  draughtsman  and  designer.  For 
many  of  the  rules  in  this  work  the  results  of  the  formulae  of  various 
authors  have  been  plotted  graphically,  and  the  rule  given  one  deemed  of 
the  greatest  weight,  not  always  by  average,  but  most  consistent  with  our 
own  experience. 

"  In  astronomical  calculations  every  decimal  may  have  its  importance. 
It  is  not  so  in  those  of  the  mechanical  or  architectural  designer ;  solutions  by 
graphics  are  sufficient  for  their  purpose,  and,  simpler  than  mathematical 
calculations,  they  are  thus  less  liable  to  error  ;  it  is  a  very  good  practice  to 
use  one  as  a  check  on  the  other.  It  is  to  be  remarked  that  inaccuracy  in 
facts,  and  carelessness  in  observation,  are  not  eliminated  from  an  equation 
by  closeness  of  calculation,  and  when  factors  are  not  established  within  the 
limits  of  units  it  is  useless  to  extend  the  results  to  many  places  of  decimals. 
It  is  of  the  utmost  importance  to  know  at  first  well  the  object  and  pur- 
poses of  the  design,  the  stresses  to  which  its  parts  are  to  be  subjected,  and 
the  strength  and  endurance  of  the  materials  of  which  it  is  to  be  composed. 
In  establishing  rules  for  ourselves,  be  sure  of  the  facts,  and  that  there  are 
enough  of  them  for  a  general  application.  Rules  are  necessary,  but  their 
application  and  usefulness  depend  largely  on  the  experience  of  the  user, 
and  life  must  be  a  record  of  applications  and  effects.  It  is  comparatively 
easy  to  make  a  work  strong  enough ;  but  to  unite  economy  with  propor- 
tion is  difficult.  .  .  .  1886." 

The  first  edition  of  this  work  was  suggested  by  "  The  Engineer  and 
Machinist's  Drawing  Book  "  of  Messrs.  Blackie  &  Son,  1855,  from  which, 
with  the  consent  of  the  publishers,  much  of  the  text  and  illustrations  were 
taken.  Since  then,  in  the  many  editions,  it  has  been  the  aim  to  keep  up 
with  mechanical  progress,  and  matter  has  been  drawn  from  all  sources. 
Credit,  as  far  as  possible,  has  been  given  to  mechanics  for  their  designs  and 
to  experimenters  for  their  results. 

Geometrical  problems  and  examples  of  orthographic  projection  of  the 
first  work  are  largely  retained,  but  examples  of  mechanical  and  archi- 
tectural construction  are  brought  up  to  the  present  age  of  steel,  with  the 
latest  illustrations  of  the  applications  of  steam,  and  some  of  electricity. 
Isometry  is  retained,  perspective  has  been  more  fully  illustrated,  and  free- 
hand drawing  now  includes  the  recent  processes  by  which,  through  pho- 
tography, the  mechanical  labour  of  sketching  is  diminished,  adding  to  the 
correctness  of  detail  and  improving  the  effectiveness  on  paper.  This  may 
be  called  an  age  of  illustration,  and  the  processes  have  enabled  a  work  like 
the  present  drawing  book  to  give  better  and  more  illustrations,  less  text, 
more  comprehensiveness,  and  greater  certainty  of  detail. 

Mr.  Robert  E.  Hawley,  brought  up  in  my  office,  has  had  charge  of  the 
new  drawings  and  has  acted  as  co-editor.  AV. 


CONTENTS. 


PAGES. 

CONSTRUCTION  OF  GEOMETRICAL  PROBLEMS 1-82 

Drawing  of  lines — straight,  curved,  perpendicular,  and  parallel :  angles,  ai'cs, 
and  circles,  13.  Triangles,  polygons  and  circles,  inscribed  and  described ; 
polygonal  angles  ;  use  of  protractor,  21.  Use  of  the  triangle  and  square  ;  areas 
of  figures  ;  scales,  25.  Similar  triangles,  squares  of  proportionate  sizes,  30.  El- 
lipse, parabola,  hyperbola,  spiral,  35.  Drawing-board,  table  ;  straight-edges  ; 
T-squares:  parallel  rulers ;  curves,  variable  and  adjustable;  splines  and  weights ; 
thumbtacks;  drawing  pens;  dotting  instrument;  compasses;  dividers;  plot- 
ting scales;  protractors;  sector;  pantographs,  51.  Drawing  paper;  tracing 
paper;  tracing  cloth  ;  heliographic  paper ;  damp  stretching  and  mounting,  55. 
Use  of  instruments;  representation  of  surfaces;  enlarging  and  reduction  of 
drawings ;  designs  in  lines,  62.  Lettering ;  profile  and  cross-section  paper,  77. 
Ornamental  designs  in  straight  and  curved  lines,  82. 

PLOTTING       ....*« 83-94 

Scales  ;  plotting  for  surveys,  plans  and  maps  ;  plotting  by  protractor,  by  lati- 
tudes and  departures,  by  triangles,  by  offsets ;  United  States  division  of  public 
lands,  94. 

TOPOGRAPHICAL  DRAWING 95-120 

Conventional  signs ;  representation  of  hills ;  chart  from  United  States  Sur- 
vey, 102.  Railway,  103.  Hydrometrical  chart,  geological  and  section,  109. 
Transferring  field  notes,  110.  Map  projections,  116.  Colored  topography; 
pen  and  brush  work,  119.  Meridians  and  borders,  120. 

ORTHOGRAPHIC  PROJECTION 121-146 

Point ;  straight  line ;  solid ;  simple  bodies :  pyramid ;  prism,  127.  Conic 
sections,  130.  Intersection  of  solids,  139.  The  helix,  141.  Development  of 
surfaces,  144.  Shade  lines,  146. 

SHADES  AND  SHADOWS 147-166 

Shadow  of  a  point,  of  a  straight  line,  of  a  solid,  of  a  pyramid,  of  a  cylinder, 
of  a  hollow  hemisphere;  niche,  154.  Lines  of  shade  on  sphere  ;  ring;  grooved 
pulley ;  screw,  159.  Manipulation  shades,  surfaces  in  light,  in  shade  by  flat 
tints,  by  softened  tints.  Examples  in  plates.  Conventional  tints,  166. 

MATERIALS 167-185 

Earth  and  rocks;  woods,  170.  Masonry,  technical  terms  for;  stones,  gra- 
nitic, argillaceous,  sand,  lime,  174.  Artificial  building  material  ;  brick,  sizes  of  ; 
fire ;  enamelled  tile ;  terra  cotta,  175.  Mortars  ;  concrete  ;  plastering  ;  weight 
of  masonry,  177.  Metals,  conventional  signs  of,  properties  of;  alloys,  strength 
of,  graphic  representation  by  Prof.  Thurston ;  sulphur:  glass;  rubber;  paints; 
coal ;  flame,  185. 

v 


VI. 


CONTENTS. 


MECHANICS 

Force  :  centres  of  gravity  ;  mechanical  powers  ;  parallelogram  of  forces  ; 
toggle  joint ;  hydraulic  press ;  statics ;  dynamics ;  velocity  of  falling  bodies, 
196.  Friction,  201.  Mechanical  work ;  unit  of  force ;  the  force  of  animals, 
water,  steam,  and  their  application  ;  the  steam-pressure  indicator  and  cards, 
211.  Motion,  example  of  the  path  of;  parts  of  machines  ;  of  the  crank ;  the 
Stanhope  lever  ;  Whitworth's  quick  return ;  parallel  motion  ;  car  coupler,  218 ; 
valve  diagram  ;  Corliss  cut  off  :  link  motion  ;  valve  gear,  228. 


HAGES 

186-228 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTION 

Stress  ;  strain  ;  dead  load  ;  factor  of  safety  ;  safe  load  of  columns,  cast  and 
wrought  iron  ;  shearing,  torsional  and  transverse  stress  ;  graphic  diagrams, 
239.  Table  of  safe  load  on  yellow-pine  beams,  on  cast  iron,  on  wrought  iron, 
on  steel ;  box  girders  ;  composite,  250.  Bolts  and  nuts  ;  screws ;  washers,  257. 
Shafts  and  axles,  cast  and  wrought  iron,  262.  Pillow  blocks ;  standards ; 
hangers ;  steps ;  suspension  and  thrust  bearings,  273.  Couplings ;  clutches, 
282.  Pulleys,  wooden  and  iron  plates ;  cone,  287.  Belts,  plain,  twist,  and 
cross.  Strength  of  rope  driving,  299;  chain  driving;  leather  links,  301. 
Gearing,  spur,  rack,  and  pinion ;  bevel.  Form  of  teeth  ;  cycloid ;  hypocycloid  ; 
involute.  310.  Diagram  of  stress  on  teeth ;  diameter  of  pitch  circle.  Adcock's 
table  of  arcs  for  gear  teeth  ;  mortise  wheels,  316.  Projections  of  a  spur,  bevel, 
and  worm  wheels  ;  screws,  330.  Frictional  and  wedge  gearing,  333.  Blocks  for 
running  rigging ;  chains ;  chain  couplings ;  wire  rope ;  sockets ;  hooks  ;  337. 
Levers,  cranks,  342.  Eccentrics;  wiper;  stamp  mill,  347.  Connections,  cot- 
ters, pins,  rods,  348.  Eccentrics  and  straps  ;  crossheads,  354.  Working  beam  ; 
guide  bars,  358.  .Steam  cylinders;  pistons  of  pumps.  Water  pumps,  362.  Wood 
and  cup  packing,  364.  Steam  jacket ;  air  chamber ;  Thames  Ditton  pump ; 
Reidler ;  Worthington,  366.  The  injector,  368.  Clearances ;  piston  rods ;  stuff- 
ing boxes,  370.  Steam  ports :  Valves,  cylindrical,  balanced,  automatic, 
disk,  rubber,  ball,  poppet,  flap,  376.  Valves  controlled  by  hand,  cocks^ 
plug.  Valves  :  compression,  air,  globe,  gate,  damper  rotary,  safety,  382.  Hy- 
drants, 383.  Riveted  joints,  389.  Boilers  :  tubular,  marine ;  water  tube ;  flue  : 
locomotive,  vertical,  398.  Connections  of  steam  and  water  pipes ;  wrought- 
iron  pipes  ;  couplings  ;  unions  ;  coils ;  joints  for  submerged  pipes,  406.  Gov- 
ernor ;  fly-wheels ;  air  chambers  ;  accumulators  ;  hydraulic  press  ;  jack  screw ; 
housings. 


229-414 


ENGINEERING  DRAWING 

Foundations  ;  concrete  base ;  crib  work  ;  New  York  dock  ;  Thames  embank- 
ment ;  breakwater  ;  screw  piles  ;  masonry  curbs ;  steel  caissons  ;  Poughkeepsie 
bridge  pier ;  pneumatic  piles ;  caissons  and  air  lock ;  freezing  process,  435. 
Retaining  walls,  436.  Dams :  earth,  crib,  masonry,  444.  Gates :  head,  waste, 
451.  Canals,  navigation,  power.  Locks  of  canals ;  flumes  and  conduits,  459. 
Reservoirs  ;  sheet-iron  pipe  ;  water  tanks,  462.  Water  mains  for  city  service  ; 
specials ;  inspection,  466.  Sewers :  brick,  vitrified  pipe,  circular,  egg-shaped, 
concrete,  man-holes,  471.  Gas  supply,  472.  Roads  and  highways ;  street  pave- 
ments :  granite,  asphalt,  wooden,  block,  479.  Railroads  ;  road  bed  :  rails  ;  elec- 
tric conduit,  483.  Roofs  and  bridges  ;  principle  of  bracing ;  frames,  wooden, 
iron ;  trestles,  498  ;  truss  bridges :  wooden,  iron,  combination,  510.  Turn  ta- 
bles ;  ferry-landing  bridge ;  high  wrought-iron  trestles ;  masonry  piers ;  arch 
bridge,  522.  Boiler  setting,  horizontal,  tubular,  526 ;  chimneys,  530.  Loca- 
tion of  machines  ;  foundation,  535.  Tunnels :  principles  of  timbering ;  Hoo- 
sac ;  bar  timbering,  539.  Railway  rolling  stock  ;  box  car  ;  standard  passenger ; 
locomotive  frame,  545.  Wave-line  principle  of  ship  construction,  547. 


415-547 


CONTENTS.  vii 

PAGES 

ARCHITECTURAL  CONSTRUCTION 548-693 

Plans  and  elevations,  553 ;  details  of  construction ;  timber  frames  and 
floors,  561.  Examples  of  fire-proofing,  old,  recent ;  skeleton  frames,  fire-re- 
tarding construction  of  mills,  571 ;  windows ;  stairs ;  doors.  Fireplaces ; 
flues  ;  roofs  ;  gutters  ;  cornices,  587.  Plastering  ;  mouldings,  590.  Sizes  of 
rooms  ;  water  appliances  and  accessories ;  Ferguson's  rules  of  proportion ;  de- 
signing of  house  ;  illustration  and  details  ;  country  and  city,  609.  Apartment 
houses  ;  store  and  warehouses  ;  machine-shop  ;  school-houses ;  churches ; 
theatres;  lecture  rooms ;  music  and  legislative  halls;  waves  of  sound;  effect 
of  air  currents ;  space  for  seats :  ancient  and  modern  churches ;  organs ;  628. 
Theatres,  dimensions  of  some,  630.  Legislative  halls,  acoustic  principles; 
hospitals ;  stables ;  cowhouses  ;  greenhouses,  634.  Ventilation  and  warming ; 
stoves ;  hot-air  furnaces ;  steam  and  hot  water  circulation,  647.  Radiators ; 
laying  out  of  pipes,  649.  Plumbing ;  soil  pipe  ;  fixtures  for  kitchens ;  baths  ; 
water-closets  ;  traps  and  bends,  656.  Lighting  :  gas,  electric,  wiring.  Orders 
of  architecture :  Greek  and  Roman,  Romanesque,  Byzantine,  Gothic,  the  Re- 
naissance. Arches  ;  domes  and  vaults ;  buttresses  ;  towers ;  bell  cots  ;  spires, 
674.  Windows,  lancet,  traceried ;  doorways,  679.  Mouldings ;  arch  and 
architrave ;  capitals ;  bases ;  string  courses  and  cornices,  682.  Ornaments,  693. 

ISOMETRICAL  DRAWING ."      .        .       .        .        .    694-705 

PERSPECTIVE 706-725 

Points  and  planes  of  perspective ;  parallel  and  angular  perspective  of  cubes 
and  other  solids,  of  buildings,  of  an  arched  bridge,  of  an  interior,  of  a  staircase, 
of  reflection  of  objects  in  water,  of  shadows  ;  perspective  as  illustration  of  ad- 
vertisements. 

FREE-HAND  DRAWING 726-764 

Materials :  paper,  pencils,  lithographic  chalk,  pens,  ink.  Proportions  of  Hu- 
man Frame,  Geometrical  drawings  of,  "  Dictionnaire  Raisone  par  Viollet  le 
Due  "  and  Dr.  Rimmer's  "  Elements  of  Design."  Half  tones  of  photographs  of 
plaster  models,  "  ecorche  "  of  wash  drawing  of  flowers,  etc.,  P.  de  Lohgpre.  Pen 
and  ink  reproduction  of  photographs  on  plain  salted  paper,  models  "ecorche," 
Sandow,  manikins,  Venus  de  Milo,  and  Dumas.  Pumping  Station  after  Emer- 
son in  toothpick  and  splatter  work.  Drawings  on  stipple  paper  or  clayboard,  Sal- 
vini  and  Venetian  fete  on  the  Seine.  Pen  and  ink  drawing,  hands,  feet,  heads, 
Electioneer,  Cow,  Donkey  from  Landseer,  hoofs,  paws,  muzzles,  Espanola  y 
Americana,  Erik  Werenskiold  and  design  by  Fortuny,  Alexandrian  pilot,  Head 
of  Sheik,  Water  Bearer,  Donkey's  Head,  Deer,  Ducks,  Landscapes,  Oak  Trees, 
Morning,  Cattle  going  Home,  Lady  of  the  Woods,  Elm,  Cedar,  Sketch  in 
chalk,  Suez  Canal  and  sea  sketch. 

APPENDIX       ......        765-861 

Patent  office,  Requirements  for  drawings  and  Registration  of  prints  and  labels. 
Mensuration,  areas  of  surfaces,  contents  of  solids  ;  measures,  lineal,  of  surface ; 
of  capacity ;  liquid :  dry.  Weights,  apothecaries',  Troy,  avoirdupois,  compari- 
son of;  Dynamic  Table:  cubic  measure;  shipping  measure;  register;  ship- 
ping ;  carpenter's  rule.  Table  of  inches  and  parts  in  decimals  of  a  foot ;  elec- 
trical units ;  units  of  heat.  Table  of  fifth  powers  of  numbers  ;  weight  of  cast- 
iron  balls,  of  cast-iron  pipe,  weights  of  rolled  iron,  773 ;  weight  of  wrought. 
Tables  of  dimensions  and  weight  of  wrought  iron  welded  tubes  ;  nominal  and 
actual  diameters  of  boiler  tubes.  Heavy  pipe  for  driven  wells ;  spiral  riveted 
tubes,  heavy  and  light ;  weight  of  copper  and  brass  rods ;  rivets ;  wrought  spikes ; 
cut  nails  and  spikes ;  wire  nails,  weight  of.  Galvanized  telegraph  wire ; 
weights ;  resistance  in  ohms ;  sizes  used.  Standard  Beams  and  Channels  of  Asso- 


vriii  CONTENTS. 

PAGES 

ciation  of  American  Steel  Manufacturers ;  grades  of  steel ;  weights  of  lead  pipe. 
Weight  of  a  cubic  foot  of  water  at  different  temperatures.  Flow  of  water, 
781-791,  over  weirs,  through  pipes  and  conduits ;  graphic  diagrams  of  Kutter 
formulae.  Table  of  equalizing  the  diameter  of  pipes ;  flow  of  air ;  comparison 
of  flow  of  water  by  the  Kutter  diagrams,  with  that  of  air;  with  that  of  gas, 
and  the  products  of  combustion  in  chimneys.  The  Babcock  and  Wilcox  boiler ; 
the  Green  economizer ;  the  Heine  boiler.  Table  of  saturated  steam,  798;  ex- 
pansive working  of  steam.  Table  of  factors  of  evaporation.  Electric  Light 
and  Power  Station,  Twenty-eighth  Street,  New  York  city,  805.  Diagram  of 
electric  wiring ;  lamp  socket  switch  and  Lundell  motor ;  Table  of  the  density 
of  gases.  Specific  gravity  of  liquids,  of  earths,  of  woods,  of  metals,  solders ; 
alloys.  Table  of  the  circumferences  and  areas  of  circles,  819.  Tables  of 
squares,  cubes,  and  roots,  826 ;  of  reciprocals  ;  Latitudes  and  Departures,  835. 
Natural  sines  and  cosines,  845.  Logarithms,  861. 

SCRAPS 862-912 

Compound  steel  cylinders ;  manholes  and  covers ;  compressed-air  locomo- 
tive ;  cranks ;  rudder  frame ;  boiler  flues ;  screw  propeller  ;  spherical  bearing ; 
conventional  signs  of  riveting ;  mechanical  stokers.  Boilers :  Stirling  and 
Abendroth  and  Root.  Engines — Corliss  stationary:  Deane  steam  pump; 
Reidler  valve ;  Locomotives ;  car  springs ;  elevated  railroad  ;  cable  grip ;  der- 
rick. Dams:  canvas,  earth,  masonry,  movable;  Builder's  hardware;  hinges; 
construction  of  safes.  Mantels  and  fireplaces ;  doors  ;  marquetry  ;  pediment ; 
brackets ;  railing ;  summer  house ;  windows ;  doorways ;  porches ;  house  fronts ; 
dormers  and  towers ;  skeleton  construction ;  Broad  Street  Station,  Philadel- 
phia. Church  spires ;  churches ;  perspective ;  buildings  of  Centennial  Exhi- 
bition ;  of  World's  Pair ;  Coney  Island. 


DESCRIPTION  OF  PLATES. 


I.  Shading  of  prism  and  cylinder  by  flat  tints.     Page  160. 
II.  Shading  of  cylinder  and  segment  of  hexagonal  pyramid.     Page  161. 
Ill,  IV.  Finished  shading  and  shadows  of  different  solids.     Page  163. 
V.  Shades  and  shadows  on  screws.     Page  164. 
VI.  Example   of   topographical    drawing,   done   entirely   with   the   pen. 

Page  101. 

VII.  The  same,  with  the  brush,  in  black.     Page  117. 
VIII.  The  same,  with  the  brush,  in  colour.     Page  118. 
IX.  Contoured  map  of  Staten  Island,  shaded  by  superimposed  washes, 
the  washes  increasing  in  intensity  or  strength  as  required  to  pro- 
duce the  effect.     Page  117. 
X.  Geological  map  of  part  of  New  Jersey,  coloured  to  show  the  different 

formations.     Page  106. 
XI,  XII.  Topographical  maps  of  parts'  of  Massachusetts. 

XIII.  Plan  and  ceiling  in  colour.     Page  548. 

XIV.  Perspective  view  of  Gothic  church,  finished  in  colour.  (Frontispiece.) 
XV.  Front  elevation  of  a  building,  in  colour. 

XVI.  Finished  perspective  drawing,  with  shades  and  shadows,  of  a  large 

bevel- wheel  and  two  pinions,  with  shifting  clutches.     Page  160. 
XVII.  Plan,  elevation,  and  section  of   bevel-wheel,  pinion,  and  clutches, 
shown  in  perspective  Plate  XVI.     Page  160. 


EEEATA. 

Page  160,  19th  line,  omit  Plate  XI,  and  for  Plates  XII  and  XV, 
substitute  Plates  XVI  and  XVII. 


APPLETONS' 


CYCLOPAEDIA  OF  DRAWING. 


CONSTRUCTION   OF   GEOMETRICAL   PROBLEMS. 


MOST  persons,  at  some  time,  have  made  use  of  the  simple  drawing  instru- 
ments, as  pencils,  straight  edges  or  rulers,  dividers  and  compasses  with  change- 
able .points,  and  many  suppose  that  there  can  be  no  skill  in  their  use;  but  to 
one  critical  in  these  matters  there  are  great  differences,  even  in  common  draw- 
ings, in  the  straightuess  and  uniformity  of  the  lines  and  in  the  care  of  the 
surface  of  the  paper. 

Pencils  are  marked  according  to  their  hardness:  H  (hard),  HH,  H  H  H, 

to  8  H ;  or  H,  V  (very)  H,  V  V  H,  M  (me- 
dium), H  M^  M  B  (black),  S  (soft),  M  S,  V  S, 
V  V  S ;  or  by  numerals,  1,  2,  3,  to  8. 

Select  for  the  geometrical  problems  and 
for  usual  drawings  a  No.  3.  or  H  H  H  pencil. 
It  should  be  sharpened  to  a  cone-point  (Fig. 
1).  Where  a  pencil  is  used  for  drawing  lines 
only,  some  draughtsmen  sharpen  the  pencil 
to  a  wide  edge,  like  a  chisel. 
In  drawing  a  straight  line,  hold  the  ruler  firmly  with  the  left  hand ;  with 
the  right  hand  hold  the  pencil  lightly  but  without  slackness,  and  a  little 
inclined  in  the  direction  of  the  line  to  be  drawn,  keeping  the  pencil  against 
the  edge  of  the  ruler,  and  in  the  same  relative  position  to  the  edge  during  the 
whole  operation  of  drawing  the  line. 

2  (1) 


FIG.  1. 


2  CONSTRUCTION  OF  GEOMETRICAL   PROBLEMS. 

To  draw  a  clean  line  and  preserve  the  point  of  the  pencil,  the  part  of  the 
cone  a  little  above  the  point  of  the  pencil  should  bear  against  the  edge  of  the 
ruler,  and  the  pencil  should  be  carried  steadily  while  drawing.  Any  oscilla- 
tion will  throw  the  point  farther  from  or  nearer  the  ruler,  and  the  line  will  not 
be  straight  (Fig.  2). 


FIG.  2. 


In  the  use  of  the  compasses  do  not  make  a  hole  through  the  paper  with 
the  needle  or  sharp  point,  but  only  into  the  paper  sufficient  to  maintain  the 
position. 

Keep  the  paper  clean,  and  use  rubber  as  little  as  possible. 

A  geometrical  point,  which  is  position  only,  is  indicated  in  drawing  by  the 
prick-mark  of  a  needle  or  sharp  point,  or  the  dot  of  a  pencil ;  sometimes'  it  is 
inclosed  0,  sometimes  designated  by  the  intersection  of  two  short  lines  X  >. 
A  line,  which  is  extension  in  length  only,  is  indicated  by  a  visible  mark  of 
pencil  or  pen  traced  upon  the  paper. 

Geometrically  lines  have  but  one  dimension,  length,  and  the  direction  of  a 
line  is  the  direction  from  point  to  point  of  the  points  of  which  the  line  is  com- 
posed :  in  drawing,  lines  are  visible  marks  of  pencil  or  pen  upon  paper. 

A  straight  line  is  such  as  can  be  drawn  along  the  edge  of  the  ruler,  and  is 
one  in  which  the  direction  is  the  same  throughout.  In  drawing  a  straight  line 
through  two  given  points,  place  the  edge  of  the  ruler  very  near  to  and  at  equal 
distances  from  the  points,  as  the  point  of  the  pencil  or  pen  should  not  be  in 
contact  with  the  edge  of  the  ruler  (Fig.  3). 


FIG.  3. 

Lines  in  geometry  and  drawing  are  generally  of  limited  extent.  A  given 
or  known  line  is  one  established  on  paper  or  fixed  by  dimensions.  Lines  of 
the  same  length  are  equal. 

Curved  Lines. — For  the  pencil-points  of  compasses,  whittle  down  the 
stumps  of  pencils  to  suit.  Insert  the  pencil-point  in  the  compasses.  With 
the  needle  or  sharp  point  resting  on  the  paper  describe  a  line  with  the  pencil 
around  this  point ;  the  line  thus  described  is  usually  called  a  circle — more 


CONSTRUCTION  OF  GEOMETRICAL  PROBLEMS.  3 

strictly  it  is  the  circumference  of  a  circle — the  circle  being  the  space  inclosed. 
A  portion  of  a  circumference  is  an  arc.  The  point  around  which  the  circum- 
ference is  described  is  the  centre  of  the  circle  (Fig.  4). 

The  line  embraced  between  the  two  points  of  the  compasses  is  called  the 
radius  of  the  circle,  and  by  mechanics  a  sweep;  a  line  passing  through  the 
centre  and  terminating  at  each  end  in  the  circum- 
ference is  a  diameter,  and  is  equal  in  length  to 
two  radii ;  any  line  not  passing  through  the  cen- 
tre and  limited  by  the  circumference  is  less  than 
a  diameter  and  is  a  chord.  The  space  embraced 
between  a  chord  and  its  lesser  arc  is  a  segment. 
The  space  embraced  between  two  radii  and  its  arc 
is  a  sector;  if  the  arc  is  the  quarter  of  the  cir- 
cumference, the  sector  is  distinguished  as  a  quad- 
rant. 

It  will  be  observed  that  arcs  are  lines  which 
are  continually  changing  the  directions,  and  are 
called  curved  lines,  but  there  are  other  curved  lines  than  those  described  by 
compasses,  of  which  the  construction  will  be  explained  hereafter. 

Lines  which  can  neither  be  drawn  by  rulers  or  compasses,  representing  the 
directions  of  brooks  and  rivers,  the  margins  of  lakes  and  seas,  points  in  which 
are  established  by  surveys,  defined  on  paper,  and  connected  by  hand-drawing, 
are  irregular  or  crooked  lines. 

Where  it  is  necessary  to  distinguish  lines  by  names,  we  place  at  their 
extremities  letters  or  figures,  as  A —  — B,  1—  — 2 ;  the  line  A  B,  or  1  2. 
But  in  lines  other  than  straight,  or  of  considerable  extent,  it  is  often  necessary 
to  introduce  intermediate  letters  and  figures,  as  a  a  a. 


FIG.  4. 


In  the  following  problems,  unless  otherwise  implied  or  designated,  where 
lines  are  mentioned,  straight  lines  are  intended. 

If  a  straight  line  moves  sideways  in  a  single  direction,  it  will  sweep  over  a 
surface  which  is  called  a  plane.  All  drawings  are  projections  on  planes  of 
paper  or  board. 

Two  lines  drawn  on  paper,  and  having  the  same  direction,  can  never  come 
any  nearer  each  other,  and  must  always  be  at  the  same  distance  apart,  however 
far  extended.  Such  lines  are  called  parallel  lines. 

To  draw  a  line  parallel  to  a  given  line,  and  at  a  given  distance  from  it 
(Fig.  5). 

Draw  the  line  A  B  for  the  given  .line,  and  take  in  the  compasses  the 
distance  A  C — the  distance  at  which  the  other  line  is  to  be  drawn.  On  A, 
as  a  centre,  describe  an  arc,  and  on  B,  as  a  centre,  a  similar  arc ;  draw  the 
line  C  D  just  touching  these  two  arcs,  which  will  be  the  parallel  line  re- 
quired. 


4  CONSTRUCTION   OF  GEOMETRICAL   PROBLEMS. 

To  draw  a  line  parallel  to  a  given  line  through  a  given  point  outside  this 
line  (Fig.  6). 

Draw  the  given  line  A  B,  and  mark  the  given  point  C.  With  C  as  a  centre, 
find  an  arc  that  shall  only  just  touch  A  B ;  and  with  B  as  a  centre,  and  the 


n 


FIG.  5. 


same  radius,  describe  an  arc  D.    Draw  through  the  point  C  a  line  just  touching 
this  last  arc,  and  the  line  C  D  will  be  the  parallel  line  required. 

Two  lines  in  the  same  plane,  not  parallel  to  each  other,  will  come  together 
if  extended  sufficiently  far.  The  inclination  or  intersection  of  two  lines  is 
called  an  angle  (Fig.  7). 

If  but  two  lines  come  together,  the  angle  may  be  designated  by  a  single 
letter  at  the  vertex,  as  the  angle  E. 

But,  if  three  or  more  lines  have  a  common  vertex,  the  angles  are  designated 
by  the  lines  of  which  they  are  composed,  as  the  angle  D  B  C  of  the  lines  'D  B 
and  B  C  ;  the  angle  A  B  C  of  A  B  and  B  C  ;  the  angle  A  B  D  of  A  B  and  B  D. 
The  letter  at  the  vertex  must  always  be  the  central  letter. 

Describe  a  circle  (Fig.  8).  Draw  the  diameter  A  B.  From  A  and  B  as 
centres,  with  any  opening  of  the  compasses  greater  than  the  radius,  describe 
two  arcs  cutting  each  other  as  at  D.  Through  the  intersection  of  these  arcs 
and  the  centre  C,  draw  the  line  D  E. 
D  E  makes,  with  the  diameter  A  B,  four 
angles,  viz.,  A  C  D,  D  C  B,  B  C  E,  and 
EGA.  Angles  are  equal  whose  lines 


Fid.  7. 


have  equal  inclination  to  each  other,  and  whose  lines,  if  placed  one  on  the 
other,  would  coincide.  By  construction,  the  points  C  and  D  have,  respectively, 
equal  distances  from  A  and  B ;  the  line  D  C  can  not,  therefore,  be  inclined 
more  to  one  side  than  to  the  other,  and  the  angle  A  C  D  must  be  equal  to  the 
angle  BCD.  Such  angles  are  called  right  angles.  The  four  angles,  formed 
by  the  intersection  of  D  E  with  A  B,  are  equal,  and  are  right  angles. 

The  angles  A  C  D  and  D  C  B,  on  the  same  side  of  A  B,  are  called  adjacent 
angles ;  as  also  DOB  and  B  C  E,  on  the  same  side  of  D  E. 


CONSTRUCTION  OF  GEOMETRICAL  PROBLEMS.  5 

If  the  base  line  be  parallel  with  the  surface  of  still  water,  it  is  called  an 
horizontal  line,  and  the  line  perpendicular  to  it  is  called  a  vertical  line. 

Draw  the  line  C  F.  It  will  be  observed  that  the  angle  F  C  B  is  less  than 
a  right  angle,  and  it  is  called  an  acute  angle ; 
the  angle  F  C  A  is  greater  than  a  right  angle, 
and  it  is  called  an  obtuse  angle.  It  will  be 
observed  that,  no  matter  how  many  lines  be 
drawn  to  the  centre,  the  sum  of  all  the  angles 
on  the  one  side  of  A  B  can  only  be  equal  to 
two  right  angles,  and,  on  both  sides  of  A  B, 
can  only  be  equal  to  four  right  angles.  It  will 
be  observed  that  the  angles  at  the  centre  in- 
clude greater  or  less  arcs  between  their  sides, 
according  to  the  greater  or  less  inclination  of 
their  sides  to  each  other ;  that  the  right  angles 
intercept  equal  arcs,  and  that,  no  matter  how 
large  the  circle,  the  proportion  of  the  circle 
intercepted  by  the  sides  of  an  angle  is  always 
the  same,  and  that  the  arcs  can  therefore  be 
taken  as  the  measures  of  angles.  For  this 
purpose  the  whole  circumference  is  supposed 
to  be  divided  into  three  hundred  and  sixty  de- 
grees (360°),  each  degree  subdivided  into  sixty  minutes  (60'),  and  each  minute 
into  sixty  seconds  (60").  Each  right  angle  has  for  its  measure  one  quarter  of 
the  whole  circumference  (-^f^),  or  90°,  and  is  called  a  quadrant. 

To  construct  an  angle  equal  to 
a  given  angle  (Fig.  9). 

Draw  any  angle,  as  C  A  B,  for 
the  given  angle,  and  the  line  a  b 


A 


FIG.  10. 


\\i 

k 
FIG.  11. 


as  the  base  of  the  required  angle.  From  A,  with  any  suitable  radius,  describe 
the  arc  B  C,  and  from  a,  with  the  same  radius,  describe  the  arc  b  c.  With 
the  compasses  take  the  length  of  the  chord  B  C,  and,  from  b  as  centre,  describe 
an  arc  cutting  the  arc  b  c  at  c,  and  draw  the  line  a  c;  cab  is  the  required 
angle. 

To  construct  an  angle  of  sixty  degrees  (Fig.  10). 

Lay  off  any  base  line,  and  from  A,  with  any  radius,  describe  an  arc,  and 
from  B,  with  the  same  radius,  describe  another  arc  cutting  the  first,  as  at  C. 
Draw  the  line  C  A,  and  the  angle  CAB  will  be  an  angle  of  sixty  degrees. 


f> 


CONSTRUCTION  OF  GEOMETRICAL  PROBLEMS. 


For  if,  on  the  circumference  of  any  circle,  chords  equal  to  the  radius  are 
stepped  off  successively,  six  will  exactly  complete  the  circle,  making  360°. 

To  draw  a  perpendicular  to  a  line  from  a  point  without  the  line 
(Fig.  11). 

Draw  a  line,  and  mark  the  given  point  A.     From  A  as  a  centre,  with  a 


\F 


B 


A 
FIG.  12. 


FIG.  13. 


suitable  radius,  describe  an  arc  cutting  the  line  at  G  and  F.  From  G  and 
F,  as  centres,  describe  arcs  cutting  each  other.  The  line  drawn  through 
the  point  A,  and  the  point  of  intersection  E,  will  be  perpendicular  to  the 
line  G  F. 

The  radial  line  A  E  divides  the  chord  G  F  and  the  arc  G  E  F  into  two 
equal  parts ;  and,  conversely,  the  line  perpendicular  to  the  middle  point  of  a 
chord  of  a  circle  is  radial — passes  through  the  centre  of  that  circle. 

To  draw  a  perpendicular  to  a  line  from  a  point  ivithin  that  line  (Fig.  12). 
1st  Method. — Draw  a  line,  and  take  the  point  A  in  the  line.     From  A,  as 
a  centre,  describe  arcs  cutting  the  line  on  each  side  at  B  and  C.     From  B  and 
C,  as  centres,  describe  intersecting  arcs  at  D.     Draw  a  line  through  D  and  A, 
and  it  will  be  perpendicular  to  the  line  B  C  at  A. 

2d  Method  (Fig.  13). — Draw  the  line,  and  mark  the  point  A  as  before. 
From  any  centre  F,  without  the  line,  and  not  directly  over  A,  with  a  radius 
equal  to  F  A,  describe  more  than  a  half-circle  cutting  the  line,  as  at  D.  From 

D,  through  the  centre  F,  draw  a 
line  cutting  the  arc  at  E.  Draw 
A  E,  and  it  will  be  the  perpendicu- 
lar to  the  line  A  D. 

The  line  D  E  is  the  diameter 
of  a  circle,  and  the  angle  DAE, 
with  its  vertex  at  A  in  the  circum- 
ference, embraces  with  its  sides  half 
a  circle.  It  has  been  shown  that 
angles  at  the  centre  of  a  circle  have 
for  their  measure  the  arc  embraced 
by  their  sides.  Angles  with  their 
vertices  in  the  circumference  have 
for  their  measure  half  the  arc  em- 
braced by  their  sides;  and,  consequently,  angles  embracing  half  a  circumfer- 
ence are  right  angles. 

To  draw  a  perpendicular  to  the  middle  point  of  a  line  (Fig.  14). 


-B 


FIG.  14. 


CONSTRUCTION  OF  GEOMETRICAL  PROBLEMS.  f 

From  the  extremities  A  and  B  of  the  line,  as  centres,  describe  similar  inter- 
secting arcs  above  and  below  the  line.  Through  these  intersections  draw  the 
line  C  D.  It  will  be  perpendicular  to  the  line  A  B,  and  bisect  or  divide  it  into 
two  equal  parts. 

If  the  line  A  B  be  considered  the  chord  of  a  circle,  its  centre  would  lie  in 
the  line  C  D. 

This  construction  is  sometimes  used  merely  to  divide  a  line  into  two  equal 
parts,  or  bisect  it;  it  can  be  more  readily  done  with  dividers  (Fig.  15). 

Place  one  point  of  the  dividers  on  one  end  of  the  line,  and  open  the 
dividers  to  a  space  as  near  as  may  be  half  the  line.  Turn  the  dividers  on  the 


FIG.  15. 


central  point ;  if  the  other  point  then  falls  exactly  on  the  opposite  extremity 
of  the  line,  it  is  properly  divided ;  but,  if  the  point  falls  either  within  or  with- 
out the  extremity  of  the  line,  divide  the  deficit  or  excess  by  the  eye,  in 
halves,  and  contract  or  extend  the  dividers  by  this  measure.  Then  apply  the 
dividers  as  before,  and  divide  deficit  or  excess  till  a  revolution  exactly  covers  the 
length  of  the  line.  By  accustoming  one's  self  to  this  process,  the  eye  is  made 
accurate,  and  one  estimate  is  sufficient  for  a  correct  division  of  any  deficit  or 
•excess.  By  a  similar  process  it  is  evident  that  a  line  can  be  divided  into  any 
number  of  equal  parts,  by  assuming  an  opening  of  the  dividers  as  nearly  as 
possible  to  that  required  by  the  division,  and,  after  spacing  the  line,  dividing 
the  deficit  or  excess  by  the  required  number  of  parts,  contracting  or  expanding 
the  dividers  by  one  of  these  parts,  and  spacing  the  line  again,  and  so  on  till  it 
is  accurately  divided. 

To  bisect  a  given  angle  (Fig.  16). 

Construct  an  angle,  and  from  its  vertex  A,  as  a  centre,  describe  an  arc 
cutting  the  two  sides  of  the  angle  at  B  and  C.  From  B  and  C,  as  centres,  de- 


FIG.  16. 


FIG.  17. 


scribe  intersecting  arcs.     Draw  a  line  through  A  and  the  point  of  intersection 
D,  and  this  line  will  bisect  the  angle. 

To  bisect  an  angle  when  the  vertex  is  not  on  the  paper  (Fig.  17). 


8 


CONSTRUCTION  OF  GEOMETRICAL   PROBLEMS. 


Let  A  B  and  E  C  be  two  lines  inclined  to  each  other ;  at  equal  distances 
and  parallel  to  the  above  lines  draw  a  b  and  a  c,  intersecting  lines;  bisect -the 
angle  b  a  c.  A  line  a  d  drawn  through  the  vertex  and  the  point  of  bisection  is 
the  required  line. 

Through  two  given  points  to  describe  an  arc  of  a  circle  with  a  given  radius 
(Fig.  18). 

From  B  and  C,  the  two  given  points,  with  an  opening  of  the  dividers  equal 
to  the  given  radius,  describe  two  arcs  intersecting  at  A.  From  A,  as  a  centre, 
with  the  same  radius,  describe  an  arc,  and  it  will  be  the  one  required. 


FIG.  18. 


FIG.  19. 


To  find  the  centre  of  a  given  circle,  or  of  an  arc  of  a  circle. 

Of  a  circle  (Fig.  19). — Draw  the  chord  A  B.  Bisect  it  by  the  perpen- 
dicular C  D,  whose  extremities  lie  in  the  circumference,  and  bisect  C  D.  Gr, 
the  point  of  bisection,  will  be  the  centre  of  the  circle. 

To  find  the  centre  of  an  arc  (Fig.  20). — Select  the  points  A,  B,  and  C  in 
the  arc,  well  apart.  From  A  and  B  as  centres,  and  then  from  B  and  C  as 
centres,  describe  arcs  of  equal  radii  cutting  each  other ;  draw  the  two  lines  D  E 
and  F  G  through  their  intersections.  The  point  0,  where  these  lines  meet,  is 
the  centre  required. 

To  describe  a  circle  passing  through  three  given  points  (Fig.  20). 

Proceed,  as  in  the  last  problem,  to  find  the  point  0.  From  0,  as  a  centre, 
with  a  radius  0  A,  describe  a  circle,  and  it  will  be  the  one  required. 


X     T. 


FIG.  20. 


FIG.  21. 


To  describe  an  arc  of  a  circle  passing  through  three  given  points,  ivhere  the 
centre  is  not  available  (Fig.  21). 


CONSTRUCTION  OF  GEOMETRICAL  PROBLEMS.  9 

From  the  extreme  given  points  A  and  B  describe  arcs  A  E  and  B  D ; 
through  the  third  given  point  C  draw  lines  from  A  and  B,  intersecting  the  arcs 
at  0  and  0  ;  from  0  and  0  cut  the  arcs  in  either  direction  by  equal  divisions, 
0  1,  0  2,  0  3,  and  0  1',  0  2' ;  draw  lines  A  1,  A  2 ;  A  1',  A  2' ;  B  1,  B  2 ;  B  1', 
B  2'.  The  successive  intersections  of  A  1  by  B  1,  A  2  by  B  2,  A  1'  by  B  1'  are 
points  in  the  required  arc  by  the  connection  of  which  the  problem  will  be 
complete. 

To  describe  this  arc  mechanically  (Fig.  22). 

Lay  off  on  a  piece  of  cardboard  the  three  points  A,  C,  B,  and  connect  them 
by  lines  extended  beyond  the  points  A  and  B ;  and  then  cut  out  the  cardboard 


FIG.  22. 

along  these  lines.  Insert  pins  at  the  points  A  and  B  on  the  drawing,  and 
placing  the  cardboard  templet  against  these  pins,  and  the  angle  against  the 
point  C,  slide  the  templet  each  way,  dotting  in  the  drawing  the  angle  C  in  its 
different  positions.  These  dots  will  be  points  in  the  curve,  which  are  to  be  con- 
nected. By  extending  the  bisecting  line  in  different  positions  of  the  templet 
to  the  drawing,  radial  lines  are  given  which  will  be  useful  in  laying  off  voussoir 
joints  on  segmental  arches  of  large  radius.  Kadial  lines  are  also  necessary  in 
perspective  drawing,  for 
which  an  instrument 
called  the  centrolinead 
(Fig.  23)  is  used.  The 
principle  is  similar  to 
that  of  the  cardboard 
templet. 

To  draw  a  tangent  to 
a  circle  from  a  given 
point  in  the  circumfer- 
ence. 

1st  Method  (Fig.  24). 
—Through  the  given 
point  A  draw  the  radial 
line  A  C.  The  perpen- 
dicular F  G  to  that  line 
will  be  the  tangent  re- 
quired. FIG.  23. 

2d  Method  (Fig.  25). 

—From  the  given  point  A  set  off  equal  arcs,  A  B  and  A  I>.  Join  B  and  D. 
Through  A  draw  A  E  parallel  to  B  D,  and  it  will  be  the  tangent  required. 
This  method  is  useful  when  the  centre  is  inaccessible. 


10 


CONSTRUCTION  OF   GEOMETRICAL   PROBLEMS. 


To  draw  tangents  to  a  circle  from  a  point  without  it  (Fig.  26). 
From  the  given  point  A  draw  A  C  to  the  centre  of  the  circle.     Bisect  A  C 
to  find  the  point  D.     From  D,  as  a  centre,  describe  an  arc  with  a  radius  D  C, 


A 


E 


FIG.  24. 


FIG.  25. 


cutting  the  circle  at  E  and  F.     Draw  A  E  and  A  F,  and  they  will  be  the  tan- 
gents required. 

To' construct  within  the  sides  of  an  angle  a  circle  tangent  to  these  sides  at  a 
given  distance  from  the  vertex  (Fig.  27). 


FIG.  26. 


FIG.  27. 


Let  a  and  b  be  the  given  points  equally  distant  from  the  vertex  A.  Draw 
a  perpendicular  to  A  C  at  a,  and  to  A  B  at  b.  The  intersection  of  these  per- 
pendiculars will  be  the  centre  of  the  required  circle. 

In  the  same  figure,  to  find  the  centre,  the  radius  being  given,  and  the 
points  a  and  b  not  known.  Draw  lines  parallel  to  A  C  and  A  B,  at  a  distance 
equal  to  the  given  radius,  and  their  intersection  will  be  the  centre  required. 

To  describe  a  circle  from  a  given  point  to  touch  a  given  circle  (Figs.  28 
and  29). 


FIG.  28. 


FIG.  29. 


D  E  being  the  given  circle,  and  B  the  given  point,  draw  a  line  from  B  to 
the  centre  C,  and  produce  it,  if  the  point  B  is  within  the  circle,  until  it  cuts 
the  circle  at  A.  From  B,  as  a  centre,  with  a  radius  equal  to  B  A,  describe  the 
circle  F  G,  touching  the  given  circle,  and  it  will  be  the  circle  required. 


CONSTRUCTION  OF  GEOMETRICAL  PROBLEMS. 


11 


In  all  cases  of  circles  tangent  to  each  other,  their  centres  and  their  points 


of  contact  must  lie  in  the  same  straight  line. 


To  draw  tangents  to  two  given  circles  (Fig.  30). 

Draw  a  straight  line  through  the  centres  of  the  two  given  circles.     From 
the  centres  A  and  B  draw  parallel  radii,  A  D  and  B  E,  in  the  same  direction. 


FIG.  30. 

Draw  a  line  from  D  to  E,  and  produce  it  to  meet  the  centre  line  at  C ;  and 
from  C  draw  tangents  to  one  of  the  circles  by  Fig.  26.  Those  tangents  will 
touch  loth  circles  as  required. 

To  construct  a  circle  through  a  given  point  tangent  to  a  second  circle  at  a 
given  point  (Fig.  31). 

Let  A  be  the  given  point  of  a  circle  A  D  C,  B  the  point  through  which  the 
required  circle  is  to  be  drawn.  Connect  A  and  B,  extend  A  O,  bisect  A  B  by 
a  perpendicular.  The  intersection  of  this  perpendicular  with  A  0  extended 
will  be  the  centre  of  the  required  circle.  The  same  method  of  construction 
would  apply  if  the  point  B  were  inside  the  circle  ADC. 

Between  two  inclined  lines  to  draiv  a  series  of  circles  touching  these  lines 
and  touching  each  other  (Fig.  32). 


Fm.  31. 


FIG.  32. 


Bisect  the  inclination  of  the  given  lines  A  B  and  C  D  by  the  line  N  0 ;  this 
is  the  centre  line  of  the  circles  to  be  inscribed.  From  a  point,  P,  in  this  line, 
draw  P  B  perpendicular  to  the  line  A  B ;  and  from  P  describe  the  circle  B  D, 
touching  the  given  lines,  and  cutting  the  centre  line  at  E.  From  E  draw  E  F 
perpendicular  to  the  centre  line,  cutting  A  B  at  F ;  from  F  describe  an  arc, 
with  a  radius  F  E,  cutting  A  B  at  G  ;  draw  G  H  parallel  to  B  P,  giving  H  the 
centre  of  the  second  touching  circle,  described  with  the  radius  H  E  or  H  G. 
By  a  similar  process  the  third  circle,  I  N",  is  described.  And  so  on. 

Inversely,  the  largest  circle  may  be  described  first,  and  the  smaller  ones  in 
succession. 


12 


CONSTRUCTION   OP  GEOMETRICAL  PROBLEMS. 


Note. — This  problem  is  of  frequent  use  in  scroll-work. 

Between  two  inclined  lines  to  draw  a  circular  arc  to  fill  up  the  angle 
(Fig.  33). 

Let  A  B  and  D  E  be  the  inclined  lines.  Bisect  the  inclination  by  the  line 
F  C,  and  draw  the  perpendicular  A  F  D  to  define  the  limit  within  which  the 
circle  is  to  be  drawn.  Bisect  the  angles  A  and  D  by  lines  cutting  at  C, 


Fio.  34. 

and  from  C,  with  radius  C  F,  draw  the  arc  H  F  G,  which  will  be  the  arc 
required. 

To  Jill  up  the  angle  of  a  straight  line  and  a  circle,  with  a  circular  arc  of  a 
given  radius  (Fig.  34). 

On  the  centre  C,  of  the  given  circle  A  D,  with  a  radius  C  E  equal  to  that 
of  the  given  circle  plus  that  of  the  required  arc,  describe  the  arc  E  F.  Draw 
G  F  parallel  to  the  given  line  H  I,  at  the  distance  G  H,  equal  to  the  radius 
of  the  required  arc,  cutting  the  arc  E  F  at  F.  Then  F  is  the  required  centre. 
Draw  the  perpendicular  F  I,  and  the  line  F  C,  cutting  the  circle  at  A  ;  and,  with 
the  radius  F  A  or  F  I,  describe  the  arc  A  I,  which  will  be  the  arc  required. 

To  fill  up  the  angle  of  a  straight  line  and  a  circle,  ivitli  a  circular  arc  to 
join  the  circle  at  a  given  point  (Fig.  35). 

In  the  given  circle  B  A  draw  the 
radius   to  A,  and  extend   it.      At    A 


FIG.  36. 


draw  a  tangent,  meeting  the  given  line  at  D.  Bisect  the  angle  A  D  E,  so 
formed,  with  a  line  cutting  the  radius,  as  extended  at  F ;  and,  on  the  cen- 
tre F,  with  radius  F  A,  describe  the  arc  A  E,  which  will  be  the  arc  required. 


CONSTRUCTION   OF  GEOMETRICAL   PROBLEMS. 


13 


To  describe  a  circular  arc  joining  two  circles,  and  to  touch  one  of  them  at  a 
given  point  (Fig.  36). 

Let  A  B  and  F  G  be  the  given  circles  to  be  joined  by  an  arc  touching  one 
of  them  at  F. 


(Lr 

FIG.  37. 


FIG.  38. 


Draw  the  radius  E  F,  and  produce  it  both  ways ;  set  off  F  H  equal  to  the 
radius,  A  C,  of  the  other  circle ;  join  0  to  H,  and  bisect  it  with  the  perpen- 
dicular L  I,  cutting  E  F  at  I.  On  the  centre  I,  with  radius  I  F,  describe  the 
arc  F  A,  which  will  be  the  arc  required. 

To  find  the  arc  which  shall  be  tangent  to  a  given  point  on  a  straight  line, 
and  pass  through  a  given  point  outside  the  line  (Fig.  37). 

Erect  at  A,  the  given  point  on  the  giv- 
en line,  a  perpendicular  to  the  line.  From 
C,  the  given  point  outside  the  line,  draw 
C  A,  and  bisect  it  with  a  perpendicular. 
The  intersection  of  the  two  perpendiculars 
at  a  will  be  the  centre  of  the  required  arc. 
To  connect  two  parallel  lines  by  a  re- 
versed curve  composed  of  two  arcs  of  equal 
radii,  and  tangent  to  the  lines  at  given 
points  (Fig.  38). 

Join  the  two  given  points  A  and  B,  and  divide  the  line  A  B  into  two  equal 
parts  at  C  ;  bisect  C  A  and  C  B  by  perpendiculars ;  at  A  and  B  erect  perpen- 
diculars to  the  given 
lines,  and  the  intersec- 
tions a  and  b  will  be 
the  centres  of  the  arcs 
composing  the  required 
curve. 

To  join  two  given 
points  in  two  given 
parallel  lines  by  a  re- 
versed curve  of  two 
equal  arcs,  whose  cen- 
tres lie  in  the  parallels 
(Fig.  39). 

Join  the  two  given 

points  A  and  B,  and  divide  the  line  A  B  in  equal  parts  at  C.  Bisect  A  C  and 
B  C  by  perpendiculars ;  the  intersections  a  and  b  of  the  parallel  lines,  by  these 
perpendiculars,  will  be  the  centres  of  the  required  arcs. 


CONSTRUCTION   OF  GEOMETRICAL   PROBLEMS. 


On  a  given  line,  to  construct  a  compound  curve  of  three  arcs  of  circles,  the 
radii  of  the  two  side  ones  being  equal  and  of  a  given  length,  and  their  centres 
in  the  given  line  ;  the  central  arc  to  pass  through  a  given  point  on  the  perpen- 
dicular, bisecting  the  given  line,  and  to  be  tangent  to  the  other  two  arcs 
(Fig.  40). 

Let  A  B  be  the  given  line,  and  C  the  given  point.  Draw  C  D  perpen- 
dicular to  A  B ;  lay  off  A  a,  B  b,  and  C  c,  each  equal  to  the  given  radius  of  the 
side  arcs ;  draw  a  c,  and  bisect  it  by  a  perpendicular ;  the  intersection  of  this 
line  with  the  perpendicular  C  D  will  be  the  required  centre  of  the  central  arc 
e  C  e'.  Through  a  and  b  draw  the  lines  D  e  and  D  e' ;  from  a  and  b,  with  the 
given  radius  equal  to  a  A  or  b  B,  describe  the  arcs  A  e  and  B  e'.  From  D,  as 
a  centre,  with  a  radius  equal  to  C  D,  and,  consequently,  by  construction,  equal 
to  D  e  and  D  e',  describe  the  arc  e  C  e'.  The  entire  curve  A  e  C  e'  B  is  the 
compound  curve  required. 

PROBLEMS    ON    POLYGONS   AND    CHICLES. 

Three  lines  inclosing  a  space  form  a  triangle  (Fig.  41).  If  two  of  the  sides 
are  of  equal  length,  it  is  an  isosceles  triangle  (Fig.  42) ;  if  all  three  are  of  equal 


Fio.  41. 


FIG.  42. 


length,  it  is  an  equilateral  triangle  (Fig.  43).  If  one  of  the  angles  is  a  right 
angle,  it  is  a  right-angled  triangle  (Fig.  44),  and  if  no  two  of  the  sides  are  of 
equal  length,  and  not  one  of  the  angles  a  right  angle,  it  is  a  scalene  triangle. 

To  construct  an  isosceles  triangle  (Fig.  42). 

Draw  any  line  as  a  base,  and,  from 
each  extremity  as  a  centre,  with  equal 
radius,  describe  intersecting  arcs.  Draw 


FIG.  43. 


FIG.  44. 


a  line  from  each  extremity  of  the  base  to  this  point  of  intersection,  and  the 
figure  is  an  isosceles  triangle. 

To  construct  an  equilateral  triangle  (Fig.  43). 

Draw  a  base  line,  and  from  each  extremity  as  a  centre,  with  a  radius  equal 


CONSTRUCTION   OP  GEOMETRICAL   PROBLEMS. 


15 


to  the  base  line,  describe  intersecting  arcs.  Draw  lines  from  the  extremi- 
ties of  the  base  to  this  point  of  intersection,  and  the  figure  is  an  equilateral 
triangle. 

To  construct  a  right-angled  triangle  (Fig.  44). 

Construct  a  right  angle  by  any  one  of  the  methods  before  described. 
Draw  a  line  from  the  extremity  of  the  one  side  to  the  extremity  of  the  other 
side,  and  the  figure  is  a  right-angled  triangle. 

It  will  be  evident,  in  looking  at  any  right-angled  triangle,  that  the  side 
opposite  the  right  angle  is  longer  than  either  of  the  other  or  adjacent  sides ; 
this  side  is  called  the  hypothenuse. 

To  construct  a  triangle  equal  to  a  given  triangle  ABC  (Fig.  45). 

1st  Method  (Fig.  46). — Draw  a  base  line,  and  lay  off  its  length  equal  to 
A  B;  from  one  of  its  extremities,  as  a  centre,  with  a  radius  equal  to  A  C, 
describe  an  arc ;  and,  from  its  other  extremity,  with  a  radius  equal  to  B  C, 
describe  an  arc  intersecting  the  first.  Draw  lines  from  the  extremities  to  the 
point  of  intersection,  and  the  triangle  equal  to  A  B  C  is  complete. 


FIG.  45. 


FIG.  46. 


2d  Method  (Fig.  47). — Draw  a  base  line,  as  before,  equal  to  A  B.  At  one 
extremity  construct  an  angle  equal  to  C  A  B,  and  at  the  other  an  angle  equal 
to  C  B  A.  The  sides  of  these  angles  will  intersect,  and  form  the  required 
triangle. 

3d  Method  (Fig.  48). — Construct  an  angle  of  the  triangle  equal  to  any  angle 
of  A  B  C,  say  the  angle  A  C  B.  On  one  of  its  sides  measure  a  line  equal  to 
C  A,  and  on  the  other  side  one  equal  to  C  B ;  connect  the  two  extremities  by  a 
line,  and  the  triangle  equal  to  A  B  C  is  complete. 


FIG.  47. 


FIG.  48. 


From  the  above  constructions  it  will  be  seen  that,  if  the  three  sides  of  a 
triangle,  or  two  sides  and  the  included  angle,  or  one  side  and  the  two  adjacent 
angles  are  known,  the  triangle  can  be  constructed. 

Construct  a  triangle,  ABC  (Fig.  49).  Extend  the  base  to  E,  and  draw 
B  D  parallel  to  A  C.  As  A  C  has  the  same  inclination  to  C  B  that  B  D  has, 
the  angle  C  B  D  is  equal  to  the  angle  A  C  B.  As  A  C  has  the  same  inclina- 
tion to  A  E  that  B  D  has,  the  angle  D  B  E  is  equal  to  C  A  B.  That  is,  the 


16 


CONSTRUCTION  OP  GEOMETRICAL  PROBLEMS. 


two  angles  formed  outside  the  triangle  are  equal  to  the  two  inside  at  A  and  0 ; 
and  the  three  angles  at  B  are  equal  to  the  three  angles  of  the  triangle,  and 
their  sum  is  equal  to  two  right  angles.  Therefore,  the  sum  of  the  three  angles 
of  a  triangle  is  equal  to  two  right  angles. 

On  one  side  of  a  triangle  (Fig.  50)  construct  a  triangle  equal  to  the  first. 
The  exterior  lines  of  the  two  triangles  form  a  four-sided  or  quadrilateral 

figure,  of  which  the   opposite  sides  are 
equal  and  parallel,  and  the  opposite  an- 


FIG.  49. 


FIG.  50. 


gles  equal.  This  figure  is  called  a  parallelogram,  and  the  line  C  B,  extend- 
ing between  opposite  angles,  is  a  diagonal. 

On  the  hypothenuse  of  a  right-angled  triangle  (Fig.  51)  construct  another 
equal  to  it,  and  the  exterior  lines  form  a  parallelogram,  which,  as  all  the  angles 
are  right  angles,  is  called  a  rectangle.  If  the  four  sides  are  all  equal,  it  is  called 
a  square. 

A  parallelogram  in  which  all  the  sides  are  equal,  but  the  angles  not  right 
angles,  is  called  a  rhombus  (Fig.  52)  ;  if  only  the  opposite  sides  are  equal,  it  is 


FIG.  51. 


FIG.  52. 


called  a  rhomboid  (Fig.  50) ;  if  only  two  sides  are  parallel,  the  figure  is  a  trape- 
zoid  (Fig.  53). 

Take  any  figure  (Fig.  54)  bounded  by  straight  lines  and  from  any  interior 
point  draw  lines  to  all  the  angles.  There  will  be  as  many  triangles  as  sides,  and 
the  sum  of  the  angles  of  the  figure  will  be  equal  to  as  many  times  two  right 


FIG.  53. 


FIG.  54. 


angles  as  sides  less  the  four  right  angles  at  the  centre,  the  sum  of  the  angles 
of  any  triangle  being  equal  to  two  right  angles.     If  a  line  be  drawn  from  the 


CONSTRUCTION   OF   GEOMETRICAL   PROBLEMS. 


interior  point  to  one  side,  another  triangle  is  added  to  the  collection  and  two 
right  angles  to  the  sum  of  the  angles. 

Polygons  are  figures  of  many  angles,  which  if  equal  and  of  equal  sides  are 


FIG.  55. 


FIG.  56. 


FIG.  57. 


FIG.  58. 


called  regular  polygons,  and  are  designated  by  the  number  of  their  sides,  as 
pentagons,  hexagons,  octagons,  nonagons,  decagons,  etc. 

To  describe  a  circle  about  a  triangle  (Fig.  59). 

Bisect  two  of  the  sides  A  B,  A  C,  of  the  triangle  at  E,  F  ;  from  these  points 
draw  perpendiculars  cutting  at  K.  From  the  centre  K,  with  K  A  as  radius, 
describe  the  circle  A  B  C,  as  required. 

To  inscribe  a  circle  in  a  triangle  (Fig.  60). 

Bisect  two  of  the  angles  A,  C,  of  the  triangle 
A  B  C,  by  lines  cutting  at  D  ;  from  D  draw  a 
perpendicular  D  E  to  any  side,  as  A  C ;  and 
with  D  E  as  radius,  from  the  centre  D,  describe 
the  circle  required. 

When  the  triangle  is  equilateral,  the  centre 
of  the  circle  is  more  easily  found  by  bisecting 
two  of  the  sides,  and  drawing  perpendiculars. 
Or,  draw  a  perpendicular  from  one  of  the  sides 
to  the  opposite  angle,  and  from  the  side  set  off 
one  third  of  the  length  of  the  perpendicular. 

To  inscribe  a  square  in  a  circle ;  and  to  describe  a  circle  about  a  square 
(Fig.  61). 

To  inscribe  the  square.  Draw  two  diameters,  A  B,  C  D,  at  right  angles, 
and  join  the  points  A,  C,  B,  D,  to  form  the  square  as  required. 


FIG.  60. 


FIG.  61. 


To  describe  the  circle.     Draw  the  diagonals  A  B,  C  D,  of  the  given  square, 
cutting  at  E  ;  on  E  as  a  centre,  with  E  A  as  radius,  describe  the  circle  as  required. 

3 


18 


CONSTRUCTION   OP  GEOMETRICAL  PROBLEMS. 


In  the  same  way,  a  circle  may  be  described  about  a  rectangle. 

To  inscribe,  a  circle  in  a  square ;  and  to  describe  a  square  about  a  circle 
(Fig.  62). 

To  inscribe  the  circle.  Draw  the  diagonals  A  B,  C  D,  of  the  given  square, 
cutting  at  E ;  draw  the  perpendicular  E  F  to  one  of  the  sides,  and  with  the 
radius  E  F,  on  the  centre  E,  describe  the  circle. 

To  describe  the  square.     Draw  two  diameters  A  B,  C  D,  at  right  angles, 


(  \     '/ 

x^ 

>*' 

X       v- 

XL  J; 

1 

F 

FIG.  62. 

1 

and  produce  them ;  bisect  the  angle  D  E  B  at  the  centre  by  the  diameter  F  G,. 
and  through  F  and  G  draw  perpendiculars  A  C,  B  D,  and  join  the  points  A,  D, 
B,  C,  where  they  cut  the  diagonals,  to  complete  the  square. 

To  inscribe  a  pentagon  in  a  circle  (Fig.  63). 

Draw  two  diameters,  A  C,  B  D,  at  right  angles ;  bisect  A  0  at  E,  and  from 
E,  with  radius  E  B,  cut  A  C  at  F ;  from  B,  with  radius  B  F,  cut  the  circum- 
ference at  G  and  H,  and  with  the  same  radius  step  round  the  circle. to  I  and  K  ; 
join  the  points  so  found  to  form  the  pentagon. 

To  construct  a  regular  hexagon  upon  a  given  straight  line  (Fig.  64). 

From  A  and  B,  with  a  radius  equal  to  the  given  line,  describe  arcs  cutting 
at  g  ;  from  g,  with  the  radius  g  A,  describe  a  circle ;  with  the  same  radius  set 


FIG.  64. 

off  from  A  the  arcs  A  G,  G  F,  and  from  B  the  arcs  B  D,  D  E.  Join  the 
points  so  found  to  form  the  hexagon. 

To  inscribe  a  regular  hexagon  in  a  circle  (Fig.  65). 

Draw  a  diameter,  A  B ;  from  A  and  B  as  centres,  with  the  radius  of  the 
circle  A  C,  cut  the  circumference  at  D,  E,  F,  G ;  draw  straight  lines  A  D, 
D  E,  etc.,  to  form  the  hexagon. 

To  describe  a  regular  hexagon  about  a  circle  (Fig.  66). 


CONSTRUCTION   OP   GEOMETRICAL  PROBLEMS. 


19 


Draw  a  diameter,  A  B,  of  the  given  circle.  With  a  radius  A  D  from  A  as  a 
centre,  cut  the  circumference  at  C ;  join  A  C,  and  bisect  it  with  the  radius 
D  E ;  through  E  draw  F  G  parallel  to  A  C,  and  with  the  radius  D  F  describe 


FIG. 


the  circle  F  H.     Within  this  circle  describe  a  regular  hexagon  by  the  preceding 
problem ;  the  figure  will  touch  the  given  circle  as  required. 

To  construct  a  regular  octagon  upon  a  given  straight  line  (Fig.  67). 

Produce  the  given  line  A  B  both  ways,  and  draw  perpendiculars  A  E,  B  F ; 


m  I 

FIG.  68. 


E .- 


- — -F 


bisect  the  external  angles  at  A  and  B  by  the  lines  A  H,  B  C,  each  equal  to 
A  B ;  draw  C  D  and  H  G  parallel  to  A  E  and  equal  to  A  B ;  and  from  the 
centers  G,  D,  with  a  radius  equal  to  A  B,  cut  the 
perpendiculars  at  E,  F,  and  draw  E  F  to  complete 
the  octagon. 

To  make  a  regular  octagon  from  a  square 
(Fig.  68). 

Draw  the  diagonals  of  the  square  intersecting 
at  e ;  from  the  corners  A,  B,  C,  D,  with  A  e  as 
radius,  describe  arcs  cutting  the  sides  at  g  h,  etc. ; 
join  the  points  so  found  to  complete  the  octagon. 

To  inscribe  a  regular  octagon  in  a  circle  (Fig. 
69). 

Draw  two  diameters,  AC,  B  D,  at  right  an- 
gles ;  bisect  the  arcs  A  B,  B  C,  etc.,  at  e,/,  etc. ;  and  join  A  e,  e  B,  etc.,  for  the 
inscribed  figure. 

To  describe  a  regular  octagon  about  a  circle  (Fig.  70). 


20 


CONSTRUCTION  OF   GEOMETRICAL   PROBLEMS. 


Describe  a  square  about  the  given  circle  A  B  ;  draw  perpendiculars  h  k,  etc., 
to  the  diagonals,  touching  the  circle. 

Or,  to  find  the  points  h,  k,  etc.,  cut  the  sides  from  the  corners  of  the  square, 
as  in  Fig.  68. 

To  inscribe  a  circle  within  a  regular  polygon. 

When  the  polygon  has  an  even  number  of  sides,  as  in  Fig.  71,  bisect  two 


FIG.  71. 


Fio.  72. 


opposite  sides  at  A  and  B,  draw  A  B,  and  bisect  it  at  C  by  D  E  drawn  between 
opposite  angles ;  with  the  radius  C  A  describe  the  circle  as  required. 

When  the  number  of  sides  is  odd,  as  in  Fig.  72,  bisect  two  of  the  sides  at  A 
and  B,  and  draw  lines  A  E,  B  D,  to  the  opposite  angles,  intersecting  at  C  ; 
from  C,  with  C  A  as  radius,  describe  the  circle  as  required. 

To  describe  a  circle  about  a  regular  polygon. 

When  the  number  of 
sides  is  even,  draw  two 
diagonals  from  opposite 
angles,  like  D  E  (Fig. 
71),,, to  intersect  at  C; 
and  from  C,  with  C  D  as 
radius,  describe  the  cir- 
cle required. 

When  the  number  of 
sides  is  odd,  find  the  cen- 
tre C  (Fig.  72)  as  in  last 
problem,  and,  with  C  D 
as  radius,  describe  the 
circle. 

For  the  construction 
of  the  regular  polygons 
Fig.  73  will  be  found 
useful. 

Divide  the  interior 
circle  into  the  number 

of  degrees  corresponding  Fja  73 

to  the  proportion  of  the 

sides  of  the  polygon  to  the  entire  circle,  e.  g.,  -2-f -2-  —  72°.     With  a  radius  of  unity 
describe  an  exterior  circle  and  extend  radii  through  the  divisions  of  the  in- 


CONSTRUCTION  OF   GEOMETRICAL   PROBLEMS. 


21 


terior  circle.     The  chords  of  th^  arcs  intersected  correspond  to  the  sides  of  the 
different  polygons. 

The  figure  gives  the  polygons  such  as  are  usually  found  in  practice,  but  a 
similar  figure  can  be  constructed  increasing  the  number  of  sides  as  far  as  may 
be  required. 


For  the  laying  out  of  angles  the  protractor  is  used.  In  its  simplest  form  it 
consists  of  a  semicircle  of  metal  or  horn  of  which  the  edge  is  divided  into  180 
degrees. 

To  lay  off  a  given  angle — say  47°  (Fig.  74) — place  the  edge  of  the  protractor, 
a  5,  along  the  given  line  and  make  the  centre  of  the  protractor  coincide  with 
the  vertex  c  of  the  angle  to  be  laid  off ;  mark  off  on 
the  edge  the  division  47°,  remove  the  protractor,  and 
through  this  mark  and   the  vertex  c  draw  a  line; 
the  angle  a  c  d  will   be  equal  to  47°,  and  b  c  d  to 
133°.     These  two  are  supplements  of  each  other,  or 
what  each  requires  to  make  up  the  sum  of  180°. 

Fig.  75  represents  the  terms  used  in  defining 
angles,  and  of  which  tables  are  given  in  the  Appen- 
dix by  which  angles  may  be  constructed  without  the 
use  of  the  protractor. 

Considering  BCD  the  angle,  the  perpendicular 
D  H  dropped  from  the  radius  at  D  and  intersecting 

the  diameter  at  II  is  the  sine,  the  line  B  A  perpendicular  to  B  C  and  inter- 
secting the  extended  radius  at  A  is  the  tangent,  the  extension  of  the  radius  C  D 
to  the  intersection  of  the  tangent  at  A  the  secant ;  the  versed  sine  is  the  line 
B  II  extending  from  the  sine  to  the  tangent.  The  cosine,  cotangent,  cosecant, 
and  coversed  sine  are  respectively  the  sine,  tangent,  secant,  and  versed  sine 
of  the  angle  D  C  F,  the  complement  of  B  C  D,  having  the  number  of  degrees 
necessary  to  complete  the  quadrant  of  90  degrees. 


FIG.  75. 


22 


CONSTRUCTION  OF  GEOMETRICAL   PROBLEMS. 


USE  OF  TKIANGLE  AND  SQUARE. 

Right-angled  triangles  constructed  of  wood,  hard  rubber,  celluloid,  or  metal 
are  very  useful  in  connection  with  a  straight-edge,  or  ruler,  in  drawing  lines 
parallel  or  perpendicular  to  other  lines. 

To  draw  lines  parallel  to  each  other,  place  any  edge  of  the  triangle  in  close 
contact  with  the  edge  of  the  ruler.  Hold  the  ruler  (Fig.  76)  firmly  with  the 


FIG 


thumb  and  little  finger  of  the  left  hand,  and  the  triangle  with  the  other  three 
fingers ;  with  a  pencil  or  pen  in  the  right  hand,  draw  a  line  along  one  of  the 
free  edges  of  the  triangle ;  withdraw  the  pressure  of  the  three  fingers  upon  the 
triangle,  and  slide  it  along  the  edge  of  the  ruler,  keeping  the  edges  in  close 
contact ;  a  line  drawn  along  the  same  edge  of  the  triangle,  as  before,  will  be 
parallel  to  the  first  line.  If  the  edge  of  the  hypothenuse  of  the  triangle  be 
placed  in  contact  with  the  ruler,  lines  drawn  along  one  edge  of  the  triangle  will 
be  at  right  angles  to  those  drawn  along  the  other. 

Through  a  given  point  to  draw  a  line  parallel  to  a  given  line  (Fig.  77). 

Place  one  of  the  shorter  edges  of  the  triangle  along  the  given  line  A  B,  and 
bring  the  ruler  against  the  hypothenuse ;  slide  the  triangle  up  along  the  edge 
of  the  ruler  until  the  upper  edge  of  the  ruler  is  sufficiently  near  to  the  given 
point  C  to  allow  a  line  to  be  drawn  through  it.  Draw  the  line,  and  it  will  be 
parallel  to  A  B. 

If  the  triangle  be  slid  farther  up  along  the  edge  of  the  ruler,  and  a  line  be 


CONSTRUCTION  OF  GEOMETRICAL  PROBLEMS. 


23 


drawn  through  C  along  the  other  edge  of  the  triangle  (Fig.  78),  this  line  will 
be  perpendicular  to  A  B.     If  the  triangle  be  slid  still  farther  up  along  the 


FIG.  77. 


edge  of  the  ruler,  and  a  third  line  be  drawn  touching  A  B,  the  figure  con- 
structed will  be  a  rectangle ;  and  if  E  D  be  laid  off  on  A  B,  equal  to  C  E,  the 
figure  inclosed  is  a  square  (Fig.  79). 

It  will  be  seen  that  the  triangle  and  ruler  afford  a  much  readier  way  of 


C                                                                                         C 
f-\                                                                          f-\ 

A 

,0,  

B                    A 

,  ^-£X-               te  

E                       D 

B 

_£X 

FIG.  78. 


FIG.  79. 


drawing  parallel  lines,  and  lines  at  right  angles,  than  the  compasses  and  ruler, 
and  may  be  used  in  solving  the  following  problems : 

The  area  of  a  figure  is  the 
quantity  of  space  inclosed  by  its 
lines. 

Construct  a  right  angle  (Fig. 
SO).  Divide  the  base  and  the 
perpendicular  by  dividers  into 
any  number  of  equal  spaces ;  for 
instance,  ten  on  the  one  and  five 
on  the  other.  Construct  a  rec- 
tangle with  this  base  and  perpen- 
dicular, and  through  the  points  of  division  lay  off  lines  parallel  to  the  base  and 
perpendicular.  The  rectangle  will  be  divided  into  fifty  equal  squares,  and  its 


FIG.  80. 


CONSTRUCTION  OF  GEOMETRICAL  PROBLEMS. 


measure  in  squares  will  be  the  divisions  ten  in  the  base,  multiplied  by  the  five 
in  the  perpendicular.     If  the  division  were  inches,  then  the  area  of  this  rec- 
tangle would  be  fifty  square  inches;  if 
feet,   then    fifty    square  feet.      If  there 


D 


Fio.  81. 


FIG.  82. 


were  but  five  divisions  in  the  base  and  five  in  the  perpendicular,  the  surface 
would  be  twenty-five  squares.  Therefore,  a  rectangle  has  for  its  measure  the 
base  multiplied  by  its  adjacent  side  or  height. 

Draw  a  diagonal,  and  the  rectangle  is  divided  into  two  equal  triangles. 
Each  triangle  must  therefore  have  for  its  measure  the  base  multiplied  by  half 
the  perpendicular,  or,  as  is  usually  said,  by  half  the  altitude. 

Take  any  triangle  (Fig.  81),  and  from  its  apex  draw  a  line  perpendicular  to 
the  base.  The  triangle  is  divided  into  two  right-angled  triangles,  which  must 
have  for  their  measure  A  D  X  i  C  D,  and  D  B  X  i  C  I),  and  the  sum  of  the 
two  must  be  A  B  X  i  C  D. 

If  the  perpendicular  from  the  apex  falls  outside  the  triangle  (Fig.  82),  then 
the  triangle  B  D  C  and  ADC  will  have  for  their  measure  B  D  X  \  C  D  and 

A  D  X  \  C  D,  consequently  their 
difference,  ABC,  must  have  for 
its  measure  A  B  X  \  C  D.  Any 
polygon  can  be  divided  into  trian- 
gles (see  Fig.  54),  and  its  area  is 
made  up  of  the  sum  of  the  areas  of 
the  triangles.  By  graphic  con- 
struction the  sum  of  the  areas  of 
the  different  triangles  composing  a 
polygon  may  be  resolved  readily 
into  a  single  triangle  and  its  area 
taken.  For  instance,  take  a  six- 
sided  polygon  (Fig.  83),  draw  a  line 
from  A  to  C,  and  a  line  parallel  to  A  C,  at  B  intersecting  the  extended  base  at 
B',  a  diagonal  drawn  from  A  to  B'  will  give  one  side  of  the  triangle ;  draw  a 
diagonal  from  A  to  E,  extend  the  side  E  D  of  the  polygon  indefinitely,  draw  a 
line  at  F  parallel  to  A  E,  and  intersect  the  extended  side  at  e,  draw  the  line 
A  D  and  a  parallel  to  this  at  e,  intersecting  the  extended  base  at  E'.  A  di- 
agonal drawn  from  A  to  E'  will,  with  the  side  previously  obtained  and  the  base, 
give  a  triangle  equal  in  area  to  the  polygon. 


FIG.  83. 


CONSTRUCTION  OF  GEOMETRICAL  PROBLEMS. 


25 


i 


g 


SCALES. 

The  distances  given  in  Fig.  80  may  represent  feet,  yards,  miles,  or  any  other 
unit  of  measure.  Thus,  if  they  represent  miles,  the  figure  represents  an  area 
of  fifty  square  miles.  With  a  scale  of  equal 
parts,  each  part  may  represent  any  unit  of 
measure,  and  a  drawing  on  paper  to  that  scale 
represents  the  object  from  which  it  is  drawn 
in  a  reduced  form,  from  which  measures  in 
detail  by  the  scale  may  be  more  readily  and 
as  accurately  taken  as  from  the  natural  ob- 
ject in  the  shop  or  on  the  estate,  and  if  de- 
signs are  made  to  a  scale  they  can  be  exe- 
cuted conformably  and  accurately  in  all  their 
parts  in  either  enlarged  or  reduced  size. 

Practically  a  two-foot  rule,  with  its  divis- 
ions into  inches,  halves,  quarters,  eighths,  and 
sixteenths,  may  be  made  use  of  as  a  scale  of 
equal  parts,  any  division  being  taken  as  the 
unit  to  represent  a  foot,  a  yard,  or  a  mile  ;  but 
among  drawing  instruments  scales  especially 
adapted  to  the  purpose  are  found  in  great 
variety  of  forms,  divisions,  and  material.  Fig. 
84  represents  a  convenient  form  of  scale,  as  it 
contains,  in  addition  to  the  simply  divided 
scales,  a  protractor  along  its  edges. 

The  simply  divided  scales  consist  of  a  series 
of  equal  divisions  of  an  inch,  which  are  num- 
bered 1,  2,  3,  etc.,  beginning  from  the  second 
division  on  the  left  hand ;  the  upper  part  of 
the  left  division  in  each  is  subdivided  into 
twelve  equal  parts,  and  the  lower  part  into  ten 
equal  parts.  The  scales  are  marked  at  the  left 
1  inch,  £ ,  £,  £,  and  when  used  in  drawing  the 
scale  is  written  as  I  inch,  f ,  £,  or  £  inch  to  a 
foot,  rod,  or  mile,  or  whatever  may  be  the 
unit  of  actual  measure.  When  the  unit  is  the 
inch  the  first  scale  will  be  full  size,  the  second 
f,  the  third  £,  and  the  fourth  £  full  size.  If 
the  scale  adopted  is  such  a  part  of  an  inch  to 
the  foot,  then  the  upper  subdivisions  will 
represent  inches. 

Above  the  simply  divided  scales  there  is  a 
scale  marked  C,  which  is  a  scale  of  chords;  taking  a  radius  equal  to  C-60,  the 
chords  of  the  different  angles  are  represented  by  the  division ;  thus  an  angle  of 
20°  the  chord  will  be  C-20. 


- 


at 

OUT 


\ 


s 


Fia.  84. 


CONSTRUCTION  OP  GEOMETRICAL  PROBLEMS. 


SIMILAR   TRIANGLES. 


Triangles  which  are  equiangular  are  similar,  and  have  their  homologous 
sides — that  is,  their  sides  adjacent  to  the  equal  angles — proportional ;  conversely, 
two  triangles  which  have  their  homologous  sides  proportional  are  equiangular. 

Two  triangles  which  have  their  sides  parallel  (Fig.  85)  or  perpendicular  to 


FIG  85. 


FIG.  86. 


each  other  (Fig.  86)  are  similar.  A  line  c  drawn  parallel  to  one  side  c'  of  a 
triangle  (Fig.  87)  forms  a  triangle  a  c  b  whose  sides  are  proportional  to  the 
original  triangle. 

In  Fig.  88  a  polygon  is  divided  into  triangles  by  lines  from  an  interior 
point  to  its  angles  and  these  lines  intersected  by  lines  parallel  to  the  sides  of 
the  polygon.  The  figure  thus  constructed  is  a  polygon  similar  to  the  original 
polygon  composed  of  triangles  similar  to  the  triangles  into  which  it  was 
divided. 

In  the  figure  the  parallel  lines  are  drawn  across  the  sides  of  the  triangles  at 
one  half  their  length,  and  the  areas  of  the  small  triangles  are  therefore  equal  to 
the  square  of  one  half  or  to  one  quarter  that  of  the  original  triangles ;  conse- 
quently the  area  of  the  interior 
polygon  is  one  quarter  that  of  the 
exterior  one.  As  this  construction 
obtains  at  any  intersecting  length, 
it  affords  a  means  of  reducing  the 
scale  of  the  original  polygon. 

To  a  scale  of  £  inch  (Fig.  89) 


lay  off  a  line  and  divide  from  0  by  equal  units  to  6 ;  at  6,  with  a  radius  equal 
to  6  on  scale  (£  inch),  describe  an  arc,  and  from  0  with  a  scale  of  f  inch,  with 
a  radius  equal  to  6,  intersect  the  previous  arc.  Complete  the  triangle  through 
this  intersection,  and  draw  lines  parallel  to  6,  6'  through  the  divisions  of  the 


CONSTRUCTION  OF  GEOMETRICAL  PROBLEMS. 


27 


first  line  ;  the  triangle  will  be  divided  into  six  similar  triangles  of  which  the 
homologous  sides  are  proportional  and  represented  on  their  different  scales  by 
the  same  number  of  units. 


FIG   89. 

Fig.  90  illustrates  the  application  of  scales  to  the  measurement  of  lines 

which  are  inaccessible.     Thus  the  lines  a  b  and  a  c,  with  their  inclosed  angle, 

can  be  measured,  and,  if  plotted  to  any  scale,  the  line  c  b  can  be  measured  on 

the  same  scale. 

The  height  of  an  object  may  be  obtained  by  the  application  of  similar  tri- 

angles, or  by  the  length  of  the  shadow  cast,  which  is  merely  another  applica- 

tion of  the  same  method.     The  observer  measures 

off,  say,  60  feet  from  a  flag  pole  (Fig.  91),  and  a 

rod  is  held  at,  say,   12   feet  from  the  observer;  a 

sight  is  then  taken  to  the  top  and  bottom  of  the 

flag  pole  at  the  60-feet  distance,  and  the  points  at 

which  the  sights  intersect  the  rod  are  found  to  be 

10  feet  apart.     Then  by  construction  the  height  of 

the  flag  pole  is  found  by  scale  to  be  50  feet.     By 

means  of  shadows,  if  the  length  of  the  shadow  is 

found  to  be  40  feet  and  the  shadow  cast  by  a  10- 

foot  rod  is  8  feet,  then  by  plotting  the  height  is  found,  as  before,  50  feet. 

The  value  of  the  above  solution  of  geometrical  problems  depends  on  the 

accuracy  of  the  drawing. 

To  construct  a  square  equal  to  one  half  of  a  given  square  (Fig.  92). 

Let  a  b  c  d  be  the  given 
square,  and  draw  diagonals 
in  it.  The  square,  e  b  f  d, 
constructed  on  one  half  of 
one  of  these  diagonals,  will 
be  equal  to  one  half  the' 
given  square. 


FIG.  91. 


To  construct  a -square  equal  to  double  a  given  square  (Fig.  93). 
Construct  a  square  on  one  of  the  diagonals  in  the  given  square,  or  inclose 
the  square  with  parallels  to  the  diagonals  of  the  square. 


28 


CONSTRUCTION  OF   GEOMETRICAL   PROBLEMS. 


To  construct  a  square  equal  to  three  times  a  given  square  (Fig.  94). 

Extend  the  base  of  the  given  square  to  the  length  of  its  diagonal.  Draw  a 
line  from  the  point  at  which  this  line  ends  to  the  extreme  angle  of  the  square, 
and  upon  this  line  erect  a  square,  which  will  be  the  square  required. 

For  a  square  four  times  the  size  of  a  given  square,  make  the  base  double 
that  of  the  given  square. 


FIG.  94. 


To  construct  a  square  equal  to  five  times  a  given  square  (Fig.  95). 

Extend  the  base  of  the  given  square,  making  the  extension  to  d  e  equal  to 
c  d.  From  e  draw  a  line  to  #,  and  on  this  line  construct  a  square,  which  will 
be  the  square  required. 


FIG.  95. 


Assuming  the  side  of  the  given  square  in  Figs.  92,  93,  94,  and  95  to  be  the 
radius  (or  diameter)  (Fig.  96)  of  a  given  circle,  then  the  side  of  the  square  to 
be  constructed  half,  twice,  three,  four,  or  five  times  the  size  of  the  given  square 
will  be  the  radii  (or  diameters)  of  the  circles  half,  twice,  three,  four,  or  five 
times  the  size  of  the  given  circle. 


CONSTRUCTION  OF  GEOMETRICAL  PROBLEMS. 


29 


It  will  be  seen  by  Fig.  93  that  the  square  constructed  on  the  diagonal  of  a 
square  is  equal  to  double  that  of  the  original  square. 


FIG 

On  any  right-angled  triangle  A  C  B  (Fig.  97)  let  fall  a  perpendicular  from 
the  vertex  of  the  right  angle  to  the  hypothenuse  A  B ;  the  triangle  will  be 
divided  into  two  similar  triangles,  similar  to  each  other  and  to  the  original 
triangle,  and 

AD:AC::AC:AB;  that  is,  A  C2  =  A  D  X  A  B ; 

BD:BC::BC:AB;  that  is,  B  C2  =  B  D  X  A  B. 

AD-(-BD  =  AB,  and  the  sum  of  the  two  equations  is  A  B2  =  A  C8  + 
BC2. 

Therefore  the  square  constructed 
on  the  hypothenuse  of  a  right-angled 
triangle  is  equal  to  the  sum  of  the 
squares  of  the  other  two  sides  (Fig. 
98). 

To  determine  how  much  is  added 
to  a  given  square  by  extending  its  base 
and  constructing  a  square  thereon 
(Fig.  99). 

Let  a  represent  the  side  C  D  of  the  given  square.  The  area  of  the  square 
is  a  X  a  or  a2. 

Extend  the  side  C  D  by  a  length,  D  G,  represented  by  b.     Then  the  new 


FIG.  97. 


30 


CONSTRUCTION  OP  GEOMETRICAL  PROBLEMS. 


square  (a  -\-  b)  X  (a  +  b)  will  be  made  up  of  the  old  square,  or  a2,  and  two  rec- 
tangles, D  G  E  H  and  P  E  K  L,  or  2  (a  X  b)  or  2  a  b,  and  one  square,  E  H  K  J, 

b   X   b,   or   b2.      The    area 


To  determine  how  much 
is  taken  from  the  area  of  a 
given  square,  by  reducing 
its  base  and  constructing  a 
square  (Fig.  99). 

Let  a  represent  C  G, 
the  side  of  the  given  square. 


FIG.  99. 

Reduce  C  G,  the  length  G  D,  represented  by  b.  The  new  square  (a  —  b)s  is 
the  given  square,  or  a2,  diminished  by  two  rectangles,  D  G  J  K  and  P  L  J  H, 
or  —  2  a  b  excepting  one  square,  E  H  J  K,  b  X  b  or  -f-  b2.  The  area  (a  —  b)2 
=  a*-2ab  +  b2. 

The  last  two  constructions,  in  default  of  a  table  of  squares,  may  often  be 
found  of  use. 


CONSTRUCTION   OF  THE    ELLIPSE,    PARABOLA,   HYPERBOLA,   AND    SPIRAL. 

An  ellipse  is  an  oval-shaped  curve  (Fig.  100),  in  which,  if  from  any  point,  P, 
lines  be  drawn  to  two  fixed  points,  F  and  F',  called  foci,  their  sum  will  always 

be  the  same.     The  line  A  B  pass- 
>£_  ing  through  the  foci  is  the  major 

axis,  and  the  perpendicular  C  D  at 
the  centre  of  it  is  the  minor  axis. 

To  construct  an  ellipse,  the  axes 
being  known  (Fig.  100). 

1st  Method. — Let  the  two  axes 
be  the  lines  A  B  and  C  D.  From 
C  as  a  centre,  with  a  radius  equal 
to  E  B  (half  the  major  axis),  de- 
scribe an  arc  cutting  this  axis  at 
two  points,  F  and  F',  which  are 
the  foci.  Insert  a  pin  in  each  of 
the  foci,  and  loop  a  thread  upon  them,  so  that,  when  stretched  by  a  pencil 


CONSTRUCTION   OF   GEOMETRICAL   PROBLEMS. 


31 


FIG.  101. 


inside  the  loop,  the  point  of  the  pencil  will  coincide  with  C.  Move  the  pencil 
round,  keeping  the  loop  evenly  stretched,  and  it  will  describe  an  ellipse.  This 
construction  follows  the  definition  above  given  of  an  ellipse,  that  the  sum  of 
the  distances  of  every  point  of  the  curve  from  the  foci  is  equal.  It  is  seldom 
used  by  the  draughtsman,  as  it  is  difficult  to  keep  a  thread  evenly  stretched  ; 
but  for  gardeners,  laying  out  beds  or  plots,  it  is  very  convenient  and  sufficiently 
accurate. 

There  are  many  forms  of  ellipsographs  for  drawing  ellipses,  and  various 
sizes  of  ellipses  in  hard  wood  and  rubber  on  sale.  Pattern-makers  usually  lay 
out  ellipses  by  means  of  a  trammel 
(Fig.  101),  which  consists  of  a 
rectangular  cross,  with  guiding 
grooves  in  which  movable  rods  at- 
tached to  sliders  on  a  bar  are 
fitted,  so  as  to  move  easily  and  uni- 
formly. In  describing  an  ellipse 
place  the  trammel  with  its  grooves 
on  the  lines  of  the  axes  with  the 
bar  on  the  line  of  the  major  axis ; 
set  the  pencil  or  marker  on  the 
extremity  of  this  axis,  and  slip  the 
outer  rod  to  the  crossing  of  the 
grooves  and  clamp  it  to  the  bar.  Now  slide  the  rod  down  the  minor  axis,  and, 
with  the  pencil  at  the  extremity  of  this  axis,  clamp  the  intermediate  rod  to  the 
bar  at  the  crossing  of  the  guides.  Revolve  the  bar,  the  intermediate  rod  fol- 
lowing the  major-axis  groove,  and  the  extreme  rod  that  of  the  minor  axis, 
and  the  pencil  will  describe  the  ellipse.  Light  trammels  are  made  for  the 

use  of  draughtsmen,  but,  as 
the  necessity  of  drawing  el- 
lipses is  not  frequent,  it  can 
be  readily  done  by  the  use 
of  a  strip  of  cardboard  (Fig. 
102).  Lay  off  the  major 
and  minor  axes  on  the  pa- 
per ;  these  represent  the 
grooves  of  the  trammel. 
Now  take  a  strip  of  card- 
board with  a  straight  edge, 
lay  it  along  the  line  of  the 

maior   axis,   and  mark   the 
FIG.  102.  J   . 

positions  a  at  the  extremity 

of  this  axis,  and  c  at  the  crossing  of  the  axes ;  place  the  mark  a  on  the  ex- 
tremity of  the  minor  axis,  and  mark  on  the  edge  of  the  card  at  b  the  cross- 
ing of  the  axes.  Revolve  the  card  as  described  for  the  trammel,  mark  the  posi- 
tions of  a  by  points,  and  connect  them  for  the  curve. 

To  construct  an  approximate  semi-ellipse  by  means  of  Jive  arcs  of  circles. 

Let  A  B  (Fig.  103)  be  the  major  axis,  and  0  D  the  semi-minor  axis.  Draw 
the  semicircles  A  C  B  and  d  D  a".  Divide  these  semicircles  into  equal  parts 


32 


CONSTRUCTION  OF  GEOMETRICAL   PROBLEMS. 


by  the  radial  lines  0  e,  Of,  0  e',  Of.  From  the  points  of  intersection  of 
these  radial  lines  with  the  semicircumference  draw  g  b,  h  a,  h'  a',  g'  b',  parallel 
to  the  major  axis.  From  e,f,  e',f,  intersections  of  the  radial  lines  with  the 


semicircumference  A  C  B,  draw  e  b,  fa,  e'  a',  and  f  V  parallel  to  the  minor 
axis.  The  intersections  of  these  lines  with  b  g,  a  h,  etc.,  will  be  points  on  the 
ellipse.  Now  through  the  three  points  a,  D  and  a'  construct  an  arc  of  a  circle. 
Connect  a  and  b  with  a  chord,  bisect  it  with  a  perpendicular ;  where  this  per- 
pendicular intersects  a  S 

at  c  is  the  centre  of  the 

, 
arc  a  b. 

Connect  b  and  c;  d, 
the  intersection  of  b  c  with 
A  B,  will  be  the  centre  of 
the  arc  b  A.  Arcs  through 
a'  b'  and  B  can  be  con- 
structed in  the  same  way, 
or  the  centres  can  be 
transferred. 

The  ellipse  can  in  the  same  way  be  made  up  of  any  number  of  arcs  of 
circles. 

To  draw  a  tangent  to  an  ellipse  through  a  given  point  in  the  curve  (Fig.  104). 


CONSTRUCTION  OF  GEOMETRICAL   PROBLEMS. 


33 


From  the  given  point  T  d  raw  i  straight  lines  to  the  foci,  F,  F' ;  produce  F  T 
beyond  the  curve  to  c,  and  bisect  the  exterior  angle  c  T  F'  by  the  line  T  d. 
This  line  T  d  is  the  tangent 
required. 

To  draw  a  tangent  to  an 
ellipse  from  a  given  point 
without  the  curve  (Fig.  105). 

From  the  given  point  T 
as  a  centre,  with  a  radius 
equal  to  its  distance  from 
the  nearest  focus  F,  describe 
an  arc  ;  from  the  other  focus 
F',  with  the  major  axis  as 
radius,  cut  the  arc  at  K,  L,  and  draw  K  F',  L  F',  touching  the  curve  at  M,  N ; 
then  the  lines  T  M,  T  N,  are  tangents  to  the  curve. 

The  Parabola. 

The  parabola  may  be  defined  as  an  ellipse  whose  major  axis  is  infinite  ;  its 
characteristic  is  that  every  point  in  the  curve  is  equally  distant  from  the  direc- 
trix E  N  and  the  focus  F  (Fig.  106). 

To  construct  a  parabola  when  the  focus  and  directrix  are  given. 

1st  Method  (Fig.  106).— Through  the 
focus  F  draw  the  axis  A  B  perpendicular 
to  the  directrix  E  N,  and  bisect  A  F 


FIG.  106. 


FIG.  107. 


at  e,  the  vertex  of  the  curve.  Through  a  series  of  points,  C,  D,  E,  on  the  di- 
rectrix, draw  parallels  to  A  B ;  connect  these  points,  C,  D,  E,  with  the  focus 
F,  and  bisect  by  perpendiculars  the  lines  F  C,  F  D,  F  E.  The  intersections 
of  these  perpendiculars  with  the  parallels  will  give  points,  C',  D',  E',  in  the 
curve,  through  which  trace  the  parabola. 

2d  Method  (Fig.  107).— Place  a  straight-edge  to  the  directrix  E  N,  and 
apply  to  it  a  square  LEG;  fasten  at  G-  one  end  of  a  cord,  equal  in  length  to 
4 


34          CONSTRUCTION  OF  GEOMETRICAL  PROBLEMS. 

E  G ;  fix  the  other  end  to  the  focus  F ;  slide  the  square  steadily  along  the 
straight-edge,  holding  the  cord  taut  against  the  edge  of  the  square  by  a  pencil, 
D,  and  it  will  describe  the  curve. 

To  construct  a  parabola  when  the  vertex,  the  axis,  and  a  point  of  the  curve 
are  given  (Fig.  108). 

Let  A  be  the  vertex,  A  B  the  axis,  and  D  the  point  in  the  curve.  Con- 
struct the  rectangle  A  B  D  C ;  divide  D  C  into,  say,  four  equal  parts  at  123, 
and  A  C  into  the  same  number  at  1'  2'  3' ;  draw  diagonals,  A  3,  A  2,  A  1 ;  and 


parallels  to  the  axis  through  1'  2'  3'.  The  intersection  of  the  diagonals  A  3, 
A  2,  A  1  with  the  parallels  3',  2',  1'  at  G,  F,  E  will  be  points  in  the  required 
curve. 

Extend  the  axis  to  B',  making  A  B'=A  B ;  draw  perpendiculars  to  the  axis 
from  G,  F,  E,  D ;  lay  off  toward  B',  a'=A.  a,  A  £'=A  b,  A  c'  =  A  c;  and  draw 
B'  D,  c'  E,  V  F  and  a'  G.  These  lines  will  be  tangents  to  the  curve  at  D,  E, 
F,  G,  and  lines  perpendicular  to  the  tangents  at  these  points  will  be  perpen- 
dicular to  the  curve. 

The  Hyperbola. 

An  hyperbola  is  a  curve  from  any  point,  P,  in  which,  if  two  straight  lines 
be  drawn  to  two  fixed  points,  F,  F',  the  foci,  their  difference  will  always  be 
the  same. 

To  describe  an  hyperbola  (Fig.  109). 

From  one  of  the  foci,  F,  with  an  assumed  radius,  describe  an  arc,  and  from 
the  other,  focus  F',  with  another  radius  exceeding  the  former  by  the  given 

difference,  describe  two  small  arcs,  cut- 
ting the  first  as  at  Pandjt?/  Let  this 
operation  be  repeated  with  two  new 
radii,  taking  care  that  the  second  shall 
exceed  the  first  by  the  same  difference 
as  before,  and  two  new  points  will  be 
determined  ;  and  this  determination  of 
points  in  the  curve  may  thus  be  con- 
tinued till  its  track  is  obvious.  By 
making  use  of  the  same  radii,  but 
transposing,  that  is,  describing  with  the 
greater  about  F,  and  the  less  about  F', 
FIG.  109.  we  have  another  series  of  points  equal- 


CONSTRUCTION  OF  GEOMETRICAL  PROBLEMS. 


35 


ly  belonging  to  the  hyperbola,  and  answering  the  definition  ;  so  that  the  hyper- 
bola consists  of  two  separate  branches. 

The  curve  may  be  described  mechanically  (Fig.  110)  by  fixing  a  ruler  to 
one  focus,  F',  so  that  it  may  be  turned  round  on  this  point,  and  connecting  the 
other  extremity  of  the  ruler,  R,  to  the 
other  focus,  F,  by  a  cord  shorter  than 
the  whole  length  of  the  ruler  by  the 
given    difference  ;   then   a  pencil,   P, 


FIG.  110. 


FIG.  111. 


keeping  this  cord  always  stretched,  and  at  the  same  time  pressing  against  the 
edge  of  the  ruler,  will,  as  the  ruler  revolves  around  F',  describe  an  hyperbola. 

To  draw  a  tangent  to  any  point  of  an  hyperbola  (Fig.  111). 

Let  P  be  the  point.  On  F'  P  lay  off  P  p,  equal  to  F  P ;  draw  the  line  F  p; 
from  P  let  fall  a  perpendicular  on  this  line,  P  p,  for  the  tangent. 

To  describe  a  spiral  (Fig.  112  and  Fig.  113,  the  primary  on  a  larger  scale). 

Divide  the  circumference  of  the  primary  into  any  number  of  equal  parts, 
say  not  less  than  eight.  To  these  points  of  division  o,  e,f,  i,  etc.,  draw  tangents, 


\ 


FIG.  112. 


FIG.  113. 


and  from  these  points  draw  a  succession  of  circular  arcs ;  thus,  from  o  lay  off 
o  g,  equal  to  the  arc  a  o  reduced  to  a  straight  line,  and  connect  a  and  g  by  a 
curve  ;  from  e,  with  the  radius  e  g,  describe  the  arc  g  h;  from  /  the  next  arc, 
and  so  on.  Continue  the  use  of  the  centres  successively  and  repeatedly  to  the 
extent  of  the  revolutions  required. 


DRAWING  INSTRUMENTS. 


THE  simple  drawing  instruments  illustrated  and  applied  in  the  construc- 
tion of  the  preceding  problems,  together  with  scales  of  equal  parts,  a  protractor, 
and  a  drawing-pen,  are  all  the  instruments  essential  for  topographical  or  me- 
chanical drawing.  It  is  often  convenient,  for  facility  in  working,  to  have  com- 
passes of  various  sizes  and  modifications,  and  these,  together  with  an  assortment 
of  rulers,  triangles,  squares,  scales,  and  protractors  adapted  to  varied  work,  are 
included  in  boxes  of  drawing  instruments  furnished  by  dealers.  The  smaller 
rulers  and  triangles  are  generally  of  hard  rubber,  and  the  larger  of  wood.  As 
it  is  often  inconvenient  to  carry  long  rulers,  or  straight-edges,  and  difficult  to 

procure  them  ready-made,  the  draughts- 
man may  have  to  depend  on  a  carpenter 
or  joiner  for  them. 

The  drawing-board  in  its  simplest 
form  consists  merely  of  narrow  strips  of 
thoroughly  seasoned  white-pine  wood, 
free  from  knots,  closely  joined  and  glued, 
and  held  together  either  with  a  ledge  at 
each  end  or  with  battens  screwed  to  the 
back.  For  small  boards,  the  former 
kind  is  in  some  ways  the  best,  as  it  ad- 
mits of  being  planed  on  all  four  edges. 

Fig.  114  is  more  elaborate  and  one 
of  the  best  drawing  boards,  possessing 
all  the  qualities  of  a  first-class  board.  It 
is  made  of  pine  wood,  glued  up  to  the 
required  width,  with  the  heart  side  of 
each  piece  of  wood  at  the  surface.  A 
pair  of  hard-wood  battens  are  screwed  to 

the  back,  the  screws  passing  through  the  ledges  in  oblong  slots  that  are  bushed 
with  brass,  which  fit  closely  under  the  heads,  and  yet  allows  the  screws  to 
move  freely  when  drawn  by  the  contraction  of  the  board.  To  give  the  battens 
power  to  resist  the  tendency  of  the  surface  to  warp,  a  series  of  grooves  are 

36 


FIG.  114. 


DRAWING   INSTRUMENTS. 


37 


sunk,  half  the  thickness  of  the  board,  over  the  entire  back.  These  grooves 
take  the  transverse  strength  out  of  the  wood  and  allow  it  to  be  controlled  by 
the  battens,  leaving  at  the  same  time  the  longitudinal  strength  of  the  wood 
nearly  unimpaired. 

To  make  the  two  working  edges  perfectly  smooth,  allowing  an  easy  move- 
ment of  the  square,  a  slip  of  hard  wood  is  let  into  the  end  of  the  board.  The 
slip  is  afterward  sawed  apart  at  about  every  inch  to  admit  of  contraction.  The 
drawing-board  should  be  truly  rectangular  and  have  perfectly  straight  sides, 
for  the  use  of  the  T  square.  Two  sizes  are  sufficient  for  ordinary  use — 41  x  30 
inches  for  double  elephant  paper,  and 
31X24  inches  for  imperial  and  smaller 
sizes.  Boards  smaller  than  these  are 
too  light,  and  unsteady  in  handling. 

The  drawing-table  should  be  about 
6  feet  long  and  4  feet  wide,  of  1£ 
inch  stuff,  constructed  similarly  to 


FIG.  115. 


the  drawing-board,  and  it  is  usually 
supported  by  a  pedestal  the  height 
and  inclination  of  which  is  adjusta- 
ble, or  on  trestles,  or  a  strong  frame  at 
such  height  that  the  draughtsman 
may  not  have  to  stoop  to  his  work. 

Fig.  115  shows  an  excellent  form 
of  trestle ;  the  upper  part  of  the  horses  is  attached  to  hard- wood  supports, 
which  slide  through  the  body  of  the  trestle  and  are  provided  with  numerous 
holes ;  by  means  of  strong  pins  passing  through  the  body  of  the  horses  and 
the  holes  the  board  may  be  set  at  various  angles,  the  steel  points  in  the  top 
preventing  the  drawing-board  from  sliding  or  slipping  off. 

Straight-edges  are  made  of  close-grained,  thoroughly  seasoned  wood,  such 
as  mahogany,  maple,  pear,  etc. ;  also  of  celluloid,  hard  rubber,  steel,  or  German 
silver.  Those  made  of  maple  or  pear  wood  answer  every  purpose  and  have  the 
advantage  of  soiling  the  paper  less  than  rubber  or  metal.  No  varnish  of  any 
description  should  be  applied  to  any  of  the  instruments  used  in  drawing,  as 
varnish  will  retain  dust  and  soil  the  paper.  Use  the  wood  in  its  natural  state, 
keeping  it  carefully  wiped.  Straight-edges  should  be  about  £  inch  thick  in  the 
square  or  slightly  rounded  edges  and  1  to  2£  inches  wide,  according  to  their 
length.  As  the  accuracy  of  a  drawing  depends  greatly  on  the  straightness  of 
the  lines,  the  edge  of  the  ruler  should  be  perfectly  straight.  To  test  this, 
place  a  sheet  of  paper  on  a  perfectly  smooth  board;  insert  two  very  fine 
needles  in  an  upright  position  through  the  paper  into  the  board,  distant  from 
each  other  nearly  the  length  of  the  ruler  to  be  tested ;  bring  the  edge  of  the 
ruler  against  these  needles,  and  draw  a  line  from  one  needle  to  the  other; 
reverse  the  ruler,  bringing  the  same  edge  on  the  opposite  side  and  against  the 
needles,  and  again  draw  a  line.  If  the  two  lines  coincide,  the  edge  is  straight ; 
but  if  they  disagree,  the  ruler  is  inaccurate,  and  must  be  rcjointed.  When 
one  ruler  has  been  tested,  others  can  be  examined  by  placing  their  edges  against 
the  correct  one,  and  holding  them  between  the  eye  and  the  light. 

Triangles  may  be  made  of  the  same  kinds  of  wood  as  the  ruler,  somewhat 


38 


DRAWING  INSTRUMENTS. 


thinner,  and  of  various  sizes.     They  should  be  right-angled,  with  acute  angles 
of  45°,  or  of  60°  and  30°.     The  most  convenient  size  for  general  use  measures 


from  3  to  6  inches  on  the  side.  A  larger  size,  from  8  to  10  inches  long  on  the 
side,  is  convenient  for  making  drawings  to  a  large  scale.  In  the  smaller  trian- 
gles circular  openings  are  made  in  the  body  for  the  insertion  of  the  end  of  the 
finger,  to  give  facility  in  sliding  the  triangle  on  the  paper.  Triangles  are 
sometimes  made  as  large  as  15  to  18  inches  on  the  side  ;  but  in  this  case  they 

are  framed  in  three  pieces,  about  1£  inch 
wide,  leading  the  centre  of  the  triangle  open. 
The  value  of  the  triangle  in  drawing  perpen- 
dicular lines  depends  on  the  accuracy  of  the 
right  angle.  To  test  this  (Fig.  116),  draw  a 
line  with  an  accurate  ruler  on  paper.  Place 
the  right  angle  of  the  triangle  near  the 
centre  of  this  line,  and  make  one  of  the  ad- 
jacent sides  to  coincide  with  the  line ;  now 
draw  a  line  along  the  other  adjacent  side, 

which,  if  the  angle  is  strictly  a  right  angle,  will  be  perpendicular  to  the  first 
line.  Turn  the  triangle  on  this  perpendicular  side,  bringing  it  into  the  position 
ABC';  if  now  the  sides  of  the  triangle  agree  with  the  line  B  C'  and  A  B, 
the  angle  is  a  right  angle,  and  the  sides  are  straight.  If  they  do  not  agree, 
they  must  be  made  to  do  so  with  a  plane,  if  right  angles  are  to  be  drawn 
by  the  triangle.  The  straightness  of  the  hypothenuse  or  longest  side  can  be 
tested  like  a  common  ruler. 


FIG.  117. 


The  T  square  is  a  thin  straight-edge  or  ruler  (Fig.  117),  fitted  at  one  end 
with  a  stock,  applied  transversely  at  right  angles.     The  stock  being  so  formed 


DRAWING  INSTRUMENTS. 


39 


as  to  fit  and  slide  against  one  edge  of  the  drawing-board,  the  blade  reaches 
over  the  surface,  and  presents  an'  edge  of  its  own  at  right  angles  to  that  of  the 
board,  by  which  parallel  straight  lines  may  be  drawn  upon  the  paper.  The 
stock  should  be  long  enough  to  give  sufficient  bearing  on  the  edge  of  the  board, 
and  heavy  enough  to  act  as  a  balance  to  the  blade,  and  to  relieve  the  operation 
of  handling  the  square.  The  blade  should  be  sunk  flush  into  the  upper  half  of 
the  stock  on  the  inside,  and  very  exactly  fitted.  It  should  be  inserted  full 
breadth,  as  shown  in  the  figure ;  notching  and  dovetailing  is  a  mistake,  as  it 
weakens  the  blade,  and  adds  nothing  to  the  security.  The  upper  half  of  the 
stock  should  be  about  ^  inch  broader  than  the  lower  half,  to  rest  firmly  on  the 
board  and  secure  the  blade  lying  flatly  on  the  paper. 

One  half  of  the  stock  c  (Fig.  118)  is  in  some  cases  made  loose,  to  turn  upon 
a  brass  swivel  to  any  angle  with  the  blade  a,  and  to  be  clenched  by  a  screwed 


FIG.  118. 

nut  and  washer.  The  loose  stock  is  useful  for  drawing  parallel  lines  obliquely 
to  the  edges  of  the  board,  such  as  the  threads  of  screws,  oblique  columns,  or 
connecting-rods  of  steam-engines. 

T  squares  are  also  made  with  a  single  movable  head,  shown  in  Fig.  119 ; 


FIGS.  119, 120. 


the  blade,  turning  on  «,  is  clamped  in  position  by  the  thumb-nut  b.  Fig.  120 
illustrates  a  T  square  with  a  protractor  at  the  head,  convenient  for  laying  off 
lines  of  designated  angles. 

In  many  drawing-cases  will  be  found  the  parallel  ruler  (Fig.  121),  consist- 


FIG.  121. 


DRAWING  INSTRUMENTS. 


ing  of  two  rulers  connected  by  two  bars  moving  on  pivots,  so  adjusted  that  the 
rulers,  as  they  open,  form  the  sides  of  a  parallelogram.  The  edge  of  one  of  the 
rulers  being  retained  in  a  position  coinciding  with,  or  parallel  to,  a  given  line, 
when  the  other  ruler  is  moved,  lines  drawn  along  its  edge  are  also  parallel  to 
the  given  line.  This  instrument  is  only  useful  in  drawing  small  parallels,  and 
in  accuracy  and  convenience  does  not  compare  with  either  the  triangle  and 
ruler  or  T  square. 

Another  form  of  parallel  ruler  (Fig.  122)  consists  of  a  strip  of  wood  with 
bevelled  edges,  having  two  holes  to  receive  two  broad  wheels,  a,  a,  which  are 


FIG.  122. 

connected  by  an  axle  passing  under  the  metal  cover,  b,  #,  and  revolving  in  the 
supports,  c,  c ;  the  wheels  come  slightly  below  the  surface  of  the  wood,  as 
shown  in  the  end  elevation.  In  drawing  parallel  lines  the  fingers  are  placed 
with  a  firm  pressure  about  the  centre  of  the  metal  cover,  and  the  ruler  is 
moved  in  the  proper  direction.  This  ruler  is  more  easily  applied  than  the 
former,  but  is  more  liable  to  error. 

VAKIABLE    CURVES. 

For  drawing  arcs  of  a  large  radius,  beyond  the  range  of  ordinary  compasses, 
and  lines  varying  in  curvature,  thin  slips  of  wood,  termed  curves,  are  usually 
employed.  These  forms  are  of  very  general  application,  but  others  of  almost 
every  form,  and  made  of  hard  rubber,  pear  wood,  or  celluloid,  can  be  pur- 
chased. Whatever  be  the  nature  of  the  curve,  some  portion  of  the  instrument 
will  be  found  to  coincide  with  its  commencement,  and  it  can  be  continued 
throughout  its  extent  by  applying,  successively,  such  parts  as  are  suitable,  care 
being  taken  that  the  parts  are  tangent  to  each  other,  and  that  the  continuity  is 
not  injured  by  unskilful  junction. 

Fig.  123  shows  an  adjustable  curve  ruler,  the  main  features  of  which  are  a 
hard-rubber  face,  «,  which  holds  the  form  of  the  required  curve  by  a  bar  of 


FIG.  123. 

soft  lead,  Z>,  kept  in  contact  with  the  rubber  face  by  the  fasteners,  c,  and  a  flat 
spring  inside  these  fasteners.  This  curve,  while  useful  in  the  coarser  kinds  of 
draughting,  does  not  do  as  neat  or  accurate  work"  as  the  separate  curves  above 
given. 

Thin  splines  are  also  to  be  had,  which,  held  in  position  by  leaden  weights, 
serve  admirably  for  a  guide  to  the  pen  in  describing  curves  (Fig.  124).    For  the 


DRAWING  INSTRUMENTS.  41 

same  purpose  a  thin,  hard-rubber  ruler,  with  soft-rubber  backing,  answers  well, 
and,  as  it  can  be  readily  rolled  up,  is  extremely  portable. 

The  weights  above  shown  are  very  convenient  in  holding  the  drawing-paper 
on  the  board,  but  thumb-tacks  (Fig.  125),  steel  points  with  large,  flat  heads, 
are  in  general  use.  They  can  be  readily  forced  into  the  wood,  and  as  readily 
raised,  but  thumb-tack  lifters  can  be  purchased. 


in 


Elliptic,  parabolic,  and  hyperbolic    (see  above)   curves  are  furnished 
sets,  but  the  draughtsman  can  make  a  model  out  of  thick  cardboard  or  cellu- 
loid, with  which  he  can  draw  a  very  uniform  curve. 

For  the  drawing  of  ellipses,  very  neat  trammels  or  compasses  with  elliptic 
guides  or  patterns  may  be  purchased. 


42 


DRAWING  INSTRUMENTS. 


Fio.  124. 


FIG.  125. 


The  drawing  or  right-line  pen  (Fig.  126)  consists  of  two  blades  with  steel 
points,  fixed  to  a  handle ;  and  they  are  so  bent  that  a  sufficient  cavity  is  left 
between  them  for  the  ink.  The  blades  are  set  with  the 
points  more  or  less  open  by  means  of  a  mill-headed  screw, 
so  as  to  draw  lines  of  any  required  fineness  or  thickness. 
For  red  inks,  the  blades  of  the  pen  should  be  nickle-plated 
or  German  silver.  One  of  the  blades  is  framed  with  a  joint, 
so  that  by  taking  out  the  screw  the  blades  may  be  complete- 
ly opened,  and  the  points  effectively  cleaned  after  use.  The 
ink  is  put  between  the  blades  by  a  common  pen.  In  using 
the  pen,  it  should  be  slightly  inclined  in  the  direction  of 
the  line  to  be  drawn,  and  care  should  be  taken  that  both 
points  touch  the  paper.  These  observations  equally  apply 
to  the  pen-points  of  the  compasses.  The  drawing  -  pen 
should  be  kept  close  to  the  ruler  or  straight- 
edge, and  in  the  same  direction  during  the 
whole  operation  of  drawing  the  line.  Care 
must  be  taken  to  hold  the  straight-edge 
firmly  with  the  left  hand,  that  it  does  not 
change  its  position. 

For  drawing  close  parallel  lines  in  me- 
chanical and  architectural  drawings,  or  to 
represent  railroads,  canals,  or  roads,  a  rail- 
road pen  (Fig.  127)  is  frequently  used,  a 
double  pen  with  an  adjusting  screw  to  set  the  pens  to  any  required  small 
distance.  This  instrument  is  also  made  with  pencil  points  (Fig.  128). 

Border  -  pens  (Fig. 
129),  for  drawing  broad 
lines,  are  double  pens 
with  an  intermediate 
blade,  and  are  applicable 
to  the  drawing  of  map- 
borders.  The  same  work 
may  be  done  by  drawing 
heavy  outer  lines  with 
the  common  drawing- 
pen,  and  filling  in  with  a 
brush  or  writing-pen. 

The  curve-pen  (Fig. 
130)  is  especially  de- 
signed for  the  ready 
drawing  of  curved  lines. 
The  axis  of  this  pen  is 
carried  through  the  han- 
dle and  fastened  by  a 
nut  on  top,  allowing  the 

pen  to  revolve,  and  thus  more  easily  follow  the  curve.     This  instrument,  made 
with  two  pens  (Fig.  131),  is  called  a  railroad  curve-pen. 


FIG.  128. 


FIG.  129. 


43 

The  dotting-pen  (Fig.  132)  has  on  the  back  blade  a  pivot,  on  which  may  be 
placed  a  dotting- wheel,  resembling  the  rowel  of  a  spur  ;  the  screw  is  for  opeu- 


FIG.  131. 


ing  the  blades  to  remove  the  wheel  for  cleaning  after  use  or  replace  it  with  one 
of  another  character  of  dot.  A  variety  of  dotting-wheels  accompanies  the  in- 
strument, each  producing  a  different-shaped  dot.  These  are  used  as  distin- 
guishing marks  for  different  classes  of  boundaries  on  maps ;  for  instance,  one 
kind  of  dot  distinguishes  county  boundaries,  another  kind  town  boundaries,  a 
third  kind  distinguishes  that  which  is  both  a  county  and  a  town  boundary,  etc. 


1 


FIG.  132. 

In  using  this  instrument,  the  ink  must  be  inserted  between  the  blades  above 
the  dotting-wheel,  so  that,  as  the  wheel  revolves,  the  points  pass  through  the 
ink,  each  carrying  with  it  a  drop,  and  marking  the  paper  as  it  passes.  It 
sometimes  happens  that  the  wheel  will  revolve  many  times  before  it  begins  to 
deposit  its  ink  on  the  drawing,  thereby  leaving  the  first  part  of  the  line  blank, 
and,  when  it  is  gone  over  again,  the  first-made  dots  are  liable  to  get  blotted. 
This  evil  may  be  avoided  by  placing  a  piece  of  blank  paper  over  the  drawing 
to  the  very  point  the  dotted  line  is  to  commence  at,  and  drawing  the  wheel 
over  the  blank  paper  first,  so  that  by  the  time  it 
reaches  the  proper  point  the  ink  begins  to  flow. 

The  dotting -instrument  (Fig.  133)  works  on  the 
principle  of  the  drawing-pen.  The  outer  wheel  is 
rolled  on  the  edge  of  a  T  square  or  straight-edge, 
and  turns  a  ratchet  wheel  which  causes  the  pen  to 
move  up  and  down.  The  flat  point  close  to  the 
pen  must  slide  on  the  paper.  To  change  the  pat- 
tern of  the  dotted  lines,  the  spring  which  holds  the 
wheels  on  the  axle  is  thrown  back,  and  the  proper  ratchet  wheel  inserted. 

The  best  pricking -point  is  a  fine  needle  held  as  in  Fig.  134,  and  is  used  to 
transfer  drawings  by  pricking  through  at  the  points  of  a  drawing  into  the  paper 


FIG.  133. 


FIG.    134. 


placed  beneath.  The  handle  of  the  ordinary  drawing-pen  often  contains  a 
pricking-point,  which  may  be  used  by  unscrewing  the  pen  where  it  is  joined  to 
the  handle. 

When  drawings  are  transferred  by  tracing — a  prepared  black  sheet  being 
placed  between  the  drawing  and  the  paper  to  receive  the  tracing— the  eye  end 
of  the  needle  forms  a  good  tracing-point. 


44: 


DRAWING  INSTRUMENTS. 


The  stylus  (Fig.  135)  is  a  piece  of  polished  agate  placed  in  a  handle,  and  is 
used  as  a  tracing-point. 


FIG.  135. 

Compasses  are  fitted  with  ink-points  and  with  lengthening  bars  for  drawing 
larger  circles.     Compasses  should  have  joints  in  the  legs,  so  that  the  points, 
pencil,  and  pen  may  be  set  perpendicular  to  the  planes  in  which  the 
circles  are  described  (Fig.  136).     Compasses  of  this  general  form  may 
be  had  in  sizes  of  3£  to  7  inches. 

For  the  measurement  and  laying  off 
of  small  spaces,  and  the  describing  of 
small  circles,  there  are  small  bow  com- 
passes (Fig.  137).  These  are  sometimes 
made  with  an  adjusting  screw  between 
the  legs. 

For  the  measurement  or  laying  off 


FIG.  136. 


FIG.  137. 


Fio.  138. 


of  distances  the  plain  dividers  are  convenient,  but  for  ready  and  close  ad- 
justment the  hair  dividers  (Fig.  138)  are  most  suitable.  The  only  difference 
is  that  in  the  hair  dividers  one  of  the  points  is  attached  to  the  body  by  a 


FIG.  139. 


spring,  and  by  means  of  the  screw  b  it  can  be  moved  a  very  little  toward  or 
from  the  fixed  point  more  accurately  than  by  closing  or  opening  the  dividers. 
In  dividing  a  line  into  equal  parts  especially,  it  enables  one  to  divide  the  excess 
or  deficit  readily. 


DRAWING  INSTRUMENTS. 


For  convenience  of  carrying  in  the  pocket,  there  are  portable  or  turn-in 
compasses  (Fig.  139).  There  is  a  small  attachment  for  a  common  pencil 
which  enables  it  to  be  used  like  compasses. 


FIG.  140. 


Three-legged  dividers  (Fig.  140)  are  convenient,  while  transferring  measures 
from  a  drawing  to  a  copy  on  an  equal  scale,  for  locating  a  third  point  when  two 
are  established. 

For  setting  off  very  long  lines,  or  describing  circles  of  large  radius,  beam 
compasses  are  used  (Fig.  141).  These  consist  of  a  mere  strip  of  wood,  A,  and 
two  brass  or  German  silver  boxes,  B  arid  C,  which  can  easily  be  attached  to  the 
beam ;  connected  with  the  brass  boxes  are  the  two  points  of  the  instrument, 
G  and  H.  The  object  of  this  instrument  is  the  nice  adjustment  of  the  points 
G  and  H  at  any  definite  distance  apart;  at  F  is  a  slow-motion 
screw,  by  which  the  point  G  may  be  moved  any  very  minute  dis- 
tance after  the  distance  from  H  to  G  has  been  adjusted  as  nicely 
as  possible  by  the  hand  alone.  The  wheel  attachment,  I,  is  to 
carry  the  weight  of  the  beam.  The  metal  parts  of  this  instru- 
ment occupy  but  little  space. 

There  are  beam  compasses  in  which  the  beam  is  graduated, 
and  in  which  the  boxes  corresponding  to  B  and  C  are  fitted  with 
vernier  or  reading  plates,  to  afford  the  means  of  minutely  subdi- 
viding the  divisions  on  the  beam. 

Beam  compasses  are  also  made  of  small  round  German-silver 
bars,  one  screwing  into  the  other,  on  which  are  slides  adapted  for 
carrying  pen  or  pencil  and  points. 


16' 


H 


FIG.  142. 


Proportional  dividers  (Fig.  142),  for  copying  and  reducing  drawings,  are 
found  in  most  cases  of  instruments. 

Closing  the  dividers  and  loosening  the  screw  C,  the  slide  may  be  moved  up 


46  DRAWING  INSTRUMENTS. 

in  the  groove  until  the  mark  on  the  index  corresponds  with  the  required  num- 
ber ;  then  clamping  the  screw,  the  space  inclosed  between  the  long  points,  A  B, 
will  be  as  many  times  that  between  the  short  points,  E  D,  as  is  shown  by  the 
number  opposite  the  index.  If  the  lines  are  to  be  reduced,  the  distances  are 
measured  with  the  long  points,  and  set  off  by  the  short  ones ;  if  the  lines  are 
to  be  enlarged,  then  vice  versa. 

Proportional  dividers  are  also  used  for  dividing  the  circumference  of  a 
circle  into  a  number  of  parts.  A  special  scale  along  the  graduated  edge, 
marked  circles,  is  used,  it  being  only  necessary  to  move  the  slider  to  the 
proper  number  on  this  scale  to  obtain  a  chord  of  the  proper  length.  It 
often  happens  that  the  length  of  the  points  becomes  reduced  by  use  or  acci- 
dent. In  this  case  it  is  only  necessary  to  loosen  the  screw  holding  the  short- 
ened point,  take  it  out,  grind  to  a  point,  and  set  to  its  former  length. 

Scales. — The  application  of  simple  scales  to  the  construction  of  diagrams 
has  been  explained ;  but  among  drawing  instruments  scales  especially  adapted 
to  plotting  are  to  be  found  in  great  varieties  of  form,  divisions,  and  material. 
It  is  usual,  especially  in  topographical  drawings,  for  the  draughtsman  to  con- 
struct a  scale  upon  the  finished  sheet  on  account  of  its  ready  application  to  the 
determination  of  measures,  and  when  the  drawing  is  to  be  reduced  or  enlarged 
by  photographing  it  is  indispensable.  Moreover,  paper  expands  and  contracts 
under  hygrometric  changes ;  the  scale  should  be  subject  to  those  same  changes. 
To  remedy  this  inconvenience  Mr.  Charles  Holzapfel  has  introduced  paper 
scales,  which  are  portable  and  cheap;  but  as  all  kinds  of  paper  are  noi 
equally  susceptible  to  changes  of  condition  on  the  atmosphere,  the  detached 
paper  scale  affords  only  a  partial  correction. 

The  scale  should  be  written  or  drawn  in  all  drawings ;  also  the  date  of  com- 
pletion and  name  or  initials  of  the  draughtsman,  as  these  data  may  be  of  value 
in  the  identification  of  the  drawing. 

In  all  working  architectural  and  mechanical  drawings,  use  as  large  a  scale 
as  possible ;  and  even  then  do  not  depend  upon  the  mechanics  employed  in  the 
construction  measuring  correctly,  but  write  in  the  dimensions  as  far  as  prac- 
ticable. For  architectural  plans,  the  scale  of  ^  of  an  inch  to  the  foot  is  in  very 
general  use  and  is  convenient  for  the  mechanic,  as  the  common  two-foot  rule 
carried  by  all  mechanics  is  subdivided  into  £ths,  iths,  and  sometimes  sixteenths 
of  an  inch,  and  the  distances  on  a  drawing  to  this  scale  can  therefore  be  easily 
measured  by  them.  This  fact  should  not  be  lost  sight  of  in  working  drawings. 
When  the  dimensions  are  not  written,  make  use  of  such  scales  that  the  dis- 
tances may  be  measured  by  the  subdivisions  of  the  common  two-foot  rule ; 
thus,  in  a  scale  of  ^  or  ^  full  size,  6  inches  or  3  inches  represent  one  foot ; 
in  a  scale  of  an  inch  to  the  foot  or  twelfth  full  size,  each  £  an  inch  repre- 
sents 6  inches,  £  of  an  inch,  3  inches ;  but  when  £  or  fa  an  inch  to  the  foot, 
or  any  similar  scale,  is  adopted,  it  is  evident  that  these  divisions  can  not  be 
taken  by  the  two-foot  rule. 

Plotting  scales  (Fig.  143)  are  scales  of  equal  parts,  with  the  divisions  usu- 
ally on  a  bevelled  edge,  by  which  any  length  may  be  marked  off  on  the  paper 
without  using  dividers.  There  are  also  small  offset  scales,  for  use  of  which  see 
"  Topographical  Drawing." 

Sometimes  these  scales  are  made  with  edges  bevelled  on  both  sides,  and 


DRAWING   INSTRUMENTS. 


47 


graduated  to  four  different  scales.     Sometimes  the  section  of  the  scale  is  tri- 
angular (Fig.  144),  with  six  scales  on  the  different  edges.     To  avoid  confusion 


NrLL 

1  II  II  1      i      1  II  II  1  1      Ml      II  II  1  1  1 

ill]'1,!          Ml       II       1  1  1   1   1  I!   1   1   1   II 

\ 

ao 

\     f              Oil-               6             1             It             19 

IS                Itr               IE                |Z               It                 0 

FIG.  143. 


from  having  many  scales  on  one  ruler,  the  triangular  scale  has  a  small  slip  of 
metal,  A,  readily  put  on,  which  covers  partially  the  scales  not  in  use. 


FIG.  145. 


FIG.  144. 

To  divide  a  given  line  into  any  number  of  equal  parts  (Fig.  145). 
Let  A  B  be  the  line,  and  the  number  of  parts  be  ten.     Draw  a  perpendicu- 
lar at  one  extremity,  A,  of  the  line ;  with  a  plotting  scale  place  the  zero  at  the 
other  extremity,  B,  of  the  line ;  make  the  mark  10 
on  the  scale  coincide  with  the  perpendicular ;  draw 
a  line  along  the  edge  of  the  scale,  and  mark  the 
line  at  each  division  of  the  scale  1  to  9 ;  draw  per- 
pendiculars through  these  marks  to  the  line  A  B, 
and  they  will  divide  A  B  into  ten  equal  parts. 

The  above  figure  illustrates  the  construction  of 
diagonal  scales.  The  simply  divided  scales  give 
only  two  denominations,  primaries  and  tenths,  or 

twelfths ;  but  more  minute  subdivision  is  attained  by  the  diagonal  scale,  which 
consists  of  a  number  of  primary  divisions,  one  of  which  is  divided  into  tenths, 

and  subdivided  into 
hundredths  by  diago- 
nal lines  (Fig.  146). 
This  scale  is  con- 
structed in  the  follow- 
ing manner  :  Eleven 
parallel  horizontal  lines 
are  ruled,  inclosing  ten 
equal  spaces ;  from  one 
end  set  off  the  primary 
unit  divisions,  0, 1,  2, 3, 
and  draw  vertical  lines 
through  these  points; 
subdivide  the  extreme  unit  to  the  left  on  the  upper  and  lower  lines  into  ten 
equal  parts,  1,  2,  3,  etc. ;  connect  0  on  the  upper  line  with  1  on  the  lower  line 


FIG.  146. 


48 


DRAWING  INSTRUMENTS. 


A 


by  a  diagonal,  and  draw  lines  parallel  to  it  through  the  other  subdivisions.  To 
take  a  measurement  of,  say,  168,  we  place  one  foot  of  the  dividers  on  the  pri- 
mary 1,  and  carry  it  down  to  parallel  8,  and  then  extend  the  other  foot  to  the 
intersection  of  the  diagonal  which  falls  from  the  subdivision  6  with  this  par- 
allel. The  primaries  may,  of  course,  be  considered  as  yards,  feet,  or  inches ; 
and  the  subdivisions  as  tenths  and  hundredths  of  these  respective  denomina- 
tions. If  the  number  of  parallel  spaces  be  eight  and  the  subdivision  be 
twelve,  we  can  measure  feet,  inches,  and  eighths.  In  the  diagonal  scale  the 
vertical  subdivisions  are  often  omitted. 

The  diagonals  may  be  applied  to  a  scale  where  only  one  subdivision  is  re- 
quired. Thus,  if  seven  lines  be  ruled  (Fig.  147),  inclosing  six  equal  spaces, 

and  the  length  be  divided 
into  primaries,  as  A  B,  B  C, 
etc.,  the  first  primary,  A  B, 
may  be  subdivided  into 
twelfths  by  two  diagonals 
running  from  6,  the  mid- 
dle of  A  B,  to  12  and  0. 
We  have  here  a  very  con- 
venient scale  of  feet  and  inches.  From  C  to  6  is  1  foot  6  inches ;  and  from 
C  on  the  several  parallels  to  the  various  intersections  of  the  diagonals  we  obtain 
1  foot  and  any  number  of  inches  from  1  to  12. 

For  the  designing  of  machinery,  it  is  very  convenient  to  have  some  scale  of 
reference  by  which  to  proportion  the  parts ;  for  this  purpose  a  vertical  and 
horizontal  scale  may  be  drawn  on  the  walls  of  the  room. 

Vernier  scales  are  preferred  by  some  to  the  diagonal  scale  already  described. 
To  construct  a  vernier  scale  (Fig.  148)  by  which  a  number  to  three  places  may 
be  taken,  divide  all  the  primary  divisions  into  tenths,  and  number  these  sub- 


7/V 

2  v 

<>L^- 

f0/       \r 

„/         \, 

/            \ 

0/2 
FIG.  147. 

10 

2        4}    6         8 

f 

f 

f 

II          I     I          II 

I     I     I     I 

I 

I          I     I     I     I     I 

I 

I     I     i     I     I     II     I 

wn  I     '          I     I     I     I     i     i     I 

wv  |/0       8          6     \    t          2 

FIG.  148. 

divisions  1,  2,  3,  from  left  to  right.  Take  off  now  with  the  compasses  eleven 
of  these  subdivisions,  set  the  extent  off  backward  from  the  end  of  the  first 
primary  division,  and  it  will  reach  beyond  the  beginning  of  this  division,  or 
zero  point,  a  distance  equal  to  one  of  the  subdivisions.  Now  divide  the  extent 
thus  set  off  into  ten  equal  parts,  marking  the  divisions  on  the  opposite  side  of 
the  divided  line  to  the  lines  marking  the  primary  divisions  and  the  subdivisions, 
and  number  them  1,  2,  3,  etc.,  backward  from  right  to  left.  Then,  since  the 
extent  of  eleven  subdivisions  has  been  divided  into  ten  equal  parts,  so  that 
these  ten  parts  exceed  by  one  subdivision  the  extent  of  ten  subdivisions,  each 
one  of  these  equal  parts,  or,  as  it  may  be  called,  one  division  of  the  vernier 
scale,  exceeds  one  of  the  subdivisions  by  a  tenth  part  of  a  subdivision,  or  a 
hundredth  part  of  a  primary  division ;  thus,  if  the  subdivision  be  considered 
10,  then  from  0  to  the  first  division  of  the  vernier  will  be  11 ;  to  the  second, 
22 ;  to  the  third,  33  ;  to  the  fourth,  44 ;  to  the  fifth,  55,  and  so  on,  66,  77, 
88,  99. 


DRAWING  INSTRUMENTS. 


49 


To  take  off  the  number  253  fr,om  this  scale,  place  one  point  of  the  dividers 
at  the  third  division  of  the  vernier  ;  if  the  other  point  be  brought  to  the  pri- 
mary division  2,  the  distance  embraced  by  the  dividers  will  be  233,  and  the 
dividers   must   be   extended 
to  the  second  subdivision  of 
tenths    to    the    right   of   2. 
If    the    number    were    213, 
then  the  dividers  would  have 
to  be  closed   to   the  second 
subdivision  of  tenths  to  the 
left  of  2.     The  number,  thus 
taken,    may    be    253,    25'3, 
2'53,  according   as   the   pri- 
mary divisions  are  taken  as 
hundreds,  tens,  or  units. 

The  construction  of  this 
scale  is  similar  to  that  of  the 
verniers  of  theodolites  and 
surveying  instruments. 

The  sector  in  its  old 
form  carried  several  scales 
on  its  faces.  As  given  in 
Fig.  149,  there  are  only 
double  scales  starting  from 
the  centre  joint,  which, 
without  drawing,  may  be 
applied  to  the  solution  of  problems  on  similar  triangles. 

Let  the  lines  A  B,  A  C,  represent  the  legs  of  the  sector,  and  A  D,  A  E,  two 
equal  sections  from  the  centre  ;  then,  if  the  points  B  C  and  D  E  be  connected, 
the  lines  B  C  and  D  E  will  be  parallel ;  therefore,  the  triangles  A  B  C,  A  D  E, 


FIG.  149. 


FIG.  150. 


will  be  similar,  and,  consequently,  the  sides  A  B,  B  C,  A  D,  D  E,  proportional 
—that  is,  as  A  B  :  B  C  :  :  A  D  :  D  E ;  so  that  if  A  D  be  the  half,  third, 
5 


50 


DRAWING  INSTRUMENTS. 


or  fourth  part  of  A  B,  then  D  E  will  be  a  half,  third,  or  fourth  part  of 
B  C  ;  and  the  same  holds  of  all  the  rest.  Hence,  if  D  E  be  the  chord, 
sine,  or  tangent  of  any  arc,  or  of  any  number  of  degrees  to  the  radius  A  D, 
then  B  C  will  be  the  same  to  the  radius  A  B.  Thus,  at  every  opening  of 
the  sector,  the  transverse  distances  D  E  and  C  B  from  one  ruler  to  another  are 
proportional  to  the  lateral  distances,  measured  on  the  lines  A  B,  A  C.  It  is  to 


FIG.  151. 


be  observed  that  all  measures  are  to  be  taken  from  the  inner  lines,  since  these 

only  run  accurately  to  the  centre. 

On  the  scale  in  common  boxes  of  drawing  instruments,  the  edges  of  the 

sides  are  divided  as  a  protractor  (Fig.  84)  for 
the  laying  out  of  angles.  The  ordinary  pro- 
tractor consists  of  a  semicircle  of  thin  metal  or 
horn  (Fig.  150),  whose  circumference  is  divided 
into  180  degrees  (180°).  In  the  larger  protrac- 
tors each  of  these  divisions  is  subdivided. 

Application  of  the  protractor. — To  lay  off  a 
given  angle  from  a  given  point  on  a  straight 
line,  let  the  straight  line  a  b  of  the  protractor 
coincide  with  the  given  line,  and  the  point  c 
with  the  given  point ;  now  mark  on  the  paper 
against  the  division  on  the  periphery  coinciding 
with  the  angle  required  ;  remove  the  protractor, 
and  draw  a  line  through  the  given  point  and  the 
mark. 

Fig.  151  is  a  protractor  with  a  straight-edge 
revolving  on  a  horn  centre.  Where  the  straight- 
edge is  intersected  by  the  edge  of  the  protractor 
a  vernier  is  attached,  and  will  be  found  useful  in 
close  work  for  dividing  the  degrees  into  tenths. 
This  protractor  is  often  extended  to  full  circles. 
For  plotting  field-notes  expeditiously,  drawing-paper  can  be  obtained  with 


FIG.  152. 


DRAWING  INSTRUMENTS. 


51 


large,  full  circular  protractors  printed  thereon,  on  which  the  courses  can  be 
readily  marked,  and  thus  transferred  to  the  part  of  the  paper  required  by  a 
parallel  ruler,  or  by  triangle  and  ruler.  These  sheets  are  of  especial  use  in 
plotting  at  night  the  day's  work,  as,  on  account  of  the  large  size  of  the  protrac- 
tor, angles  can  be  laid  off  with  greater  accuracy  than  by  the  usual  protractor  of 
a  drawing-instrument  case,  with  less  confusion  of  courses,  and  more  expe- 
ditiously. 

The  pantograph  is  used  for  the  copying  of  drawings,  either  on  the  same 
scale,  on  a  reduced  scale,  or  on  an  enlarged  scale. 

Fig.  152  shows  its  simplest  form  and  its  application.  The  lower  left-hand 
point,  around  which  the  frame  is  turned,  is  fixed,  and  the  proportion  of  the 
drawing  is  determined  by  the  position  of  the  screw  eyes  in  the  holes  of  the 
arms. 

Fig.  153  is  another  form,  of  more  finished  construction.  It  consists  of  a 
set  of  jointed  rulers,  A,  B,  and  another,  C,  D,  about  one  half  the  length  of  the 


FIG.  153. 

former.  The  free  ends  of  the  smaller  set  are  jointed  to  the  larger  at  about  the 
centre.  Casters  are  placed  at  a  a,  etc.,  to  support  the  instrument  and  to  allow 
an  easy  movement. 

DBAWING-PAPERS. 

Papers  adapted  to  drawing  may  be  obtained  of  various  qualities,  thicknesses, 
and  dimensions,  either  in  sheets,  pads,  or  rolls.  Machine-made  papers  are 
generally  used,  and  are  to  be  had  from  stock  in  rolls  up  to  62  inches  in  width, 
but  to  order  much  wider.  They  are  generally  made  from  cotton  for  the  more 
finished  drawings ;  but  stronger  papers  for  working  drawings  and  details  are  of 
manilla  or  of  coarse  heavy  stock. 

Eoll  and  sheet  papers  can  be  had  mounted  or  backed  with  cotton  cloth, 
which  prevents. them  from  being  torn,  and  permits  of  their  being  hung  to  the 
walls  as  maps. 

Hand-made  drawing-papers  are  usually  made  in  certain  standard  sizes,  about 
as  follows : 


Cap 13  inches  by  17  inches. 

Demy 15        »         20      " 

Medium 17        "         22      " 

Royal 19        "         24      " 

Super  Royal 19        "         27      " 

Tracing-paper  is  a  prepared  tissue  paper,  transparent  and  qualified  to  re- 
ceive ink  lines  and  tinting  without  spreading.     When  placed  over  a  drawing 


Imperial 22  inches  by  30  inches. 

Atlas 26        "         34      " 

Double  Elephant 27        "         40     " 

Antiquarian 31        "         53      " 


52  DRAWING  INSTRUMENTS. 

already  executed,  the  drawing  is .  distinctly  visible  through  the  paper,  and  it 
may  be  copied  directly  or  traced  in  pencil  or  ink. 

Tracing-paper  often  becomes  tender  with  age,  is  apt  to  break  in  the  folds, 
is  not  easily  rolled.  It  is  not  suitable,  therefore,  for  permanent  drawings ;  but 
the  tracing  can  be  readily  transferred  to  drawing-paper  by  means  of  transfer 
paper.  Place  the  fair  sheet  on  the  drawing-board,  above  it  the  transfer  sheet 
with  the  prepared  face  down,  then  the  tracing,  and  steady  the  whole  by  weights 
or  by  thumb-tacks  fixed  into  the  drawing-board.  A  fine,  smooth  point  is  then 
passed  over  each  boundary  and  line  on  the  tracing  with  a  pressure  of  the  hand 
sufficient  to  cause  a  clear  line  to  be  left  by  the  transfer  paper  on  the  fair  sheet. 
Finish  these  lines  in  ink.  The  copyist  should  be  careful  in  his  manipulation 
that  no  unnecessary  lines  or  smutches  be  left  on  the  fair  sheet.  Transfer  paper 
can  be  readily  obtained  in  sheets,  either  in  black,  blue,  vermilion,  or  graphite, 
or  it  can  be  made  by  smearing  with  a  piece  of  flannel  one  surface  of  thin  paper 
with  a  coating  of  lard  and  graphite  and,  after  a  day's  drying,  wiping  off  the 
superfluous  portion  with  a  soft  rag. 

Parchment  papers  are  much  stronger  than  tracing-papers,  and  are  usually 
transparent  enough  to  serve  the  same  purpose ;  the  thicker  kinds  are  well 
adapted  for  drawing  and  engrossing.  De  La  Rue's  process  for  the  manufac- 
ture of  parchment  paper  is  to  plunge  unsized  paper  for  a  few  seconds  into 
sulphuric  acid,  diluted  with  half  to  a  quarter  its  bulk  of  water,  the  solution 
being  of  the  same  temperature  as  the  air,  and  afterward  wash  with  'weak 
ammonia. 

A  drawing  may  be  made  to  accompany  a  letter  by  saturating  the  letter 
paper  with  benzine  till  it  becomes  transparent,  then  using  it  as  tracing-paper, 
copying  the  design  in  pencil,  and  finishing  in  copying-ink  after  the  benzine 
has  evaporated,  so  that  it  can  be  transferred  with  the  descriptive  writing  to  the 
letter  book. 

Transparent  tracing-cloth  can  be  had  in  wide  and  long  rolls.  It  is  much 
stronger  than  tracing-paper,  and  serves  a  permanent  purpose.  Should  the 
tracing-cloth  refuse  to  take  ink  lines  well,  almost  any  fine  white  powder  will 
remedy  this,  such  as  chalk,  fuller's  earth,  pipe  clay,  or  plaster  of  Paris  sprinkled 
on  and  rubbed  in  well. 

It  is  usual  to  draw  on  the  dull  side  of  the  cloth,  except  where  colour  is  to 
be  put  in,  when  the  ink  lines  are  drawn  on  the  glossy  side  and  the  colour  on 
the  dull  back.  Designs. and  finished  drawings  made  in  pencil  on  paper  are 
traced  on  cloth  in  ink,  and  in  this  form  are  preserved  as  originals  and  can  be 
copied  by  the  heliographic  process,  either  wholes  or  details  as  needed.  When  a 
white  sheet  of  paper  is  placed  behind  the  tracings,  the  drawing  may  be  readily 
photographed  on  a  reduced  or  enlarged  scale,  and  much  more  cheaply  than  by 
any  other  process ;  and  such  negatives  may  be  used  in  process  engraving  for 
book  illustrations. 

Heliographic  paper  can  readily  be  had  in  sheets  or  rolls,  and  the  mixture 
for  the  preparation  of  the  paper  can  also  be  purchased,  or  can  be  made  by 
dissolving  If  ounce  of  common  citrate  of  iron  in  8  ounces  of  water,  and  1£ 
ounce  of  red  prussiate  of  potash  in  8  ounces  of  water,  and  then  mixing  them 
just  previous  to  using.  Papers  and  mixtures  must  be  kept  from  the  light  or 
they  will  lose  their  sensitiveness.  The  above  is  a  mixture  for  the  most  com- 


DRAWING  INSTRUMENTS 


53 


mon  form  of  sun  prints,  called, the  ferro-prussiate  or  blue  process,  in  which 
white  lines  are  developed  on  a  blue  ground.  By  the  cyanotype  process  blue 
lines  are  developed  on  a  white  ground  ;  by  the  nigrosine  process,  black  lines  on 
a  white  ground ;  by  the  chromide  dry  process,  dark  lines  on  a  tinted  ground. 
Papers  for  all  of  the  above  processes  are  on  sale,  with  directions  for  use.  If 
none  can  be  had,  and  it  is  desired  to  prepare  some,  use  the  ferro-prussiate 
process  as  the  simplest,  of  which  a  recipe  has  been  given  above,  the  paper 
should  be  chemically  neutral,  of  even  material,  and  capable  of  being  washed. 
Inks  are  to  be  had  especially  adapted  for  the  tracings  in  bottles  and  cakes.  It 
is  necessary  for  a  good  print  that  the  lines  should  be  of  a  deep  black.  If  not 
sufficiently  opaque,  burnt  Sienna,  burnt  umber,  or  gamboge  added  to  the  ink 
improves  the  prints. 

For  the  manipulation  there  is  needed  plate  glass  and  a  blanket  a  little  larger 
than  the  drawing,  also  a  shallow  tray,  that  the  drawing  can  be  placed  in  flat  for 
washing. 

Lay  down  the  blanket  on  the  drawing-board,  above  that  the  ferro-prussiate 
paper,  next  the  drawing,  and  then  the  glass.  Expose  to  the  sunlight  until  the 
background  is  a  metallic  gray.  The  length  of  exposure  may  be  from  five  min- 
utes up,  depending  on  the  intensity  of  the  sunlight,  the  age  of  the  prepared 
paper,  and  the  transparency  of  the  tracing.  Now  lay  the  ferro-prussiate  paper 
in  the  tray,  cover  with  water,  and  leave  it  for  five  to  ten  minutes ;  wash  thor- 
oughly and  dry. 

The  usual  form  of  printing-frame,  as  purchased  of  dealers,  shown  in  Fig. 
154,  consists  of  a  frame  into  which  fits  a  sheet  of  glass,  preferably  of  plate  glass, 


-  -O.  rnacin 

N  g/ass 


FIG.  154. 


with  a  hinged  backboard,  to  the  inner  side  of  which  a  piece  of  felt  is  glued  in 
the  smaller  sizes,  while  in  the  larger  the  felt  is  separate ;  on  the  back  of  this 
board  are  two  brass  springs  fitting  under  the  metal  catch,  making  a  close  con- 
tact with  the  glass.  As  shown  in  the  small  sectional  drawing,  the  frame  is 
turned  upside  down.  The  glass  is  placed  in  first,  then,  successively,  the  tracing 
with  its  face  to  the  glass,  the  prepared  paper  with  the  prepared  side  to  the 
tracing,  and  the  felt ;  then  the  backboard  is  placed  and  held  in  position  by  the 
springs,  the  frame  is  turned  up,  and  the  directions  given  above  as  to  exposure 
and  washing  are  properly  carried  out. 

When  it  is  necessary  to  make  additions  and  alterations  on  blue  prints,  a 


54  DRAWING  INSTRUMENTS. 

special  ink  can  be  procured;  lines  made  with  this  preparation  on  the  blue 
ground  turn  white.  (See  FREE-HAND  DRAWING.) 

The  helios  process  is  useful  for  copying  not  only  drawings,  but  contracts, 
estimates,  tables,  etc.,  when  they  are  written  on  transparent  paper  or  cloth;  and 
so  is  the  nigrosine  process. 

Bristol  board  is  a  cardboard  with  a  very  fine  surface.  It  can  be  obtained  of 
various  thicknesses  and  of  the  same  dimensions  as  sheet  drawing-papers.  It  is 
adapted  to  water-colours,  pen-and-ink  sketches,  and  fine  line-drawings ;  the 
Patent  Office  requires  sheets  10  by  15  inches,  and  these  can  be  obtained  with 
border  and  wording  of  witness,  inventor,  and  attorney  properly  printed  in. 

Mouth  glue,  for  the  sticking  of  the  edges  6f  drawing-paper  to  the  board,  is 
made  of  glue  and  sugar  or  molasses ;  it  melts  at  the  temperature  of  the  mouth, 
and  is  convenient  for  the  draughtsman. 

Drawing-paper  may  be  fixed  down  on  the  drawing-board  by  thumb-tacks  at 
the  corners,  by  weights,  or  by  gluing  or  pasting  the  edges.  The  first  is 
sufficient  when  no  shading  or  colouring  is  to  be  applied,  and  if  the  sheet  is 
not  to  be  a  very  long  time  on  the  board ;  and  it  has  the  advantage  of  preserv- 
ing the  paper  in  its  natural  state.  For  shaded  or  tinted  drawings,  the  paper 
must  be  damped. 

Damp-stretching  is  done  as  follows :  The  edges  of  the  paper  should  first  be 
cut  straight,  and,  as  near  as  possible,  at  right  angles  to  each  other.  The  sheet 
should  be  enough  larger  than  the  intended  drawing  and  its  margin  to  admit  of 
being  afterward  cut  from  the  board,  leaving  the  pasted  or  glued  border. 

The  paper  must  first  be  placed  on  the  drawing-board  and  thoroughly  and 
equally  damped  with  a  sponge  and  clean  water  on  the  side  on  which  the  draw- 
ing is  to  be  made.  This  done,  lay  a  straight  flat  ruler  on  the  paper,  with  its 
edge  parallel  to,  and  about  half  an  inch  from,  one  of  its  edges.  The  ruler  must 
now  be  held  firm,  while  the  projecting  half  inch  of  paper  is  being  turned  up 
along  its  edge ;  then  a  piece  of  mouth  glue,  having  its  edge  partially  dissolved 
by  holding  it  in  warm  water  for  a  few  seconds,  must  be  passed  once  or  twice 
along  the  turned-up  edge  of  the  paper,  after  which,  by  sliding  the  ruler  over 
the  glued  border,  it  will  be  again  laid  flat,  and,  the  ruler  being  pressed  down 
upon  it,  that  edge  of  the  paper  will  adhere  to  the  board.  If  sufficient  glue  has 
been  applied,  the  ruler  may  be  removed  directly,  and  the  edge  finally  rubbed 
down  by  an  ivory  book-knife  or  by  the  bow  of  a  common  key,  rubbing  it  on  a 
slip  of  paper  placed  on  the  drawing-paper,  so  that  the  surface  of  the  latter  may 
not  be  soiled  ;  this  will  firmly  cement  the  paper  to  the  board.  Another  edge  of 
the  paper  is  then  treated  in  like  manner,  and  the  remaining  edges  in  succession. 
Sometimes  strong  paste  or  mucilage  is  used  instead  of  glue. 

The  wetting  of  the  paper  is  done  for  the  purpose  of  expanding  it ;  and  the 
edges,  being  fixed  to  the  board  in  its  enlarged  state,  act  as  stretchers  upon  the 
paper,  while  it  contracts  in  drying,  which  it  should  be  allowed  to  do  gradually. 
All  creases  or  undulations  by  this  means  disappear  from  the  surface,  and  it 
forms  a  smooth  plane  to  receive  the  drawing. 

After  the  drawing  is  finished,  cut  off  the  paper  inside  the  pasted  edge,  and 
remove  the  edge  by  warm  water  and  the  knife. 


DRAWING  INSTRUMENTS. 


55 


MOUNTING   PAPEE    AN.D    DBAWINGS,    VAENISHING,    ETC. 

When  paper  of  the  requisite  quality  or  dimension  can  not  be  purchased 
already  backed,  it  may  be  mounted  on  muslin.  The  cloth  should  be  well 
stretched  upon  a  smooth  flat  surface,  being  damped  for  that  purpose,  and  its 
edges  glued  down,  as  was  recommended  in  stretching  drawing-paper.  Then 
with  a  brush  spread  strong  paste,  beating  it  in  till  the  grain  of  the  cloth  be  all 
filled  up ;  for  this,  when  dry,  will  prevent  it  from  shrinking  when  subsequently 
removed ;  then,  having  cut  the  edges  of  the  paper  straight,  paste  one  side  of 
every  sheet,  and  lay  them  upon  the  muslin  sheet  by  sheet,  overlapping  each 
other  slightly.  If  the  drawing-paper  is  strong,  it  is  best  to  let  every  sheet  lie 
five  or  six  minutes  after  the  paste  is  put  on  it,  for,  as  the  paste  soaks  in,  the 
paper  will  stretch,  and  may  be  better  spread  smooth  upon  the  cloth  ;  whereas, 
if  it  be  laid  on  before  the  paste*  has  moistened  the  paper,  it  will  stretch  after- 
ward and  rise  in  blisters  when  laid  upon  the  cloth.  The  paper  should  not  be 
cut  off  from  its  extended  position  till  thoroughly  dry,  which  should  not  be 
hastened.  Leave  it  in  a  dry  room  to  do  so  gradually,  if  time  permit ;  if  not,  it 
may  be  exposed  to  the  sun ;  in  the  winter  season  the  help  of  a  fire  may  be  neces- 
sary ;  but  it  should  not  be  placed  too  near  a  scorching  heat. 

In  joining  two  sheets  of  paper  together  by  overlapping,  it  is  necessary,  in 
order  to  make  a  neat  joint,  to  feather-edge  each  sheet ;  this  is  done  by  care- 
fully cutting  with  a  knife  half  way  through  the  paper  near  the  edges  on  the 
sides  which/ are  to  overlap  each  other  and  then  stripping  off  a  feather-edged 
slip  from  each,  which,  if  done  dexterously,  will  produce  a  very  neat  and  effi- 
cient joint. 

For  mounting  and  varnishing  drawings  or  prints,  stretch  a  piece  of  linen 
on  a  frame,  to  which  give  a  coat  of  isinglass  or  common  size  ;  paste  the  back  of 
drawing,  which  leave  to  soak;  and  then  lay  it  on  the  linen.  When  dry,  give  it 
at  least  four  coats  of  well-made  isinglass  size,  allowing  it  to  dry  between  each 
coat.  Take  Canada  balsam  diluted  with  the  best  oil  of  turpentine,  and  with  a 
clean  brush  give  it  a  full  flowing  coat. 

When  drawings  are  not  mounted  on  muslin,  the  edges  may  be  protected 
from  tearing  by  binding  with  gummed  tape,  or  strips  of  paper  which  may  be 
cut  or  purchased. 

Drawings,  as  far  as  possible,  should  be  preserved  flat  in  drawers,  and  this  is 
especially  desirable  for  tracings  which  are  to  be  often  sun-printed. 

The  classification  of  drawings  is  varied.  The  common  method  is  to  devote 
a  separate  drawer  to  the  drawings  of  each  machine,  or  of  each  group  or  class  of 
machine ;  another  is  to  have  drawers  of  various  sizes  and  arrange  the  drawings 
according  to  sizes. 

MANAGEMENT   OF   THE    INSTEUMENTS. 

In  constructing  preparatory  pencil-drawings,  it  is  advisable,  as  a  rule  of 
general  application,  to  make  no  more  lines  upon  the  paper  than  are  necessary 
to  the  completion  of  the  drawing  in  ink ;  and  also  to  make  these  lines  just 
dark  enough  to  be  sufficiently  distinct. 

It  is  often  beneficial  to  ink  in  one  part  of  a  drawing  before  touching  other 
parts  at  all ;  it  prevents  confusion,  makes  the  first  part  easy  of  reference,  and 


56  DRAWING  INSTRUMENTS. 

allows  of  its  being  better  done,  as  the  surface  of  the  paper  inevitably  contracts 
dust  and  becomes  soiled  in  the  course  of  time,  and  therefore  the  sooner  it  is 
done  with  the  better. 

Circles  and  circular  arcs  should,  in  general,  be  inked  in  before  straight  lines, 
as  the  latter  may  be  more  readily  drawn  to  join  the  others  than  can  the  former. 
When  a  number  of  circles  are  to  be  described  from  one  centre,  the  smaller  ones 
should  be  inked  first,  while  the  centre  is  in  better  condition.  When  a  centre 
is  required  to  bear  some  fatigue,  it  should  be  protected  with  a  thickness  of  stout 
card  glued  or  pasted  over  it,  to  receive  the  compass-leg. 

India-rubber  is  the  ordinary  medium  for  cleaning  a  drawing  and  for  cor- 
recting errors  of  the  pencil.  For  slight  work  it  is  quite  suitable ;  that  sub- 
stance, however,  operates  to  destroy  the  surface  of  the  paper  ;  and,  by  repeated 
application,  it  so  ruffles  the  surface  as  to  spoil  it  for  fine  drawing,  especially  if 
ink  shading  or  colouring  is  to  be  applied.  It  is  much  better  to  leave  trivial 
errors  alone,  if  corrections  by  the  pencil  may  be  made  alongside  without  confu- 
sion, and  not  clear  away  superfluous  lines  till  the  inking  is  finished. 

WThen  ink  lines  have  to  be  erased  to  any  considerable  extent,  the  best  way 
is  to  use  an  ink-erasing  rubber.  Single  lines  may  be  erased  by  cutting  a  long 
narrow  slit  in  a  piece  of  thin  cardboard  or  celluloid  and  erasing  through  it. 

For  cleaning  a  drawing,  a  piece  of  bread  two  days  old  is  preferable  to  India- 
rubber,  as  it  cleans  the  surface  well  and  does  not  injure  it.  A  sponge  rubber 
may  also  be  used  for  this  purpose.  For  ordinary  small  erasures  of  ink  lines,  a 
sharp  rounded  pen-blade,  applied  lightly  and  rapidly,  does  well,  and  the  sur- 
face may  be  smoothed  down  by  the  thumb-nail.  In  drawings  intended  to  be 
highly  finished,  particular  pains  should  be  taken  to  avoid  the  necessity  for  cor- 
rections, as  everything  of  this  kind  detracts  from  the  appearance. 

The  best  work  can  only  be  accomplished  by  keeping  the  instruments  in 
good  order;  their  working  parts  should  be  carefully  preserved  from  injury. 
The  scales  must  be  kept  scrupulously  clean ;  the  inking  tools  should  have 
especial  care,  and  the  blades  kept  well  set,  for  which  a  small  oil-stone  is  con- 
venient. 

To  dress  up  the  tips  of  the  blades  of  the  pen  or  of  the  bows,  as  they  usually 
become  worn  unequally,  they  may  be  screwed  up  into  contact  in  the  first  place, 
and  passed  along  the  stone,  turning  upon  the  point  in  a  directly  perpendicular 
plane,  till  they  acquire  an  identical  profile.  Being  next  unscrewed  and  exam- 
ined to  ascertain  the  parts  of  unequal  thickness  round  the  nib,  the  blades  are 
laid  separately  upon  their  backs  on  the  stone,  and  rubbed  down  at  the  points, 
till  they  be  brought  up  to  an  edge  of  uniform  fineness.  It  is  well  to  screw 
them  together  again,  and  to  pass  them  over  the  stone  once  or  twice  more,  to 
bring  up  any  fault ;  to  retouch  them  also  on  the  outer  and  inner  side  of  each 
blade,  to  remove  barbs  or  fraying;  and,  finally,  to  draw  them  across  the  palm 
of  the  hand. 

India  ink,  which  is  commonly  used  for  line-drawing,  should  be  rubbed 
down  in  water  to  the  degree  that  avoids  the  sloppy  aspect  of  light  lining  with- 
out making  the  ink  too  thick  to  run  freely  from  the  pen.  This  medium  degree 
may  be  judged  of  after  a  little  practice  by  the  appearance  of  the  ink  on  the 
palette.  The  best  quality  of  ink  has  a  soft  feel  when  wetted  and  smoothed^ 
being  then  free  from  grit  or  sediment,  and  has  a  musky  smell. 


DRAWING   INSTRUMENTS. 


57 


Slabs  of  many  forms  and  different  materials  are  used  in  grinding  down  the 
ink.  The  one  shown  in  Fig.  155  is  a  square  slab  of  slate,  with  a  countersunk 
circular  recess  and  a  well  in  the  centre  to  hold  the  ink ;  the  cover  is  a  piece  of 
heavy  glass. 

A  quantity  of  ink  may  be  prepared  at  one  time,  but  it  must  be  kept  well 
covered  to  exclude  dust  and  prevent  evaporation.  The  pen  should  be  filled  by 


FIG.  155. 

a  narrow  strip  of  paper,  dipped  in  the  ink  and  inserted  between  the  blades. 

India  ink  and  ink  of  various  colours  can  be  purchased  in  bottles,  and  this 
answers  very  satisfactorily  for  most  work.  Waterproof  ink,  which  admits  of 
being  washed  over,  can  be  bought  in  sticks  or  in  bottles. 

It  is  of  primary  importance  to  keep  the  blades  of  the  inking  tools  free  from 
obstruction ;  this  may  be  readily  accomplished  without  unscrewing  the  pen  by 
passing  a  slip  of  paper  between  the  blades,  or  by  drawing  the  point  firmly  over 
a  piece  of  paper  or  on  the  fleshy  part  of  the  hand. 


EXERCISES  WITH  THE  DRAWING-PEN. 

Before  proceeding  to  the  construction  of  finished  drawings,  skill  should  be 
acquired  in  the  use  of  the  drawing-pen,  supplemented  often  by  the  writing-pen. 
Beginning  with  lines,  outlines  of  figures,  alphabets,  and  the  like,  the  draughts- 
man should  strive  to  acquire  the  habit  of  readily  drawing  clean,  uniform  lines, 
without  abruptness  or  breaks  where  straight  lines  connect  with  curved  ones. 
Draw  straight  lines  of  different  grades  : 


as,  fine 

medium 

coarse 


at  first,  lines  of  indefinite  length,  taking  care  that  they  are  drawn  perfectly 
straight  and  of  uniform  width  or  grade.  Then  draw  lines  of  definite  length 
between  assumed  points,  taking  care  to  terminate  the  lines  exactly  at  these 
points.  Lines  as  above  are / till  lines.  The  grades  depend  on  the  effect  which 
the  draughtsman  wishes  to  give. 

Draw  dotted  lines,  broken  lines,  and  broken  and  dotted  lines,  of  different 
grades : 


58 


DRAWING  INSTRUMENTS. 


Draw  fine  lines  at  uniform  distances  from  each  other  : 


FlO.  156. 


To  give  uniform  appearance,  the  lines  must  be  of  uniform  grade  and  equally 
spaced.  Practice  in  lines  of  this  sort  is  important,  as  they  are  much  used  in 
drawing  to  represent  sections,  shades,  and  conditions,  as  soundings  on  charts, 
density  or  characteristics  of  population,  areas  of  rain,  temperature,  and  the  like. 
Draw  lines  as  in  Fig.  156.  These  lines  are  diagonal  with  the  border-lines,  and 

are  used  to  represent  sections 
of  materials.  In  the  figure, 
lines  differently  inclined  .rep- 
resent different  pieces  of  the 
same  material. 

Instruments  called  section- 
liners  are  to  be  had  for  draw- 
ing these  lines,  but  for  the  usual  needs  of  a  drawing  office  the  triangle  and 
straight-edge,  with  the  drawing-pen,  will  be  sufficient. 

Sections  of  different  materials  may  be  represented  in  different  kinds  of 
lines  (see  page  177). 

To  represent  cylindrical  surfaces  (Fig.  157). 

Draw  a  semi-circumference,  and  mark  on  it  a 
number  of  points,  at  equal  distances  apart,  and 
through  these  points  draw  lines  perpendicular  to 
the  diameter  across  the  surface  to  be  represented. 
It  is  not  absolutely  necessary  that  the  central  space 
should  be  equal  to  the  others;  it  will  be  more 
effective  to  leave  out  two  of  the  lines,  and  make 
it  to  this  extent  wider. 

To  construct  a  mass  of  equal  squares  (Fig. 
158). 

Lay  off  a  right  angle,  and  on  its  sides  mark 
as  many  points  at  equal    distances  apart  as  may 
be  necessary  ;   through    these   points   draw  lines 
parallel  to  the  sides. 
Or,  construct  a  rectangle ;  mark  on  its  sides  as  many  points,  at  equal  dis- 
tances apart,  as  may  be  necessary ;  through  these  points  draw  the  lines. 
To  construct  the  squares  diagonally  to  the  base  (Fig.  159). 


FIG.  157. 


DRAWING  INSTRUMENTS. 


59 


Mark  on  the  sides  of  the  right  angle  as  many  points,  at  distances  apart 
equal  to  the  diagonal  of  the  required  squares,  as  may  be  necessary.  Connect 
these  points  by  lines  as  shown,  and 
through  the  same  points  draw  lines 
at  right  angles  to  the  others. 

To  cover  a  surface  with  equilat- 
eral triangles  (Fig.  160^. 

Construct  an  angle  of  60°,  and 
mark  on  its  sides  points  at  dis- 
tances apart  equal  to  the  side  of 
the  triangle.  Connect  these  points  5 
and  through  these  points  draw  lines 


FIG.  158. 


parallel  to  the  sides  of  the  angle. 

Two  such  triangles  joined  at  the 
base  form  a  lozenge.     Six  triangles  may  be  arranged  as  a  hexagon.     The  whole 
surface  may  be  arranged  in  lozenges  or  hexagons. 

To  cover  a  surface  with  octagons  and  squares  (Fig. 
161). 

Lay  off  the  surface  in  squares  having  sides  equal  to  the 
width  of  the  octagons.  Corner  the  outer  squares  to  form 
octagons  (Fig.  68).  Extend  the  sides  of  these  octagons 
across  the  other  squares,  and  similar  corners  will  be  cut 
off,  and  the  octagons  and  squares  required  will  be  com- 
plete. 

With  the  aid  of  paper  thus 
covered  with  squares,  triangles, 
or  lozenges,  various  geometrical 
designs  may  be  readily  con- 
structed, pleasing  in  their  effect, 
and  affording  good  practice  to 
young  draughtsmen. 

Any  design  can  be  copied  by 
covering  it  and  the  clean  sheet 
with  squares.  Mark  the  positions  of  points  in  the  design  or  the  sides  of  cor- 

C 

F 


FIG.  159. 


FIG.  160. 


FIG.  161. 


60 


DRAWING  INSTRUMENTS. 


responding  squares,  and  draw  the  connecting  lines.     To  enlarge  or  reduce 
the  design,  make  the  squares  or  triangles  proportionately  larger  or  smaller. 


FIG  162. 


FIG.  163. 


FIG.  164. 


In  transferring  designs  and  drawings  from  books  or  plates,  on  which  squares 
can  not  be  drawn,  it  is  very  convenient  to  have  a  square  of  glass,  with  squares 
upon  it,  which  may  be  laid  on  the  drawing,  and  thus  serve  the  same  purpose  as 

if  squares  had  been  drawn.  The 
glass  may  be  readily  prepared  by 
painting  one  of  its  surfaces  with  a 
thin  coat  of  gum,  and  drawing 
squares  upon  it  with  the  drawing- 
pen  ;  if  every  fifth  or  tenth  line  be 
made  fuller  or  in  a  different  colour, 
it  will  be  still  more  convenient  for 


reference. 

Fig.  162  gives  the  front  and  side 
views  of  an  acanthus  leaf,  the  surface  being  covered  with  squares,  and  on  a 
ground  of  like  squares  in  Fig.  163  the  side  view  is  transferred,  but  in  a  re- 
versed position.  This  is  done  by  making  the  position  of  the  outline  and  then 
of  the  interior  lines  with  reference  to  the  squares,  as  designated  by  letters  and 
numerals.  Fig.  164  is  a  transfer  of  both  figures  on  a  reduced  scale. 

Designs  for  woven  goods,  oil  cloths,  ceiling  and  wall  ornamentation,  and  the 
like  are  usually  based  on  geometrical  figures,  and  in  certain  proportions  sym- 
metry and  subordination  of  one  part  to  another  fall  within  the  term 
of  artistic. 

The  following  are  designs  in  which  the  ruling  figure  is  a  trefoil : 
"In  the  equilateral  triangle  (Fig.  165),  each  side  is  divided  by 
a  dot,  and  from  the  centre  of  the  triangle  lines  are  drawn  to  each 
angle,  and  from  the  dot  in  the  middle  of  each  side  to  the  opposite  sides  of  the 
figure.  The  geometrical  plan  of  the  design  is  thus  laid  out,  and  the  figure  is 
easily  filled  in  by  drawing  simple  curves  from  the  centre  of  the  form  to  the 


DRAWING  INSTRUMENTS. 


61 


dot  on  each  side  of  it,  and,  lastly,  filling  in  the  form  of  the  trefoil  a  little  below 
the  point  of  each  corner  of  the  triangle. 

"The  square  (Fig.  166),  which  is  the  next  form,  is  developed  in  much  the 
same  manner.     The  sides  are  bisected,  and  from  a  point  in  the  centre  lines  are 


FIG.  165. 


FIG.  166. 


FIG.  167. 


carried  to  each  angle,  and  to  all  the  dots  on  the  sides.  As  in  the  preceding 
figure,  slight  curves  are  made  on  either  of 'the  side-lines,  and  the  trefoil  is 
added  to  each  angle,  with  the  base  of  the  middle  leaf  touching  the  transverse 
working-lines  between  the  sides. 
It  will  be  seen  that  the  penta- 
gon (Fig.  167)  and  the  hexagon 
(Fig.  168)  also  are  formed  in 
the  same  general  manner,  but 
the  proportion  of  the  top  of 
the  trefoil  varies  from  its  sides. 
"  In  drawing  the  circular 
rosette  (Fig.  169),  the  circum- 
ference should  be  constructed 
on  a  vertical  and  a  horizontal  diameter,  with  two  other  diameters  bisecting 
it  at  equal  angles,  which  divide  it  into  eight  sections,  the  half  diameters,  upon 


FIG.  168. 


FIG.  169. 


FIG.  170. 


all  of  which  curved  lines  and  the  top  of  the  trefoil  are  made.  A  series  of 
arcs  may  be  added  at  the  pleasure  of  the  designer.  In  the  two  pieces  of 
moulding  (Figs.  170  and  171)  the  trefoil  is  inserted  vertically  to  the  sides  in 
one  and  horizontally  in  the  other.  In  the  latter,  a  half  of  the  trefoil  is  added 
upon  the  sides  to  enrich  the  elementary  figure ;  and  the  double  line  and  the 
transverse  lines  which  form  the  squares  are  repeated  for  the  sake  of  symmetry, 
and  as  affording  an  impression  of  agreeable  repose. 

"  It  is  from  such  a  basis  as  this  that  all  these  various  patterns  are  derived, 
and  they  produce  a  result  which  an  inexperienced  eye,  unaccustomed  to  analyze 
designs,  could  scarcely  resolve  into  its  elements." 


62 


DRAWING  INSTRUMENTS. 


Figs.  172-175  are  other  illustrations  of  the  same  principle,  of  varieties  of 
rosettes  constructed  on  a  similar  plan. 


FIG.  171. 


All  of  these  designs  can  be  constructed  mechanically,  but  more  grace  is 
given  to  the  design  by  the  filling  in  with  free  hand,  and  it  is  an  excellent  prac- 


FIG.  172. 


Fio.  173. 


FIG.  174. 


FIG.  175. 


tice  in  the  execution  of  the  more  elaborate  Saracenic  and  Moorish  diaper. 
In  all  of  these  where  there  are  repetitions  of  the  same  figures  it  is  usual  to 
draw  but  one,  and  then  transfer  this,  with  the  finish  in  crayon  or  pencil. 

LETTERING. 

In  Fig.  176  are  examples  of  block  letters  constructed  on  squares,  a  rudimen- 
tary form  of  mechanical  letters,  which  can  be  made  with  the  aid  of  cross-sec- 
tion paper. 

Although  lettering  admits  of  an  endless  variety  of  forms,  the  draughtsman 
should  comprehend  that  there  are  rules  on  which  letters  should  be  constructed 
before  he  undertakes  the  free-hand  method. 

Fig.  177  gives  the  designation  of  various  parts  of  a  letter  to  which  reference 
is  made  in  the  description.  In  the  Roman  letters  the  square  is  taken  as  the 
scale  of  construction.  Fig.  178  gives  the  scale  of  proportionate  width.  W 
takes  the  whole  square,  its  height  and  width  being  equal ;  I  is  one  quarter  as 
wide ;  A,  five  sixths,  etc.  To  obtain  the  width  of  any  letter  according  to  this 
scale,  the  height  may  be  marked  off  on  the  vertical  0  12.  Where  the  horizontal 
line  from  this  point  intersects  the  diagonals  of  the  desired  letter  the  width  is 
measured. 

The  thickness  of  the  body  stroke  of  the  letters  is  about  one  fifth  the  height; 
the  thickness  of  the  body  curve  is  slightly  in  excess  of  this,  and  the  excess  is 
added  outside  the  letter ;  otherwise  in  comparison  with  the  straight  body 
strokes  the  curved  stroke  would  appear  too  thin. 

All  letters  are  of  the  same  height,  except  those  curved  or  pointed  at  the  top  or 


DRAWING  INSTRUMENTS. 


63 


bottom,  such  as  C,  G,  J,  0,  S,  U,  A,  V,  W.    When  the  curved  or  pointed  parts 
are  at  the  top  they  must  extend  a  little  above  the  line  and  when  at  the  bottom 


below  the  line,  otherwise  they  will  look  smaller  than  those  of  square  outline. 
The  lower  feet  of  letters  and  the  feet  of  T  extend  about  one  third  the  height, 
but  the  upper  feet  are  a  trifle  smaller. 

The  intermediate  horizontal  hair  stroke  in  B,  E,  F,  H,  and  E  is  a  little 


N 

D  _l> 

z  u.  x 

UJ  > 


r 


a 


Fia.   177. 


above  the  centre,  P  slightly  below  the  centre,  and  A  about  one  third  of  the, 
height  above  the  lower  line. 

The  hair  strokes  and  outlines  are  first  put  in  ;  the  outline  is  then  filled  with 
a  writing-pen,  toothpick,  or  brush. 


DRAWING  INSTRUMENTS. 


Fio.  179. 


However  well  proportioned  the  letters  may  be,  an  even  effect  is  not  produced 
unless  a  proper  space  is  made  between  them.     In  letters  of  square  form  the 
spacing  is  equal,  but  where  such  combinations  as  LT,  AT,  AA,  and  numerous 
others  occur  the  spacing  must  be  less.     No  general  rule 
can  be  given  for  this,  and  it  must  be  left  to  the  practised 
eye  of  the  draughtsman. 

The  only  rule  necessary  for  the  construction  of  small 
Koman  letters  is  that  for  ascertaining  their  height  as 
compared  with  the  capitals :  Let  a  vertical  line  a  b  (Fig. 
179),  equal  to  the  height  of  the -capital,  be  drawn,  and 
a  line  at  right  angles  at  the  top  of  this  line,  equal  to  one 
half  its  length ;  connect  d  to  ec,  and  lay  off  the  length 
of  the  line  d  e,  equal  to  b  d ;  then  a  e  will  be  the  height 
required.  When  the  learner  has  acquired  some  dexterity 
in  lettering,  the  upper  and  lower  line  alone  will  be  nec- 
essary for  his  guidance ;  he  may  then  attempt  the  ex- 
ecution of  the  curves,  without  the  compass,  by  free 
hand. 

In   Italic  letters  the   proper  angle   for  their  slant 
is  23°  from  the  vertical ;    the  proportions  are  the  same 
as  in  the  Roman  letters 

In  stump  letters  the  capitals  are  the  same  as  Italics.  The  small  letters  differ 
somewhat,  and  are  made  with  one  bold  stroke  of  the  pen,  the  hair  line  gliding 
imperceptibly  into  the  body  stroke. 

Block  letters,  of  which  an  example  has  been  given,  constructed  on  squares, 
are  one  of  the  most  valuable  types,  being  very  distinct  and  readily  drawn  by 
the  drawing-pen.  The  letters  are  of  the  same  proportional  width  as  the  Roman, 
except  that  the  M  is  a  square.  The  height  and  width  of  the  letters  are  varied 
to  suit  their  application.  There  are  lettering 
triangles  (Fig.  180)  made  to  give  the  angles 
with  the  verticals  of  inclined  letters. 

Old  English  and  German  text  and  other  let- 
ters of  a  similar  character  may  be  quickly  and 
neatly  written  by  the  use  of  a  wooden  toothpick 
for  the  body  strokes,  the  hair  lines  and  termina- 
tions being  afterward  put  in  with  a  fine  pen. 

An  old  style  of  writing  that  has  lately  gained 
considerable  popularity  in  this  country  is  round 
writing.  This  resembles  ordinary  writing  in 
that  one  letter  is  joined  to  the  next,  and  each 
word  written  as  a  whole.  There  are  special  pens 
made  for  this  writing,  which  are  very  useful; 
but  in  place  of  these  the  ordinary  stub  pen  can 
be  used.  This  writing  consists  of  a  very  few 
elements,  merely  shaded  semicircles,  straight 
shaded  lines,  and  diagonal  hair  strokes ;  the  pen  is  held  in  such  a  manner  that 
you  are  able  to  draw  a  fine  hair  line  at  an  angle  of  45°  with  both  nibs  of  the 
pen,  and  the  pen  is  held  in  this  position  for  all  letters. 


NXY 


AMV 


W 


FIG.  180. 


DRAWING  INSTRUMENTS. 

HOMAET 


ABCDEFGHIJK 
LMNOPQRSTW 

abcdeWXYZ  fghij 
klmnopqrstuvwxyz 


ITALIC 


LMNOPQRSTUV 

alcdeWXYZ  fghij 
klm  n  op  qrs  t  uvwxyz 

acefg  h  ik  ms  u  wxy  z 
i  n  m  iv  v  vi  yn  w  ix  XLC  DM 

O12 34 5 6 780 


V  r. 


66  DRAWING  INSTRUMENTS. 

ABCDEGHJKLMNOPRSTUWY 
ABCDEGHJKLMNOPRSTUVWY 

ABCDEFGHJKLMNOPRSTUVWr 
ABCDEFGHIJKLMNOPQBSTUVWY 


DRAWING  INSTRUMENTS.  67 

ENGLISH    GOTHIC. 

ABC  DE  FGH  IJ  KLMN  OP 

QRST  UV  WX  YZ 

1234567890 


ITALIC. 


ABC    DE    FGH   IJ   KLMN    OP    QRST 

UV    WX     YZ 

a  be   de  fgh    ij  klmn  op  qrst  uv  fivx  yz 


TUSCAN. 


ABC  DE  FGH  IJ  KLMN  OP  QRST 

UV  WX  YZ 

1234567890 

ABC  DE;  PGH  IJ 
KLMUOPQEST 

UVWX  YZ 

ate  de  fgh.  ij  klmn  op 

qrst  uvwxyz 


• 


DRAWING   INSTRUMENTS. 


ENGLISH    CHURCH    TEXT. 


ic  / 

iC  fl  ' 
abr  fa  fglj  ij  klntn  np  qrst  tin  rax 


g 


MEDIAEVAL. 


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adr  bp  fg|  ij  hlran  09  qrsf  ufi  fDf  g? 


131  K3LWB 

WX  f  25 

lic  d.e    fgh    ij   ttlmn   np   qrst   utr    wx 


COAST  CHART  No.  20 

NEW  YORK  BAY  AND  HARB  OR 

NEW  YORK 


DRAWING  INSTRUMENTS. 


69 


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70  DRAWING  INSTRUMENTS. 

Cxmfrart 

PLAN  FRONT  ELEVATION 
REAR  SIDE  TRANSVERSE 
LONGITUDINAL  SECTION 

The  character  and  size  of  the  letters  should  be  in  accordance  with  the  draw- 
ing on  which  they  are  to  appear.  Thus  in  engineering  or  mechanical  drawing 
nothing  is  so  appropriate  as  the  block  and  Koman  letter. 

In  topographical  or  map  drawing  several  styles  of  various  sizes  are  used ; 
Koman  capitals  of  different  sizes  are  used  in  designating  States,  countries,  and 
cities,  while  State  boundaries  and  towns,  large  villages,  summits,  and  boundaries 
of  countries  are  written  with  an  initial  capital  and  small  Roman  letters.  Large 
bodies  of  water  are  denoted  in  Italic  capitals,  smaller  bodies,  such  as  streams, 
creeks,  small  lakes,  and  ponds,  with  an  initial  Italic  capital  and  stump  letters, 
the  general  direction  of  the  letters  following  the  course  of  the  stream.  Capital 
block  letters  differing  in  size  represent  ranges  of  mountains,  railroads,  stations, 
streets,  and  prominent  objects  on  a  map.  Oblique  capital  block  letters  repre- 
sent railroads  and  canals. 

Old  English  and  German  text  are  the  styles  most  employed  for  the  en- 
grossing of  certificates  and  similar  uses. 

Letters  on  topographical  drawings  are  written  horizontally,  so  as  to  be  read 
from  the  lower  right-hand  corner  of  the  map,  except  such  as  follow  the  course 
of  a  stream  or  a  railroad ;  and  these  can  usually  be  arranged  to  be  read  from 
the  same  direction. 

A  number  of  specimen  titles  are  given,  illustrating  the  use  of  the  different 
styles  of  letters,  but  it  will  be  found  that  the  plainer  the  letters  the  better  the 
effect  produced,  and  for  this  reason  it  is  generally  well  to  omit  fancy  letters. 
No  better  example  of  neat  and  dignified  titles  can  be  found  than  those  on  the 
maps  issued  by  the  United  States  Coast  Survey,  the  chief  beauty  of  which  con- 
sists in  the  admirable  adjustment  of  the  sizes  of  letters,  the  few  styles,  and  the 
almost  perfect  execution. 

The  illustrations  of  letters  and  titles  given  are  taken  from  those  in  general 
use,  but  the  draughtsman  should  make  a  large  collection  of  titles  of  maps  and 
books,  drawings  of  machinery,  advertisements,  and  business  cards,  copying 
carefully  such  as  may  suit  him,  by  which  he  will  gain  ease  of  manipulation 
and  taste  in  selection,  to  give  character  and  finish  to  his  own  drawings. 


DRAWING  INSTRUMENTS. 


71 


PROFILE  AND  CROSS-SECTION  PAPER. 

Paper  printed  in  squares  is  used  by  designers  of  figures  for  calicoes,  silks, 
and  woollens.  For  the  engineer,  there  is  a  class  of  papers  called  profile  and 
cross-section  papers,  sold  in  sheets  or  rolls,  and  of  various  scales.  In  the  first, 
which  is  almost  entirely  applicable  to  lines  of  surveys  of  railroads  and  high- 
ways, the  vertical  scale  is  to  the  horizontal  as  20  to  1.  This  is  the  usual  dis- 
tortion to  make  grades,  with  the  cuts  and  fills  apparent.  The  latter  originally 


UNITED  STATES  UNITS. 
FIG.  181. 


intended,  as  the  name  implies,  for  cross-sections  of  railway  or  canal  cuts, 
bat  now  extensively  employed  by  the  architectural  and  mechanical  designer 
for  the  rough  sketches  of  works  either  executed  or  to  be  executed  ;  by  the 


72 


DRAWING  INSTRUMENTS. 


sanitarian,  for  the  plotting  of  death-rates ;  for  thermometric  and  hygrometric 
readings ;  by  the  broker  and  merchant,  for  the  graphic  representation  of 
the  prices  of  gold,  stocks,  or  articles  of  merchandise,  during  a  term  of  years ; 
by  the  railway  superintendent,  for  the  movement  of  trains ;  and  for  a  multitude 
of  other  uses.  Cross-section  papers  most  generally  applicable  are  in. divisions 
of  tenths ;  but  as  mechanics  are  more  conversant  with  the  two-foot  rule,  of 
which  the  divisions  are  in  eighths,  paper  with  like  divisions  are  more  convenient, 
and  designs  on  it  more  intelligible  to  them. 

Fig.  181  shows  a  graphical  method  of  determining  the  equivalent  values  of 
the  metric  system  of  measurements  in  United  States  units,  or  vice  versa.  The 
vertical  scale  represents  the  metric  units,  and  the  horizontal  the  common  or 
United  States  units. 

Example. — What  is  the  equivalent  value  of  seven  kilometres  in  miles  ?  Read 
upward  on  the  metric  scale  to  7,  then  read  on  that  horizontal  line  to  the  point 
of  intersection  with  the  line  designated  "  Miles  and  Kilometres,"  that  is,  at 
the  point  on  the  United  States  scale  of  units  representing  4*35,  and  you  find 
that  seven  kilometres  are  equal  to  4-35  miles. 

What  is  the  value  of  five  pounds  in  kilogrammes  ?  The  process  is  the  same 
as  the  foregoing,  except  that,  to  change  United  States  units  into  the  metric 
units,  you  first  read  horizontally,  then  upward.  In  this  case  five  pounds  is 
found  equal  to  2*25  kilogrammes.  The  divisions  may  represent  single  units, 
ten  units,  one  hundred  units,  etc.  Of  late  it  has  been  common  here  and  in 
England,  to  write  ft.  Ibs.,  instead  of  Ibs.  ft.,  but  where  French  weight  and 
measures  obtain,  the  rule  is  to  say  kilogrammetres,  that  is  the  weight  before 
the  distance  moved. 

Fig.  182  shows  the  method  of  finding  the  average  of  a  number  of  observa- 
tions, to  determine  the  velocity  of  a  current  of  water.  The  figure  represents 
the  path  of  a  float  in  a  wooden  flume  or  channel,  of  rectangular  section,  from 

WIDTH  OF  FLUME 
1O'  20" 


FIG.  182. 


Francis's  "  Lowell  Hydraulic  Experiments."  The  width  of  the  cut  represents 
the  width  of  the  flume,  each  abscissa  being  one  foot ;  the  ordinates  are  the 
speeds  of  float  in  divisions  of  O'l  foot  per  second  ;  the  small  circles  represent 
the  floats  in  their  observed  path  and  speed ;  and  the  curved  line  shows  the 
average  velocity  in  the  different  threads  of  the  stream,  from  which  the  lines 
of  average  velocities  of  the  entire  width  of  flume  are  deduced. 

The  velocities  were  taken  by  tin  tubes  loaded  so  as  to  float  within  about  an 
inch  of  the  bottom  of  the  flume,  with  the  top  plugged  and  projecting  a  few 
inches  above  the  surface  of  the  water.  The  results  were  checked  by  flows 


DRAWING  INSTRUMENTS.  73 

measured  over  a  weir ;  but  for  all  practical  purposes  the  velocities  as  taken  by 
the  floats  may  be  considered  averages  on  each  thread  of  the  stream.  A  full 
set  of  tubes  were  prepared  adapted  to  the  depths  of  the  water,  and  taken  to 
the  flumes  while  experimenting.  For  general  use  a  cylinder  may  be  adapted 
as  a  float  with  an  open  pipe  sliding  down  it  adjustable  to  the  depth. 

Fig.  183  is  a  diagram  illustrating  graphically  the  difference  between  the 
charge  on  a  ton  of  merchandise  per  mile  on  the  New  York  Central  and  Hud- 
son Eiver  Railroad  and  the  Erie  Canal  for  every  year  between  1857  and  1880. 
The  higher  values  in  every  case  represent  the  railroad  rates  and  the  lower  the 
canal  rates.  The  black  band  shows  the  difference  between  them. 


FIG.  183. 


Fig.  184  is  a  graphic  representation  made  up  from  the  records  of  "  The 
Engineering  and  Mining  Journal,"  exhibiting  the  amount  of  pig  iron  made  in 
the  United  States  per  year  for  thirty-one  years.  In  constructing  the  diagram 


Y4  DRAWING  INSTRUMENTS. 

cross-section   paper  was  used,  but   in   tracing   the  vertical    cross   lines  were 
omitted. 


FIG.  184. 


Fig.  185  is  made  up  from  the  time-table  of  the  New  York,  New  Haven  and 
Hartford  Railroad,  showing  the  movement  of  trains,  two  from  New  York  and 
two  from  New  London,  the  horizontal  lines  being  cut  off  on  a  scale  of  miles  for 
each  station,  and  the  vertical  lines  being  a  scale  of  hours.  If  the  speed  had 
been  uniform,  the  line  showing  the  movement  of  trains  would  have  been 
straight,  but  the  line  represents  the  practical  running  time. 


DRAWING  INSTRUMENTS. 


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76                                               DRAWING  INSTRUMENTS. 

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Fio.  186. 


DRAWING  INSTRUMENTS.  ff 

Fig.  186  is  a  graphic  representation  of  the  mortality  and  general  classes  of 
diseases  as  registered  by  the  New  York  City  Board  of  Health  for  the  months 
of  June,  July,  August,  and  September,  1870 ;  with  the  daily  records  of  tem- 
perature and  humidity ;  to  complete  these  diagrams  there  should  be  one  of  the 
daily  rainfalls.  For  meteorological  purposes  it  is  usual  to  take  at  observatories 
the  commencement,  termination,  and  amount  of  rainfall. 


Above  is  an  ornamental  design  in  straight  lines  on  the  bases  of  lines  parallel 
to  the  sides  of  an  equilateral  triangle. 

In  pages  78,  79  are  given  designs  on  the  bases  of  lin'es  ruled  in  rectangles 
and  lozenges.  The  figure,  page  80,  illustrates  how  colors  may  be  represented 
in  a  design. 

In  pages  81,  82  are  illustrations  in  single  lines  of  the  tracery  of  Gothic 
windows  of  which  the  lines  of  construction  are  left  to  assist  the  draftsman 
in  completion  of  the  design,  which  will  afford  excellent  practice  in  the  intricate 
work  of  making  lines  tangent  to  each  other. 


DRAWING  INSTRUMENTS. 


DRAWING  INSTRUMENTS. 


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80 


DRAWING   INSTRUMENTS. 


DRAWING   INSTRUMENTS. 


81 


82 


DRAWING  INSTRUMENTS. 


PLOTTING. 

PLOTTING  is  the  laying  out  on  paper  in  plan,  or  horizontal  projection,  the 
boundaries  of  portions  of  the  earth's  surface  of  greater  or  less  extent,  from  the 
notes  of  surveys  or  other  records.  When  the  extents  are  large,  embracing  de- 
grees of  latitude  and  longitude,  the  plots  are  designated  as  maps ;  but  if  of 
small  extent,  as  lots,  estates,  and  farms,  they  are  usually  designated  as  plans  or 
plots.  After  completing  the  outlines,  it  is  usual  to  fill  up  the  plot  with  the  charac- 
teristic features,  geographical,  geological,  agricultural,  industrial,  and  domestic, 
which  are  expressed  conventionally,  as  will  be  shown  under  the  head  of  "  Topo- 
graphical Drawing." 

Scales. — The  choice  of  the  scale  for  the  plot  depends  on  the  purpose  for 
which  the  drawing  is  intended.  It  should  be  large  enough  to  express  all  de- 
sirable details  which  it  is  intended  to  illustrate,  and  the  place  it  is  to  oc- 
cupy. 

Plans  of  house-lots  and  small  plots  of  farm  surveys  are  usually  so  many 
feet  to  the  inch ;  maps  of  surveys  of  States,  so  many  miles  to  the  inch ;  and 
maps  of  railway  surveys,  so  many  feet  to  the  inch  or  so  many  inches  to  the 
mile.  Formerly  the  lines  of  farms  were  measured  by  the  four-rod  chain.  Two 
to  three  chains  to  the  inch  was  then  a  very  common  scale. 

On  the  United  States  Coast  Survey  all  the  scales  are  expressed  fractionally 
and  decimally.  The  original  surveys  are  generally  on  a  scale  of  one  to  ten  or 
twenty  thousand,  but  in  some  the  scale  is  larger  or  smaller.  The  public  sur- 
veys embrace  three  general  classes:  1.  Small  harbour  charts.  2.  Charts  of 
bays,  sounds,  etc.  3.  General  coast  charts. 

The  scales  of  the  first  class  vary  from  go^6  to  60^00,  according  to  the  nature 
of  the  harbour  and  the  objects  to  be  represented. 

The  scale  of  the  second  class  is  usually  fixed  at  -g-^^n,-.  Preliminary  charts, 
are,  however,  issued  of  various  scales,  from  -g-jj-J-j-o  to  2  0  0*0  0  0 . 

Of  the-  third  class  the  scale  is  fixed  at  4  0  fa  0  6  for  the  general  chart  of  the 
coast  from  Gay  Head  to  Cape  Henlopen,  although  considerations  of  the  prox- 
imity and  importance  of  points  on  the  coast  may  change  the  scales  of  charts  of 
other  portions  of  our  extended  coast. 

On  all  plots  of  large  surveys,  it  is  very  desirable  that  the  scales  adopted 
should  bear  a  definite  numerical  proportion  to  the  linear  measurement  of  the 
ground  to  be  mapped,  and  that  this  proportion  should  be  expressed  fractionally 
on  the  plan,  even  if  the  scale  be  drawn  or  expressed  some  other  way,  as  miles  to 
the  inch.  The  decimal  system  has  the  most  to  recommend  it,  and  is  generally 
adopted  in  government  surveys. 

For  railroad  surveys,  the  New  York  general  railroad  law  directs  the  scale  of 

83 


84  PLOTTING. 

map  which  is  to  be  filed  in  the  State  Engineer's  office  to  be  500  feet  to  ^  foot, 


For  canal  maps,  a  scale  of  two  chains  to  the  inch,  i  g*8  4  ,  is  employed.  In 
England  plans  and  sections  for  projected  lines  of  inland  communication,  or 
generally  for  public  works  requiring  the  sanction  of  the  legislature,  are  re- 
quired by  a  standing  order  to  be  drawn  to  scales  not  less  than  four  inches  to 
the  mile,  1  :  15,840,  for  the  plan,  and  100  feet  to  the  inch,  1  :  1,200,  for  the 
profiles. 

In  the  United  States  engineer  service  the  following  scales  are  prescribed  : 

General  plans  of  buildings    ......  10  feet  to  the  inch,  1  :  120 

Maps  of  ground  with  horizontal  curves  1  foot  apart  .  50  "                "      1  :  600 

Topographical  maps,  1£  mile  square    ....     1  mile  to  2  feet,  1  :  2,640 

Topographical  maps,  3  miles  square    ....     1  "         1  foot,  1  :  5,280 

Topographical  maps,  between  4  and  8  miles                .     1  "         6  in.,     1  :  10,560 

Topographical  maps,  9  miles  square    .        .        .        .1  "         4     "     1  :  15,840 

Maps  not  exceeding  24  miles  square    .....     1  "         2     "      1  :  31.680 

Maps  comprising  50  miles  square        .        .        .        .1  "         1  inch,  1  :  63,360 

Maps  comprising  100  miles  square       .        .        .        .1  "         £     "      1  :  126,720 

Surveys  of  roads  and  canals  ......  50  feet  to  1     "      1  :  600 


Many  government  maps  are  made  on  a  scale  of  -^oVo-  or 

It  is  always  desirable  that  the  scale  should  be  drawn  on  maps  and  plans,  as 
they  are  often  reduced  by  photography. 

In  cities  and  towns,  plots  of  lots  and  squares  are  generally  rectangular,  and 
they  can  be  readily  plotted  on  any  convenient  scale. 

Fig.  187  is  a  plan  of  the  usual  New  York  city  lot,  25  X  100,  on  a  scale  of  20 
feet  to  the  inch,  or  -g-^. 

Fig.  188  is  a  city  square  containing  thirty-two  of  these  lots,  on  a  scale  of 
100  feet  to  the  inch,  or  12100.  The  most  accurate  way  is  to  plot  the  large  rec- 
tangle 400x200  feet,  and  then  subdivide  it. 

Fig.  189  is  a  plan  of  the  city  squares,  with  the  inclosing  streets,  on  a  scale 
200  feet  to  the  inch,  or  -y^Vff- 

But  many  lots  and  most  estates  are  not  rectangular,  and  these,  the  angles 
being  recorded,  must  be  plotted  by  the  aid  of  a  protractor. 

If  the  survey  has  been  made  by  triangles,  the  principal  triangles  are  first 
laid  down  in  pencil  by  the  intersection  of  their  sides,  the  length  being  taken 
from  the  scale  and  described  with  compasses.  In  general,  when  the  surveys 
have  been  conducted  without  instruments,  the  positions  of  the  points  on  paper 
are  determined  by  the  intersection  and  construction  of  the  same  lines  as  has 
been  done  in  the  field. 

Surveys  are  mostly  conducted  by  measuring  the  inclination  of  lines  to  a 
meridian  or  to  each  other  by  the  compass  or  by  the  transit.  In  the  survey  of 
farms,  where  great  accuracy  is  not  required,  the  compass  is  mostly  used. 
The  compass  gives  the  direction  of  a  line  with  reference  to  the  magnetic 
meridian.  The  true  meridian  can  be  obtained  from  the  observations  of  the 
polar  star  or  from  the  magnetic  meridian  corrected  from  the  records  of  the 
variations  by  the  geodetic  surveys  of  the  United  States  at  the  place  and 
time. 

The  plane  table  is  very  convenient  for  filling  in  the  details  of  a  survey  when 


PLOTTING. 


85 


the  principal  points  have  been  determined  by  triangulation,  and  its  records  are 
readily  transferred  to  the  drawing. 

At  the  left  of  Fig.  190  are  the  notes  of  a  compass  survey,  from  which  the 
figure  is  plotted  by  drawing  a  meridian  through  each  station  and  laying  off  the 


FIG.  187. 


angle  of  deflection.  In  small  drawings  it  is  more  convenient,  as  shown  in  Fig. 
191,  to  plot  all  the  bearings  on  a  single  meridian  and  then  transfer  them  to  the 
places  where  they  are  wanted  by  any  instrument  for  drawing  parallel  lines,  or 
to  lay  off  on  a  single  meridian  as  many  bearings  as  convenient  and  then  trans- 
fer the  meridian  for  another  plot. 

If,  as  in  Fig.  192,  the  plot  fails  to  close— that  is,  if  the  termination  a  of  the 
last  line  does  not  join  the  commencement  of  the  first  line  at  1,  either  the  sur- 
vey or  the  plotting  is  incorrect.  If  the  latter  be  correct,  the  error  of  the  sur- 
vey must  be  balanced,  or  distributed  through  the  lines  and  angles  of  the  plot 
(Fig.  192).  Connect  1  with  a,  and  draw  lines  parallel  to  1  a  through  2,  3,  4, 


86 


PLOTTING. 


5,  of  the  plot.     Draw  an  indefinite  line,  I  a  (Fig.  193),  and  on  this,  with  any 
convenient  scale,  lay  off  consecutively  the  lines  of  the  survey,  1-2,  2-3,  3-4, 


J 


FIG.  189. 


5?  5_#.     Erect  perpendiculars  at  the  extremities  of  the  lines,  2,  3,  4,  5,  and 
a.     On  the  perpendicular  a  b,  lay  off  1  a  from  the  plot  and  connect  b  1.     The 


3.23 


la 

-(5)- 
3.55 


cd 

-(4)- 
222 


-(8)- 
1.29 


-(2)- 
2.70 


-OH 


FIG.  190. 


intersections  of  the  perpendiculars  by  this  line  will  determine  how  much  each 
of  the  points  of  the  plot  is  to  be  moved  on  the  parallels  to  1  a  to  distribute 
the  error.  The  dotted  lines  on  the  figure  show  the  corrected  outline.  If  the 
amount  by  which  the  plot  fails  to  close  is  large,  the  plot  should  be  resurveyed. 


PLOTTING. 


By  the  aid  of  the  Traverse   Table  a  plot   of  a  survey  may  be  balanced. 
The  Traverse  Table  (see  appendix)  is  a  table  of  differences  of  latitudes  and 


FIG.  192. 

departures,  the  difference  of  latitude  between  two  stations  being  the  difference 
north  and  south  between  them ;  the  difference  of  departure,  the  difference  east 
and  west. 

Thus,  N  S  (Fig.  194)  being  the  meridian,  N 

and  A  B  the  course,  A  C  is  the  difference  of 
latitude,  and  A  D  the  departure. 

The  differences  vary  according  to  the  length 
of  A  B,  and  the  angle  it  makes  with  the  merid- 
ian. 

Taking  the  field  notes  of  the  following  sur- 


FIG.  193. 


vey,  we  make  a  table  as  follows  of  the  stations,  bearings,  and  distances,  leaving 
columns  for  latitudes  and  departures : 


STATION. 

Bearing. 

Distance. 

LATITUDES. 

DEPARTURES. 

N. 

S. 

E. 

w. 

1  

N.  52°  B. 
S.  29f  °  E. 
S.  31|°  W. 
N.  61°  W. 

1,063 
410 
769 
713 

655 
346 

356 
654 

&38 
203 

405 
624 

2  

3  

4  

Find  by  the  Traverse  Table  the  number  of  degrees  of  the  angle  or  bearing 
on  the  left-hand  side  of  the  page  if  less  than  45°,  and  on  the  right-hand  side  if 
more.  The  numbers  on  the  same  line  running  across  the  page  are  the  latitudes 
and  departures  for  that  angle  and  for  the  distances  which  may  represent  any 


88 


PLOTTING. 


unit,  as  feet,  chains,  links,  metres,  etc.  The  traverse  table  gives  the  latitudes 
or  departures  for  a  single  unit ;  10,  100,  1,000,  or  any  other  decimal  quantity 
may  be  obtained  by  moving  the  decimal  point  one,  two,  three,  or  more  places 
to  the  right. 

Thus  let  us  take  station  1  in  previous  survey,  in  which  the  latitude  and  de- 
partures of  a  course  having  a  distance  of  1,063  feet  and  a  bearing  of  52°,  and 
then  take  out  the  latitude  and  departure  for  1,  6,  3,  and  place  them  as  below  : 


Distance. 
1,000 
60 


1,063 


Latitudes. 
616-0° 
36-94 
1-847 

654-787 


Departures. 

788-0 
47-28 
2-364 

837-644 


If  the  survey  has  been  accurately  performed,  the  northings  and  southings 
of  the  latitude  and  the  eastings  and  westings  of  the  departures  will  balance  and 
the  survey  will  close.  In  the  preceding  survey  they  do  not  balance ;  it  there- 
fore becomes  necessary  to  balance  it.  This  operation  consists  in  correcting  the 
latitudes  and  departures  of  the  courses  so  that  the  sums  of  the  northings  and 
southings  of  the  latitudes  and  the  eastings  and  westings  of  the  departures  shall 
be  equal.  This  is  done  by  distributing  the  difference  of  their  sums  among  the 
courses  in  proportion  to  their  length. 

The  difference  between  the  northings  and  southings  of  latitude,  which  is  9, 
is  divided  by  the  total  length,  2,955,  which  gives  the  amount  per  foot  to  be 
added  to  the  lesser  column  and  subtracted  from  the  greater  column  in  propor- 
tion to  the  length  of  the  courses  to  cause  the  northings  and  southings  to 
balance.  The  departures  are  balanced  in  a  similar  manner. 

The  following  table  gives  the  original  latitudes  and  departures  and  the  cor- 
rected ones : 


i^.  09  to  M  Stations. 

Bearings. 

Dis- 
tances. 

LATITUDES. 

DEPARTURES. 

CORRECTED 
LATITUDES. 

CORRECTED 
DEPARTURES. 

N. 

S. 

E. 

W. 

N. 

S. 

E. 

vv. 

N.  52°  B. 
S.  29J°  E. 
S.  31f  °  W. 
N.  61°  W. 

1,063 
410 
769 
713 

655 
"346 

"356 
654 

838 
203 

658 

"355 
651 

834 

201 

408 
627 

405 
624 

"348 

2,955 

1,001 

1,010 

1,041 

1,029 

1,006 

1,006 

1,035 

1,035 

After  the  latitudes  and  departures  have  been  corrected,  it  is  necessary  to 
make  a  drawing  of  the  plot.  How  this  is  done  will  be  readily  seen  by  the  accom- 
panying illustration  of  this  survey  (Fig.  195).  This  figure  also  illustrates  a 
very  convenient  and  accurate  method  of  determining  the  area  of  the  survey 
mathematically.  By  means  of  the  latitudes  and  departures  the  area  of  the 
full  parallelogram  is  taken,  and  the  triangles  on  the  four  sides  of  the  plot  are 
deducted  from  it,  leaving  489,245  square  feet  as  the  area  of  the  figure. 

The  use  of  the  compass  is  now  confined  to  the  surveying  of  land  areas  of 
large  extent  and  little  value,  or  as  a  means  of  checking  the  bearings  as  taken  by 
the  theodolite  or  transit.  Forcing  should  not  be  attempted  with  the  latter  in- 
struments. If  the  survey  does  not  balance  almost  exactly,  it  should  be  resur- 


PLOTTING. 


89 


veyed ;  otherwise  it  could  not  be  used  in  a  court  of  law  except  as  approximately 
correct.     The  steel  tape  divided  decimally  is  almost  exclusively  used  in  accu- 


rate work. 

The  system  of  plotting  by  traverse  is  the  same  for  the  survey  by  transit  as 


Pep.  834 


*>    Dep.  20l' 


Dep.  627' 


Fio.  195. 


by  compass,  except  as  the  angles  are  taken  to  minutes  and  seconds.  The  latitudes 
and  departures  are  to  be  taken  by  logarithmic  sines  and  cosines ;  if  these  are 
not  obtainable,  the  table  for  natural  sines  and  cosines  in  the  appendix  will  give 
minutes,  and  seconds  can  be  obtained  by  interpolation  of  differences. 

Fig.  196  is  the  plot  of  a  survey  by  transit.     Any  side  of  the  plot  may  be 
assumed  as  a  meridian.     The  bearings  are  always  taken  to  the  right  of  it.. 
After  it  has  been  plotted  it  can  be  checked  by  the  traverse.     Meridians  de- 
scribed through  each  of  the  angles  will  show  the  meridional  angle, 
tudes  and  departures  may  be  obtained  as  follows : 


The  lati- 


Angle. 

Nat.  sine. 

Distance. 

Departure. 

41°  40' 

0-66480 

X 

350 

=        233 

Angle. 

Nat.  cosine. 

Distance. 

Latitude. 

41°  40' 

0-74703 

X 

350 

=        261 

In  the  third  line  of  the  third  column  the  angle,  instead  of  120°,  is  set 
down  at  30°,  because,  when  an  angle  is  in  excess  of  90°,  180°,  or  270°,  the  ex- 
cess is  the  angle  of  which  sine  and  cosine  are  to  be  found. 

There  can  be  no  division  of  distance  into  latitude  and  departure  when  the 
course  is  either  at  right  angles  to  or  parallel  with  the  meridian.  It  is  then 


90 


PLOTTING. 


FIG.  196. 


either  all  departure  or  all  latitude.  In  the  tables  the  latitudes  are  identical  for 
angles  and  for  their  supplements,  and  so  are  the  departures.  Reference  to  Fig. 
75  will  illustrate  this,  calling  the  sine  latitude  and  the  cosine  departure. 


Course. 

Azimuth. 

Angle. 

Dis- 
tance. 

Latitudes. 

Depar- 
tures. 

Triangles  deducted. 

Rectangles  deducted. 

0-1 

41°  40' 

41°  40' 

350 

261 

23R 

261  x  233  _   30106 

1  2 

85    30 

85     30 

280 

22 

279 

2 
22  x  279  _     g  069 

233x22   =    5,126 

2-3 

120    00 

30    00 

320 

160 

277 

2 
277  x  160  _   00160 

3-4 

154    29 

64    29 

300 

271 

129 

2 
129  x  271  _    17479 

129  x  160  =  20,640 

4-5 

228    00 

48    00 

700 

469 

520 

2 

5-6 

288    30 

18    30 

420 

133 

3Q8 

2 

133  x  398       Og  16? 

6-0 

360    00 

00    00 

484 

484 

000 

2 

221,521 

25,766 

Circumscribed  rectangle,  918  x  900  =  826,200 
Deduct  221,521  +  25,766  =  247,287 


578,913  square  feet. 


PLOTTING. 


91 


When  it  is  difficult  to  measure  along  the  boundaries  of  an  estate,  the  sur- 
veys should  be  made  along  more  convenient  and  accessible  lines,  which  may  be 
by  a  closed  plot,  as  in  Fig.  196,  or  by  base  lines  from  which  the  intersections  of 
boundaries  are  established  by  offsets  carefully  determined  by  measures  and 
angles  from  points  of  the  survey. 


Fro.  197. 

The  first  work  of  the  draughtsman  is  to  complete  the  plot  along  the  lines 
of  the  survey;  work  up  the  estimate  of  contents  by  traverse,  and  check  by 
measures  on  -the  plot. 

Fig.  197  is  an  illustration. 

Find  the  cosine  49°  40'  distance  215  =  140-1  sine  163-1 
"      55°  25'       "         152=    86-3    "     125-1 


226-4 
Line  525—226-4  =  298-6 

=  301-0  the  line  of  plot. 


38 


=  •12708  =  Bine  of  7'  18' 


90°  -7°  18'  =  82°  42'     90°  -  49°  40'  =  40°  20'. 

By  similar  construction  34°  30'  and  78°  30'  are  calculated. 

360°-  (82°  42'  +  40°  20'  +  34°  30'  +  78°  30')  =  123°  58'. 

The  line  of  the  plot,  301,  and  the  adjacent  angle,  123°  58',  are  thus  ob- 
tained, and  all  lines  and  angles  of  the  plot  are  established  in  the  same  way. 
The  plot  is  then  transferred  to  a  clean  sheet,  with  lines  and  angles  as  calcu- 
lated, but  without  any  lines  of  survey. 

When  the  lines  of  a  plot  are  irregular,  as  in  Fig.  198,  divide  the  plot  into 
equal  spaces,  and  draw  parallel  lines  across  the  figure  through  the  points  of 
division,  add  together  the  two  extreme  lines,  divide  the  sum  by  two,  and  to 
this  dividend  add  the  lengths  of  the  other  lines  and  multiply  their  sum  by  the 


92 


PLOTTING. 


equal  vertical  distance  between  the  parallel 
lines,  which  will  give  very  closely  the  entire 
area. 

Having  completed  the  plot,  that  is,  the 
main  lines  of  the  survey,  the  filling  of  other 
points  may  in  general  be  done  on  paper  in 
the  same  way  as  they  have  been  established  in  the  field.  Intersections  of  the 
main  lines  by  roads,  streams,  fences,  and  the  like  are  measured  off ;  other  points 


FIG.  198. 


FIG.  199. 

not  intersecting,  are  usually  fixed  by  triangles  or  by  offsets,  or  lines  run  on 
purpose  by  angles  from  the  main  lines. 

In  case  of  unimportant  lines,  as  the  crooked 
brook,  for  instance  (Fig.  199),  offsets  are  taken  to 
the  most  prominent  angles,  as  a  a  a,  and  the  inter- 
mediate bends  are  sketched  by  eye  into  the  field- 
book,  and  similarly  on  the  plan. 

The  most  rapid  way  of  plotting  the  offsets  is  by 
the  use  of  a  plotting  and  offset  scale  (Fig.  200),  the 
one  being  fixed  parallel  to  the  line  A  B  from  which 
the  offsets  are  to  be  laid  off,  at  such  a  distance  from 
it,  that  the  zero-line  on  the  movable  or  offset  scale 
coincides  with  it,  while  the  zero  of  its  own  scale  is 
on  a  line  perpendicular  to  the  position  of  the  station 
A  from  which  the  distances  were  measured.  In  the 
field-book  all  the  offsets  are  referred  to  the  point  of 
beginning  on  any  one  straight  line.  Move  the  offset 
scale  to  the  first  distance  by  the  scale  at  which  an 
offset  has  been  taken,  and  mark  off  the  length  of  the 
offset  on  its  corresponding  side  of  the  line ;  establish 
thus  repeated  points,  and  join  the  points  by  lines  as 
they  are  on  the  ground.  It  may  not  always  be  pos- 
sible to  obtain  the  same  scales  as  those  of  the  plan ; 
but  they  may  be  made  of  thick  drawing-paper  or 
pasteboard.  For  extensive  plotting,  as  in  govern- 
ment surveys,  the  offset  scale  may  be  made  to  slide 
in  a  groove  upon  the  plotting  scale. 

In  protracting  the  triangles  of  an  extended  trigo- 
nometrical survey  in  which  the  sides  have  been  cal- 
culated or  measured,  it  is  better  to  lay  down  the 
triangles  from  the  length  of  their  sides ;  for  ordina- 
ry surveys,  the  triangulation  is  most  expeditiously 
plotted  by  the  means  of  a  protractor. 


PLOTTING. 


93 


The  outlines  of  the  survey  having  been  balanced  and  plotted  in,  with  the 
subsidiary  points,  as  established  by  offsets  and  by  triangles,  the  filling  in  of  the 
interior  detail,  with  the  natural  features  of  the  ground,  from  the  skeleton  or 
suggestions  in  the  field-book  or  other  records,  is  done  according  to  conventional 
signs,  to  be  shown  under  "  Topographical  Drawing." 

The  public  lands  of  the  United  States  are  surveyed,  mapped,  and  divided 
into  nearly  square  tracts,  according  to  the  following  system : 

Ranges. — Standard  lines  must  first  be  determined  from  which  to  measure. 
Accordingly,  in  each  land-district  some  meridian  line  is  run  due  north  and 
south ;  this  is  called  the  principal  meridian.  From  some  point  of  the  principal 
meridian  is  also  run  a  line  due  east  and  west,  called  the  base  line. 

Other  lines  are  then  run  in  the  same  direction  as  the  principal  meridian,  at 
distances  of  six  miles,  measured  on  the  base  line,  on  each  side  of  it.  The  strip 
between  the  principal  meridian  and  the  first  line,  thus  run  east  of  it,  is  known 
as  Range  1  East,  the  second  strip  as  Range  2  East,  etc.  And  so  on  the  west. 
This  division  is  shown  in  Fig.  201. 


FIG.  201. 


j 

? 

Tp.2 

North 

tn 

. 

. 

S 

S3 

a 

w 

i? 

a 

^ 

*§ 

1 

1 

Tp.l 

* 

K* 

* 

*• 

North 

W 

BASE 

LINK 

_j 

. 

Tp.l 

I 

! 

i 

* 

South 

MERIDIAN 

PRINCIPAL 

Tp.2 
South 

FIG.  202. 


Townships. — In  like  manner,  lines  are  run  north  and  south  of  the  base 
line  at  intervals  of  six  miles.  These  lines  cut  at  right  angles  those  which 
separate  the  ranges,  and  with  them  form  squares  six  miles  on  each  side,  called 
toiunslrips.  Each  township  contains  thirty-six  square  miles. 

The  township  nearest  the  base  line  on  the  north  is  known  as  Township  1 
North,  of  the  particular  range  it  is  in ;  the  next  farther  north  is  Township  2 
North,  of  that  range,  and  so  on.  In  like  manner,  going  south  from  the  base 
line,  we  have  in  succession  Township  1  South,  Township  2  South,  etc. 
(Fig.  202). 

Sections.— Each  township  is  divided  into  thirty-six  squares,  called  sections, 
each  one  mile  long  and  one  mile  wide,  and  therefore  having  an  area  of  one 
square  mile.  The  sections  of  a  township  are  numbered  1,  2,  3,  etc.,  up  to  36, 


PLOTTING. 


beginning  at  the  northeast,  and  running  alternately  from  right  to  left  and  from 
left  to  right,  as  shown  in  Fig.  203. 

A  section  may  be  subdivided  into  half-sections,  quarter-sections,  eighths,  and 
sixteenths,  designated  as  in  the  example  that  follows : 

Let  F  G  (Fig.  204)  be  Section  3  of  Township  2  North,  in  Eange  1  West ; 
then — 


6 

5 

4 

3 

2 

1 

7 

8 

9 

10 

11 

12 

18 

17 

16 

15 

14 

13 

19 

20 

21 

22 

23 

24 

30 

29 

28 

27 

26 

25 

31 

32 

33 

34 

35 

36 

1  mile. 


D 


E 


FIG.  203. 


FIG.  204. 


A  is  N.  (north)  £  of  Section  3,  Township  2  North,  Range  1  West. 

B  is  S.  W.  (southwest)  £  of  Section  3,  Township  2  North,  Eange  1  West. 

C  is  W.  (west)  £  of  S.  E.  (southeast)  £  of  Section  3,  Township  2  North, 
Range  1  West. 

D  is  N.  E.  i  of  S.  E.  i  of  Section  3,  Township  2  North,  Range  1  West. 

E  is  S.  E.  i  of  S.  E.  i  of  Section  3,  Township  2  North,  Range  1  West. 

Correction  Lines. — If  the  meridian  lines  were  parallel  to  each  other,  the 
townships  and  sections  would  be  exact  squares.  But  as  these  lines  gradually 
converge  toward  the  north,  meeting  at  the  pole,  the  townships  deviate  some- 
what from  squares,  being  narrower  on  the  north  than  on  the  south ;  and  the 
northern  sections  of  a  township  are  a  little  smaller  than  the  southern  ones.  In 
order  that  the  townships  of  a  range  may  not  thus  keep  getting  smaller  and 
smaller  as  we  go  toward  the  north,  a  new  base  line,  called  a  correction  line,  is 
taken  at  intervals,  differing  in  length  in  different  land-districts,  and  new  north- 
and-south  lines  are  run  at  distances  of  six  miles  measured  on  the  correction 
lines. 

The  system  of  survey  described  above  is  not  used  in  Texas,  the  public  lands 
there  being  State  property. 


TOPOGRAPHICAL    DRAWING. 

TOPOGRAPHICAL  DRAWING  is  the  delineation  of  the  surface  of  a  locality, 
with  the  natural  and  artificial  objects,  as  houses,  roads,  rivers,  hills,  etc.,  upon 
it  in  their  relative  dimensions  and  positions,  giving,  as  it  were,  a  miniature 
copy  of  the  farm,  field,  district,  etc.,  as  it  would  be  seen  by  the  eye  moving 
over  it.  Many  of  the  objects  thus  to  be  represented  can  be  defined  by  regular 
and  mathematical  lines,  but  many  other  objects,  from  their  irregularity  of  out- 
line, it  would  be  very  difficult  thus  to  distinguish;  nor  are  the  particular 
irregularities  necessary  for  the  expression.  Certain  conventional  signs  have 
therefore  been  adopted  in  general  use  among  draughtsmen,  some  of  which 
resemble,  in  some  degree,  the  objects  for  which  they  stand,  while  others  are 
purely  conventional.  These  signs  may  be  expressed  by  lines,  by  tints,  or  by 
botb. 

Figs.  205  and  206  represent  meadow  or  grass  land,  the  short  lines  being 


FIG.  205. 


FlO.  206. 


FIG.  208. 


supposed  to  represent  tufts  of  grass ;  the  bases  of  the  tufts  should  always  be 
parallel  to  the  base  of  the  drawing,  whatever  may  be  the  shape  of  the  in- 
closure. 

Figs.  207,  208,  209,  and  210  give  various  methods  of  representing  trees. 
Figs.  207  and  208  represent  in  plan  a  forest  and  an  orchard  respectively.     The 


FIG  209. 


FIG.  210. 


FIG.  211. 


method  of  Figs.  209  and  210,  showing  the  same  in  elevation,  while  it  is  not 
consonant  with  the  projection  of  the  plan,  to  many  is  more  expressive  and  in- 
telligible. 

95 


96 


TOPOGRAPHICAL  DRAWING. 


Fig.  211  represents  cultivated  land.  The  lines  are  supposed  to  represent 
plough-furrows,  and  adjacent  fields  should  be  distinguished  from  each  other 
by  different  inclinations  of  lines. 

Figs.  212  and  213  represent  marsh  or  bog  land.  Fig.  212  is  the  more  ordi- 
nary mode  of  representing  fresh- water  bog ;  Fig.  213,  salt  marsh. 


FIG.  213. 


FIG.  214. 


Fig.  214  represents  a  river,  with  mud  and  sand  banks.  Sand  is  designated 
by  tine  dots,  made  with  the  point  of  the  pen ;  mud  by  a  series  of  short  parallel 
lines.  Gravel  is  represented  by  coarser  dots,  and  stones  by  irregular  angular 
forms. 

Water  is  almost  invariably  represented,  except  in  connection  with  bogs,  by 
drawing  a  line  parallel  to  the  shore,  following  its  windings  and  indentations 
closely,  then  another  parallel  a  little  lighter  and  a  little  more  distant,  a  third 
still  more  so,  and  so  on.  Brooks,  and  even  rivers  when  the  scale  is  small,  are 
represented  by  one  or  two  lines.  Fig.  215  gives  a  plan  and  sectional  view  of 
water,  in  which  the  white  curves  represent  the  character  and  direction  of  the 


FIG.  215. 


Fio.  216. 


flow  of  streams,  retarded  at  bottom  and  sides,  and  more  rapid  near  the  surface 
and  at  centre.     The  direction  of  the  current  may  also  be  shown  by  arrows. 
Fig.  216  represents  a  bold  shore  bounded  by  cliffs. 


TOPOGRAPHICAL  DRAWING. 


97 


Fig.  217  represents  a  turnpike. .  If  the  toll-bar  and  marks  for  a  gate  be 
omitted,  it  is  a  common  highway.  Fig.  218  represents  a  road  as  sunk  or  cut 
through  a  hill ;  Fig.  219,  one  raised  upon  an  embankment.  Fig.  220  is  a  rail- 


Via.  217. 


FIG.  218. 


FIG.  219. 


FIG.  220. 


road,  often  represented  without  the  cross-ties  by  two  heavy  parallel  lines,  some- 
times by  but  one. 

Fig.  221  represents  a  bridge  with  a  single  pier ;  Fig.  222,  a  swing  or  draw 
bridge ;  Fig.  223,  a  suspension  bridge ;  and  Fig.  224,  a  ford.    Fig.  225  is  a  lock 


FIG.  221. 


FIG.  222. 


FIG.  223. 


FIG.  224. 


of  a  canal.     Canals  may  be  represented  like  roads,  except  that  in  the  latter  the 
side  from  the  light  is  the  shaded  line  ;  in  the  former,  the  side  to  the  light.     Or 

by  

Conventional  signs  for  the  more  important  ob- 
jects that  are  likely  to  need  representation  on  a 
map  are : 

Saw-mill, 


FIG.  225. 


Signal  of  Survey,       A 

Telegraph,  $MP 

Court-house,  III 

Post-office,  jjj% 

Tavern,  ^J^ 

Blacksmith's  shop,  ^L 

Guide-board,  •£ 

Quarry,  ^ 

Grist-mill,  0 


Wind-mill, 

Steam-mill, 

Furnace, 

Woolen-factory, 

Cotton-factory, 

Dwellings, 

Churches, 

Grave-yards, 


•HE  CURRENT 


Anchorage  for  ships, 
Anchorage  for  coasters,    J^, 

Rocks  always  covered,      ^ 
8 


Buoys,        f  \ 
Wrecks,        • 
Harbors, 


Light-house, 

Signal-house, 

Channel-marks, 


98 


TOPOGRAPHICAL  DRAWING. 


The  localities  of  mines  may  be  represented  by  the  signs  of  the  planets,  which 
were  anciently  associated  with  the  various  metals,  and  a  black  circle  is  used 
for  coal,  thus,  $  Mercury,  ?  Copper,  ^  Lead,  D  Silver,  0  Gold,  $  Iron,  21 
Tin,  •  Coal. 

The  Representation  of  Hills. — The  two  methods  in  general  use  for  rep- 
resenting with  pen  or  pencil  the  slopes  of  ground  are  known  as  the  vertical 
and  the  horizontal.  In  the  former  (Fig.  226),  the  strokes  of  the  pen  follow  the 
course  that  water  would  take  in  running  down  these  slopes.  In  the  second 
(Fig.  227),  they  represent  horizontal  lines  traced  round  them,  such  as  would  be 
shown  on  the  ground  by  water  rising  progressively  by  stages,  1,  2,  3,  4,  5,  6,  up 
the  hill.  The  last  is  the  more  correct  representation  of  the  general  character 
and  features  of  the  ground,  and,  when  vertical  levels  or  contours  have  been 
traced  by  level  at  equal  vertical  distances  over  the  surface  of  the  ground,  they 
should  be  so  represented ;  or  when,  by  any  lines  of  levels,  these  contours  can 
be  traced  on  the  plans  with  accuracy,  the  horizontal  system  should  >be  adopted : 
but  where,  as  in  most  plans,  the  hills  are  but  sketched  in  by  the  eye,  the  verti- 
cal system  should  be  adopted ;  it  affords  but  proximate  data  to  judge  of  the 
slope,  whereas,  by  the  contour  system,  the  slope  may  be  measured  exactly.  It 
is  a  good  maxim  in  topographical  drawing  not  to  represent  as  accurate  any- 
thing which  has  not  been  rigorously  established  by  surveys.  On  this  account, 
for  general  plans,  when  the  surface  of  the  ground  has  not  been  levelled,  nor  is 
required  to  be  determined  with  mathematical  precision,  use  the  vertical  system 
of  representing  slopes. 

On  drawing  hills  on  the  vertical  system,  it  is  very  common  to  draw  contour- 
lines  in  pencil  as  guides  for  the  vertical  strokes.  If  the  horizontal  lines  be 
traced  at  fixed  vertical  intervals,  and  vertical  strokes  be  drawn  between  them 
in  the  line  of  quickest  descent,  they  supply  a  sufficiently  accurate  representa- 
tion of  the  face  of  the  country  for  ordinary  purposes.  It  is  usual  to  make  the 
vertical  strokes  heavier  the  steeper  the  inclination,  and  systems  have  been  pro- 
posed and  used  by  which  the  inclination  is  defined  by  the  comparative  thick- 
ness of  the  line  and  of  the  intervening  spaces. 


FIG.  226. 


Fio.  227. 


TOPOGRAPHICAL   DRAWING. 


99 


In  describing  ground  with  the  pen,  the  light  is  generally  supposed  to 
descend  in  vertical  rays,  and  the  illumination  received  by  each  slope  is  di- 
minished in  proportion  to  its  divergence  from  the  plane  of  the  horizon.  Thus, 
in  Fig.  228,  it  will  be  seen  that  a  horizontal  surface  receives  an'  equal  portion 
of  light  with  the  inclined  surface 
resting  upon  it,  and,  as  the  inclined 
surface  is  of  greater  extent,  it  will  be 
darker  than  the  horizontal  in  propor- 
tion to  the  inclination  and  conse- 
quent increase  of  the  surface,  and  on 
this  principle  varied  forms  of  ground 
are  represented  by  proportioning  the  FIG.  228. 

thickness  of  stroke  to  the  steepness  of  the  slope. 

In  the  German  system  proposed  by  Major  Lehmann  for  representing  the 
slopes  of  ground  by  a  scale  of  shade,  the  slope,  at  an  angle  of  45°,  is  indicated 
by  black,  the  horizontal  plane  by  white. 

A  modification  of  Lehmann's  method,  proposed  by  the  United  States  Coast 


FIG.   229. 

Survey,  has  the  advantage  of  discriminating  between  slopes  of  greater  inclina- 
tion than  45°.    The  table  gives  the  proportions  of  black  and  white  for  different 
inclinations,  and  the  construction  may  easily  be  un- 
derstood from  Fig.  229. 

Contour  -  Lines.  —  Conceive  a  hill  to  be  com- 
pletely covered  with  water.  Then  suppose  the  water 
to  be  drawn  down,  say  five  feet  at  a  time.  Each 
line  of  contact  of  the  hill  and  the  water  will  be  a 
contour-line,  or  a  line  every  point  of  which  is  at  the 
same  height  or  level  above  a  fixed  horizontal  plane, 
called  the  datum-plane.  For  a  small  hill,  stake  out 
the  ground  in  squares  of  say  fifty  feet  to  the  side, 
and  take  levels  at  each  point  of  these  squares,  and  as 

many  intermediates  as  the  change  of  slope  makes  necessary.  To  draw  the  map, 
lay  off  these  squares  to  a  scale,  and  mark  the  elevation  of  each  point  and  the 
intermediates  in  pencil.  Then  by  the  eye  draw  in  the  contours  at  such  vertical 
distances  apart  as  the  requirements  of  the  map  call  for.  For  a  large  survey, 
say  of  a  mountain,  such  a  method  is  impracticable.  In  this  case,  the  surveyor 
fixes  a  number  of  points  at  the  same  level,  the  points  being  absolutely  estab- 
lished by  the  transit  or  compass,  so  that  they  can  be  plotted  accurately.  Con- 
nect all  points  on  each  level,  and  fill  in  the  distances  between  by  the  eye,  on  the 
supposition  that  the  slope  is  uniform  between  these  lines.  The  lines  absolutely 


Slope. 

Propor 
Black. 

tion  of 
White. 

2 

1°  or  2f  ° 

1 

10 

5 

or  6 

2 

9 

10 

or  11 

3 

8 

15 

or  18 

4 

7 

25 

or  26 

5 

6 

35 

6 

5 

45 

7 

4 

60 

8 

3 

75 

9 

2 

100 


TOPOGRAPHICAL  DRAWING. 


established  and  those  merely  sketched  in  must  not  be  confounded,  and  should 
be  distinguished  apart  either  by  colour,  by  size  of  lines,  or  by  dotting.  The 
contour-lines  denoting  every  five,  ten,  etc.,  feet  above  the  datum  or  plane  of 
reference  may  be  numbered  with  such  height.  This  is  an  effective  way  of  rep- 


resenting hills,  but  is  only  to  be  recommended  when  lines  have  been  traced 
and  it  becomes  a  record  of  facts.     Fig.  230  represents,  on  double  the  scale,  the 


FIG.  230. 


half  of  the  hill  (Fig.  227),  with  one  half  completed  by  drawing  the  interme- 
diate contour-lines. 

The  objection  to  the  drawing  of  hills  by  any  system  is  that  the  depths  of 
shade  representing  different  slopes  conflict  with  the  lights  and  shades  of  the 


TOPOGRAPHICAL  DRAWING. 


101 


drawing,  and  are  therefore  confusing.  The  plan  adopted  by  Von  Eggloff stein 
in  his  maps  was  to  form  a  model  by  cutting  out  of  sheet-wax  under  the  needle 
of  a  sewing  machine,  on  the  lines  of  contours,  and  then  properly  superimposing 
them  on  one  another.  A  mould  was  then  taken  from  them  in  plaster.  A 


FIG.  231. 


model  from  the  mould,  also  in  plaster,  was  then  taken.  This  was  watered  while 
fresh  by  a  vertical  rain  from  a  water-pot,  which  broke  down  the  vertical  edge 
of  the  contours,  and  gave  natural  lines  of  watershed.  This  model  was  then 
photographed  under  an  inclined  light,  and  gave  an  admirable  projection. 

Fig.  231  is  a  contoured  map  of  Greenwood  Cemetery  and  vicinity,  Brook- 
lyn, N.  Y. 

Fig.  232  is  a  map  of  the  harbour  and  city  of  New  Haven,  reduced  from  the 
charts  of  the  United  States  Coast  Survey. 

Plate  VI  is  a  map  of  a  farming  country.  These  two  maps  illustrate^the 
practical  applications  of  topographical  conventionalities. 


r-, 

•/A  : 


102 


TOPOGRAPHICAL   DRAWING. 


FIG.  232. 


TOPOGRAPHICAL  DRAWING. 


103 


Railway  Surveys  are  usually  plotted  by  tangents.    The  curves  are  then  put 
in,  and  the  topographical  features'  for  the  width  necessary.     The  curves  are 
designated  by  degrees,  as  a  curve  of  1°,  2°,  3°,  etc., 
according  as  the  angle  subtended  at  the  centre  by  a 
100-feet  chord  is  1°,  2°,  3°,  etc. 

Knowing  the  tangent  points,  it  is  easy  to  plot  in 
the  curve,  as  •  the  centre  of  the  curve  must  be  the 
intersection  of  the  perpendiculars  to  the  tangents 
at  these  points ;  or,  with  one  point  of  tangency, 
erect  a  perpendicular  at  this  point,  and  lay  off  the 
radius  on  it  to  get  the  centre  of  the  curve. 

When  the  curves  are  larger  than  can  be  de- 
scribed by  the  dividers  or  beam  compasses,  they  can 
be  plotted  as  shown  in  geometrical  problems,  or 

points  of  a  curve  may  be  obtained  by  calculation  of  their  ordinates,  and  the 
curves  drawn  from  point  to  point  by  variable  curves.  Knowing  the  central 
ordinate  of  the  curve  between  two  points,  the  central  ordinate  of  one  half  that 
curve  will  be  approximately  one  quarter  of  the  first ;  but  the  greater  the  num- 
ber of  degrees  in  the  arc,  the  less  near  to  the  truth  is  the  rule. 

^,  3l.43PeAEattperSlilt  ^,  Level 


Degree. 

Radii,  ft. 

Central 
ordinate. 

1° 

5729-65 

0-218 

2 

2864-93 

0-436 

3 

1910-08 

0-655 

4 

1432-69 

0-873 

5 

1146-28 

1-091 

6 

955-37 

1-309 

7 

819-02 

1-528 

8 

716-78 

1-746 

9 

637-27 

1-965 

10 

573-69 

2-183 

FIG.  234. 


Fig.  234  represents  a  plot  of  a  railway  line ;  in  this  plot  the  curve  is  repre- 
sented as  a  straight  line,  the  radius  of  curvature  being  written  in.  This  method 
is  sometimes  adopted  when  it  is  desirable  to  confine  the  plot  within  a  limited 
space  upon  the  sheet,  and  it  is  convenient  plotted  thus  directly  beneath  the 
profile  or  longitudinal  section  (Fig.  233). 

In  plotting  the  section,  a  horizontal  or  base  line  is  drawn,  on  which  are  laid 
off  the  stations  or  distances  at  which  levels  have  been  taken ;  at  these  points 
perpendiculars,  or  ordinates,  are  erected  ;  upon  them  are  marked  the  heights  of 
the  ground  above  the  base ;  and  the  marks  are  joined  by  straight  lines. 

Where  borings  or  soundings  have  been  made,  and  it  is  necessary  to  indicate 
the  character  and  define  the  limit  of  the  material,  the  rock  may  be  shown  by 
diagonal  hatchuring,  streams  as  in  Figs.  222  and  223,  and  other  substances  by 
a  combination  of  lines  and'dots,  resembling  as  nearly  as  possible  the  material 


104 


TOPOGRAPHICAL  DRAWING. 


which  it  is  to  represent,  and  the  name  inserted.  If  there  is  a  bog  or  mud  in 
which  soundings  have  been  made,  the  position  and  depth  of  soundings  should 
be  given ;  but  when  work  is  to  be  done  by  contract,  characteristics,  unless  well 
established,  should  not  be  definitely  marked. 

Since  it  would  be  in  general  impossible  to  express  the  variations  of  the  sur- 
face of  the  ground  in  the  same  scale  as  that  adopted  for  the  plan,  it  is  cus- 
tomary to  make  the  vertical  scale  larger  than  the  horizontal,  usually  in  the 
proportion  of  10  or  20  to  1.  Thus,  if  the  horizontal  scale  of  the  plan  be  400 


feet  to  the  inch,  the  vertical  scale  would  be  40  or  20  feet  to  the  inch.  For  the 
purpose  of  facilitating  the  plotting  of  profiles,  profile-paper  can  be  obtained 
from  stationers,  on  which  are  printed  horizontal  and  vertical  lines. 

In  the  plotting  of  sections  across  the  line  which  are  extended  but  little 
beyond  the  line  of  the  cut  or  embankment,  equal  vertical  and  horizontal  scales 
are  adopted ;  these  plots  are  mostly  to  determine  the  position  of  the  slope,  or 
to  assist  in  calculating  the  excavation.  When  cross  sections  are  extended  to 
show  the  grade  of  cross-road,  or  changes  of  level  at  considerable  distance  from 
the  line  of  rail,  the  same  scales,  vertical  and  horizontal,  are  adopted  as  in  the 
longitudinal  section  or  profile. 

In  Fig.  233  the  upper  or  heavy  line  represents  the  line  of  the  rail,  the 
grades  being  written  above ;  this  is  the  more  usual  way,  but  sometimes,  as  in 
Fig.  235,  the  profile  and  plan  are  combined ;  that  is,  the  heights  and  depths 
above  and  below  the  grade  line  of  the  road  are  transferred  to  the  plan,  and  re- 


Fio.  235. 


ferred  to  the  line  in  plan,  which  becomes  thus  a  representation  both  in  plan 
and  elevation. 

Cross  sections,  for  grades  of  cross-roads,  etc.,  are  usually  plotted  beneath  or 
above  the  profile  or  across  the  line  when  plan  and  profile  are  combined. 

Besides  the  complete  plans,  as  above,  giving  the  details  of  the  location,  land 
plans  are  required,  showing  the  position  and  direction  of  all  lines  of  fences  and 
boundaries  of  estates,  with  but  very  few  of  the  topographical  features.  The 
centre  line  of  the  road  is  represented  in  bold  line,  and  at  each  side,  often  in 
red,  are  represented  the  boundaries  required  for  the  purposes  of  way.  In  gen- 


TOPOGRAPHICAL  DRAWING. 


105 


eral,  a  width  of  100  feet  is  the  amount  of  land  set  off,  lines  parallel  to  the  cen- 
tral line  being  at  a  distance  of  50  feet  on  each  side ;  but  when,  owing  to  the 
depth  of  the  cut  or  embankment,  the  slopes  run  out  beyond  this  limit,  the  ex- 
tent is  determined  by  plotting  a  cross  section  and  transferring  the  distances 
thus  found  to  the  plan,  and  inclosing  all  such  points  somewhat  within  the 
limits  as  set  off  for  railway  purposes.  These  plans  are  generally  filed  in  the 
register's  office  for  the  county  through  which  the  line  passes. 

Hydrometrical  or  Marine  Surveys. — In  plotting  hydrometrical  or  marine 
surveys,  the  depths  of  soundings  are  seldom  expressed  by  sections,  but  by 
figures  written  on  the  plan,  expressing  the  sounding  or  depth  below  a  datum 


FIG.  236. 


line,  generally  that  of  high  water,  the  low-water  line  being  usually  represented 
by  a  single  continued  line.  The  soundings  are  expressed  in  fathoms  or  in  feet. 
Fig.  236  is  a  map  of  Cape  Cod  Bay  plotted  by  this  method.  The  depths  are 
expressed  in  feet,  and  the  dotted  lines  are  contour-lines  or  lines  of  equal  depths. 


106 


TOPOGRAPHICAL  DRAWING. 


An  effective  way  of  making  a  marine  chart  is  to  express  the  different  depths 
by  lines  varying  in  direction,  distance  apart,  width,  etc.  Fig.  237  is  a  chart  of 
the  Isle  of  Wight  and  the  surrounding  water,  with  the  depths  expressed  as 
shown  at  the  bottom  of  the  cut.  Sections  are  often  used  for  rivers,  especially 
rivers  like  those  of  the  West,  that  have  a  very  changeable  bottom.  By  plot- 
ting sections,  taken  at  different  times,  over  one  another,  distinguishing 


Depth  under  5  Fathoms.         5  to  10  Fathoms. 


10  to  20  Fathoms. 


Over  20  Fathoms. 


5  Miles. 


FIG.  237. 


them  apart  by  a  difference  in  colour  and  variety  of  line,  the  changes  that  take 
place  in  the  bottom  of  the  river,  and  the  erosion  of  the  banks,  are  boldly  shown. 

In  a  geological  profile  the  different  rocks  or  formations  are  sometimes  dis- 
tinguished by  colours,  explained  by  marginal  notes  and  squares,  but  more  often 
by  marks,  dots,  or  cross-hatchings. 

The  geological  and  statistical  features  of  a  country  may  be  expressed  simi- 
larly and  graphically  in  lines,  as  in  Fig.  238,  a  preliminary  survey  of  Kentucky, 
illustrating  the  principal  geological  features;  and  in  Fig.  239,  in  a  broader 
form,  giving  a  larger  extent  of  country,  including  the  portion  of  the  United 
States  east  of  the  Eocky  Mountains  and  the  southeasterly  portion  of  Canada. 

These  maps  give  the  larger  geological  divisions,  and  are  suited  for  books, 
but  are  not  as  effective  nor  comprehensive  of  the  smaller  subdivisions,  of  which 
Plate  X  is  an  example  of  a  portion  of  a  map  of  the  State  of  New  Jersey. 


TOPOGRAPHICAL   DRAWING. 


107 


'4\ 


108 


TOPOGRAPHICAL   DRAWING. 


FIG.  239. 


STRATIFIED  ROCKS 


1  .  1.1,  L-l 


Sections  of  horizontal  and  inclined  strata. 
Fio.  240. 


TOPOGRAPHICAL  DRAWING. 


109 


Psycho 


Quater- 
nary. 


Tapir,  Peccary.  Bi 
Equus.     Megatheri 


,  Llama. 


Equus  Beds. 

/fjjaiu,  Tapiriu,  Elefhat. 

Pliohippus  Beds. 

P/iohipput,  Mastodon,  B<a,  ete. 

Miohippus  Beds. 


,  alherium,  TAinohyui. 

Oreodon  Beds. 

Edentates,  Hyanodon,  Hyracodon. 

Brontotherium  Beds. 

Afesokippus,  Menodwt,  Kbitlierium. 

Diplacodon  Beds. 

hpMppus,  Amynodon. 

Dinoceras  Beds. 

Tinixeras,  Uintatherium,  Limnohyut, 
OroUppju,  Helaletft,  Colonocerat. 

Coryphodon  Beds. 

Eohipput,  Monkeys,  Carnivores,  Ungulates,  Tillodonts,  Rodents, 
Serpents. 

Lignite  Series. 

HtfdrcuauruSj  Drypkaaurvs. 


Pteranodon  Beds. 

Birds  with  Teeth,  Ifesptn 


Birds  with  Teeth,  llesperornit 
Pterodactyls,  Plesiosaure. 


is,  Ichthyornia. 


Dakota  Group. 


Atlantosaurus  Beds. 

Dinosaurs,  Apatosaurus,  Allot 


a,  Nanosa 


Connecticut  River  Beds. 

First  Mammals  (Marsupials),  (Dromatherw 
Dinosaur  Foot-prints,  Amphitaurun. 
Crocodiles  (Belodon). 


Permian. 


Coal-Measures. 

First  Reptiles  («). 

Sub-carboniferous. 

First  known  Amphibians  (Labyrinthodonts). 


Corniferous. 


Schoharie  Grit. 
First  known  Fishes. 


Upper  Silurian. 
Lower  Silurian. 


Primordial. 


Huronian. 


Laurentian. 


No  Vertebrates  known. 


Section  of  the  earth's  crust  to  illustrate  vertebrate  life  in  America. 
Fio.  241. 


Fig.  241  is  an  ideal  section  from  Le  Conte,  in  which  all  the  most  important 
American  strata  occurring  in  different  places  are  brought  together  and  ar- 
ranged in  the  order  of  time. 

In  the  diagram  the  different  rock-systems  are  placed  one  on  top  of  the 
other,  and  the  vertical  black  spaces  represent  by  their  breadth  the  relative 
dominance  of  different  classes  at  different  times. 

The  subdivisions  of  these  again  into  periods  and  epochs  are  founded  on 
more  local  unconformities,  and  especially  on  less  important  changes  in  the 
species. 


HO  TOPOGRAPHICAL  DRAWING. 

Transferring. — It  is  usual,  in  plotting  from  a  field-book,  to  make  first  a 
rough  draft,  and  then  a  finished  copy  on  another  sheet. 

In  the  copy,  only  the  established  points  and  lines  for  the  outlines  are  to  be 
transferred.  Many  lines  of  construction,  balances  of  surveys,  and  trial  lines  of 
the  rough  draft  are  to  be  omitted,  and  it  is  well  to  sketch  in  roughly  the  natural 
features  on  the  rough  draft  for  aid  in  the  completion  of  the  finished  copy. 

The  most  common  way  of  transferring,  for  a  fair  copy,  is  by  superposition 
of  the  plan  above  the  sheet  intended  for  the  copy,  and  pricking  through  every 
intersection  of  lines  on  the  plan  and  all  points  necessary  to  preserve.  The 
clean  paper  should  be  laid  and  fastened  smoothly  on  the  drawing-board ;  the 
rough  draft  should  be  laid  on  smoothly,  and  retained  in  its  position  by  weights, 
glue,  or  tacks.  The  needle  must  be  held  perpendicular  to  the  surface  of  the 
plan,  and  pressed  through  both  sheets ;  begin  at  one  side  and  work  with  sys- 
tem, so  as  to  prick  through  each  point  but  once,  nor  omit  any ;  make  the 
important  points  a  trifle  the  larger.  For  the  irregular  curves,  as  of  rivers,  make 
frequent  points,  but  very  small  ones.  On  removing  the  plan,  select  the  impor- 
tant points,  those  defining  leading  lines ;  draw  in  these,  and  the  other  points 
will  be  easily  recognised  from  their  relative  position  to  these  lines.  When  any 
point  has  not  been  pricked  through,  its  place  may  be  determined  by  taking  any 
two  established  points  adjacent  to  the  one  required,  and  with  radii  equal  to 
their  distance  on  the  plan  from  the  point  required,  describing  arcs  on  the  copy 
on  the  same  side  of  both  points ;  the  arcs  will  intersect  at  the  point  de&ired. 
In  this  way,  as  in  a  trigonometrical  survey,  having  established  the  two  extremes 
of  a  base,  a  whole  plan  may  be  copied.  In  extensive  drawings  it  is  very  com- 
mon to  prick  off  but  a  few  of  the  salient  points,  and  fill  in  by  intersections,  as 
above,  or  by  copying  detached  portions  on  tracing-paper  and  transferring  them 
to  the  copy  ;  the  position  of  each  sketch  being  determined  by  the  points  pricked 
off,  the  transfer  is  made  by  pricking  through,  as  above,  or  by  transfer-paper 
placed  between  the  tracing  and  the  copy. 

Plans  may  be  copied,  on  a  reduced  or  enlarged  scale,  by  means  of  the  pan- 
tagraph  or  by  the  method  of  squares. 

Map  Projections. — For  a  farm  or  other  small  survey,  the  surface  of  the  earth 
is  conceived  to  be  flat,  and  the  map  as  a  horizontal  projection  of  the  plane  sur- 
face on  a  reduced  scale.  But  for  large  maps,  as  of  countries,  States,  rivers,  or 
the  like,  where  the  meridians  and  parallels  of  latitude  are  represented,  such  a 
system  would  be  erroneous.  Tfre  surface  of  the  earth  being  a  sphere,  it  is  in- 
capable of  development  on  a  plane,  so  that  it  becomes  necessary  to  make  the 
best  approximation  possible  in  form,  relation,  and  proportional  area  of  the  por- 
tions to  be  represented  on  a  map  or  chart.  There  are  many  different  kinds  of 
projection,  all  more  or  less  imperfect. 

In  general,  map  projections  may  be  divided  into  two  classes :  perspective 
and  developments.  The  most  useful  of  the  perspective  projections  are  the 
orthographic,  the  stereographic,  and  the  globular  or  equidistant. 

Orthographic  Projection  (Figs.  242  and  243). — In  this  projection  the  eye  is 
supposed  to  be  at  an  infinite  distance,  and  the  plane  of  projection  perpendicu- 
lar to  the  line  of  sight.  Let  the  circle  A  L  A'  M  (Fig.  242)  represent  a  hemi- 
sphere ;  draw  the  diameters  A  A'  and  L  M  at  right  angles ;  divide  the  arc  A  L 
and  A  M  into  nine  parts,  making  the  parallels  thus  10°  apart ;  and  through 


TOPOGRAPHICAL   DRAWING. 


Ill 


these  divisions  draw  lines  across  the  sphere  parallel  to  A  A' ;  mark  off  consecu- 
tively on  a  strip  of  paper  the  points  where  the  parallels  intersect  the  central 
meridian  L  M,  and  apply  and  mark  off  these  points  along  the  equatorial  diam- 
eter A  A'.  Draw  meridians  with  centres  on  the  extension  of  the  line  of  the 
equator  intersecting  the  points  marked  off  on  this  line,  and  meeting  at  the  poles. 
Stenographic  Projection  (Figs.  244  and  245). — As  in  the  last  example,  draw 
a  circle  with  a  central  and  an  equatorial  diameter  (Fig.  244) ;  on  the  central 
meridian  describe  a  circle  0  E  D  F,  with  a  diameter  equal  to  the  radius  of  the 


FiQ.  243. 

larger  circle ;  through  the  centre  of  this  smaller  circle  draw  a  diameter  E  F,  and 
divide  the  arcs  E  0  and  0  F  into  nine  equal  parts ;  and  from  the  pole  D, 
through  each  of  these  points,  draw  lines  intersecting  the  equator.  These  lines 
divide  the  equator  into  eighteen  parts,  each  containing  10°  of  longitude,  and 
through  these  points  and  the  poles  meridians  are  described.  Mark  off  the  equa- 
torial divisions  on  a  slip  of  paper  and  transfer  them  to  the  central  meridian ; 


FIG.  244. 


FIG.  245. 


divide  each  quarter  of  the  circumference  of  the  sphere  into  nine  equal  parts, 
though  these  points  and  the  divisions  on  the  central  meridian  describe  arcs. 
Globular  or  Equidistant  Projection  (Fig.  246).— A  good  practical  projec- 


112 


TOPOGRAPHICAL  DRAWING. 


tion  can  be  made  by  drawing  a  circle  with  a  diameter  for  the  equator  and 
another  at  right  angles  for  the  central  meridian,  dividing  each  quadrant  and 
each  radius  into  nine  equal  parts.  Meridians,  with  centres  on  the  line  of  the 
equatorial  diameter,  can  now  be  drawn  passing  through  the  equatorial  divisions, 
and  the  poles  and  parallels  of  latitude  on  the  line  of  the  central  meridian 
through  the  divisions  of  this  line  and  those  of  the  quadrant. 

The  foregoing  perspective  projections  in  their  application  to  astronomy  and 
geography  are  usually  confined  to  the  representation  of  the  hemisphere,  and 
but  rarely  to  smaller  surfaces ;  they  are  therefore  of  but  little  practical  use  to 

the  engineer  or  surveyor,  and  for  land  and 
sea  charts  on  a  large  scale  and  of  limited 
extent  they  are  not  well  adapted.  To  ren- 
der developments  possible  a  cylindric  or 
conic  surface  is  substituted  in  place  of  the 
ordinary  plane  of  projection,  which  surface 
is  afterward  developed  in  a  plane.  The 
eye  is  supposed  either  at  the  centre  of  the 
sphere  or  else  its  position  is  arbitrary.  This 
conception  gives  rise  to  two  kinds  of  de- 
veloped projections,  one  kind  employing 
a  cylinder,  tangent  generally  at  the  equa- 
tor, the  other  employing  a  cone,  tangent 
no.  246.  generally  at  the  middle  parallel. 

The  more  useful   of   these  projections 
are  Mercator's,  the  conic,  Bonne's,  and  the  polyconic. 

Mercator's  Projection  (Fig.  247). — This  is  especially  valuable  to  the  navi- 


/6O  /go  /60  140  120  /OO  <3O  6(? 


IOO  /2O 


TOPOGRAPHICAL  DRAWING. 


113 


gator,  as  by  it  he  can  lay  off  his  course  on  a  straight  line.  In  this  projection 
the  surface  of  the  sphere  is  developed  on  a  tangent  cylinder.  Conceive  the 
.outlines  of  the  continents  to  be  drawn  on  this,  and  afterward  the  surface  to  be 
unrolled  and  laid  flat ;  the  result  is  a  chart  on  Mercator's  projection. 

Let  P  Q  P'  R  (Fig.  248)  be  the  projection  of  a  sphere,  P  P'  and  R  Q  its 
diameters,  and  U  Y  X  Z  a  portion  of  the  tangent ,  cylinder  in  the  axis  of  which 

.  X 
U 


60      120 

FIG.  248. 


180 


240 


oOO 


00 


00 


70 
300 


is  contained  the  axis  of  the  sphere.  Divide  the  quadrant  P  Q  into  10°  parts,  a 
line  drawn  from  C  through  these  points,  intersecting  the  tangent  X  Z,  will  be 
the  point  for  the  parallel  of  that  degree.  Make  the  equator  of  the  projection 
3'14  times  the  diameter  of  the  cylinder,  and  divide  it  into  twenty-four  equal 
parts ;  these  points  will  be  15°  apart,  or  hour  distances.  Verticals  are  drawn 
through  these  points,  giving  us  parallels  of  latitude. 

Conic  Projection. — Instead  of  on  the  surface  of  a 
sphere,  the  map  is  projected  on  the  surface  of  a  cone. 
The  projection  may  be  developed  either  on  a  tangent 
cone  or  an  intersecting  cone.  The  developed  arc  of  the 
middle  latitude  is  employed  for  the  graduation  of  longi- 
tudes. Fig.  249  gives  an  illustration  of  the  development 
on  a  tangent  cone  in  which  P  0  B  is  the  sphere  and 
A  M  is  the  distance  from  the  apex  of  the  cone  to  the 
middle  parallel  and  point  of  contact ;  A  M  will  be  the 
radius  for  the  central  parallel  and  A  the  point  from  which  all  parallels  are 
described.  Fig.  250  shows  the  cone  developed  on  a  plane  surface.  The 
length  of  a  degree  on  a  meridian  of  the  earth  is  69*41  miles  at  the  poles  and 
68-70  at  the  equator. 

Bonne's  Projection. — In  this  projection  a  central  meridian  and  a  central 
parallel  are  employed,  the  latter  being  the  development  of  the  circle  of  contact 
of  the  tangent  cone.     The  other  parallels  are  concentric  arcs,  as  in  the  simple 
9 


Fio.  249. 


114 


TOPOGRAPHICAL  DRAWING. 


conic  projection  drawn  through  the  graduation  of  the  central  meridian.  Each 
parallel,  however,  is  divided  in  accordance  with  the  varying  lengths  of  a  degree 
of  longitude  in  the  different  latitudes  (see  table)  and  an  arc  passed  through 


FIG.  250. 


these  points.  The  map  is  slightly  distorted  at  the  corners  on  account  of  the 
parallels,  as  projected,  being  concentric  arcs.  The  great  advantage  of  Bonne's 
projection  is  that  true  proportions  of  areas  are  preserved.  This  method  is  al- 


most universally  employed  for  the  detailed  topographical  maps  based  on  the 
trigonometrical  surveys  of  the  different  countries  of  Europe. 


TOPOGRAPHICAL  DRAWING. 


115 


Polyconic  Projection. — This  employs  a  tangent  cone  for  every  parallel. 
Each  parallel  of  latitude  therefore  is  independently  developed.  This  has  the 
effect  of  increasing  the  length  of  the  degrees  of  latitude  in  proportion  as  we 
recede  from  the  central  meridian.  To  draw  a  map  according  to  the  tables, 
lay  off  (Fig.  251)  on  the  straight  line  N"  S,  representing  the  middle  meridian^ 
the  lengths  representing  the  10°  of  latitude  between  20°,  30°,  40°,  etc. 
Through  these  points  draw  circular  arcs  with  the  radii  designated  by  R  in  the 
table.  On  these  arcs  lay  off  the  lengths  of  10°  of  longitude  for  each  corre- 
sponding 10°  of  latitude  on  each  side  of  the  central  meridian.  Through  the 
points  thus  formed  draw  the  meridians,  which  will  be  found  slightly  concave 
toward  the  middle  one.  If  the  scale  is  so  large  that  it  is  impossible  to  draw 
the  circular  arcs  with  beam  compasses,  erect  perpendiculars  at  the  points  20°, 
30°,  40°,  and  50°,  and  on  them  lay  off  the  values  D  M  from  the  tables.  At 
each  of  the  points  so  found  erect  perpendiculars,  and  set  off  on  them  the  corre- 
sponding values  of  D  P.  Through  the  points  thus  found  draw  the  parallels 
and  meridians.  By  this  projection  there  is  little  distortion  at  any  portion  of 
the  map ;  a  scale  of  degrees  and  minutes  of  the  parallels  and  meridians,  by 
means  of  which  positions,  determined  by  their  latitudes  and  longitudes,  may 
be  inserted  in  the  maps ;  the  use  of  a  linear  scale  in  any  portion  or  direction ; 
and  the  intersection  of  parallels  and  meridians  at  nearly  right  angles. 

Co-ordinates  of  Curvature  in  Miles  for  Maps  of  Large  Extent. 


Latitude  20°. 

Latitude  24°. 

Latitude  28°. 

Latitude  32°. 

LONGI- 

TUDE. 

D.  M. 

D.  P. 

D.  M. 

D.  P. 

D.  M. 

D.  P. 

D.  M. 

D.  P. 

2° 

130-0 

0-8 

126-4 

0-9 

122-2 

1-0 

117-4 

1-1 

4 

260-0 

3-1 

252-8 

3-6 

244-4 

4-0 

234-8 

4-3 

6 

390-0 

6-9 

379-2 

8-1 

366-5 

9-0 

352-0 

9-8 

8 

520-0 

12-4 

505-5 

14-4 

488-6 

16-0 

469-3 

17-3 

10 

649-8 

19-4 

631-7 

22-4 

610-4 

25-0 

586-3 

27-1 

12 

779-7 

27-8 

757-9 

32-2 

732-4 

36-0 

703-5 

39-1 

14 

909-2 

38-0 

883-6 

43-9 

853-7 

49-0 

819-6 

53-1 

16 

1039-2 

49-6 

1009-9 

57-4 

975-7 

64-1 

936-8 

69-5 

18 

1168-1 

62-8 

1134-8 

72-6 

1096-0 

80-9 

1051-9 

87-8 

20 

1298-0 

77-6 

1261-2 

89-7 

1218-8 

100-1 

1169-2 

108-6 

R. 

10892 

8905 

7458 

6348 

Latitude  36°. 

Latitude  40°. 

Latitude  44°. 

Latitude  48°. 

LONGI- 

TUDE. 

D.  M. 

D.  P. 

D.  M. 

D.  P. 

D.  M. 

D.  P. 

D.  M. 

D.  P. 

2° 

112-0 

1-2 

106-1 

1-2 

99-7 

1-2 

92-7 

1-2 

4 

224-0 

4-6 

212-2 

4-8 

198-9 

4-8 

185-4 

4-8 

6 

335-9 

10-3 

318-1 

10-7 

298-7 

10-9 

277-9 

10-8 

8 

447-7 

18-4 

423-9 

18-9 

398-0 

19-3 

370-3 

19-2 

10 

559-2 

28-7 

529-4 

29-7 

497-1 

30-2 

462-3 

30-0 

12 

670-5 

41-3 

634-7 

42-8 

595-9 

43-4 

554-1 

43-2 

14 

781-6 

56-2 

739-7 

58-2 

694-3 

59-1 

645-6 

58-8 

16 

892-3 

73-4 

844-3 

76-0 

792-3 

77-1 

736-5 

76-7 

18 

1002-6 

92-8 

948-5 

96-1 

889-9 

97-5 

827-0 

97-0 

20 

1112-5 

114-5 

1052-3 

118-5 

986-9 

120-2 

916-9 

119-6 

R. 

5461 

4729 

4110 

3575 

116 


TOPOGRAPHICAL  DRAWING. 


Length  of  a  Degree  of  Longitude  at  Different  Latitudes,  and  at  Sea-Level. 


Deg. 
of 

Miles. 

Deg. 
of 

Miles. 

Deg. 
of 

Miles. 

Deg. 
of 

Miles. 

Deg. 
of 

Miles. 

Deg. 
of 

Miles. 

Lat. 

Lat. 

Lat. 

Lat. 

Lat. 

Lat. 

0 

69-16 

14 

67-12 

28 

61-11 

42 

51-47 

56 

38-76 

70 

23-72 

2 

69-12 

16 

66-50 

80 

59-94 

44 

49-83 

58 

36-74 

72 

21-43 

4   • 

68-99 

18 

65-80 

32 

58-70 

46 

48-12 

60 

34-67 

74 

19-12 

6 

68-78 

20 

65-02 

34 

57-39 

48 

46-36 

62 

32-55 

76 

16-78 

8 

68-49 

22 

64-15 

36 

56-01 

50 

44-54 

64 

30-40 

78 

14-42 

10 

68-12 

24 

63-21 

38 

54-56 

52 

42-67 

66 

28-21 

80 

12-05 

12 

67-66 

26 

62-20 

40 

53-05 

54 

40-74 

68 

25-98 

82 

9-66 

COLOTJKED    TOPOGRAPHY. 

Topographical  features  may  be  represented  effectively  and  expeditiously  by 
means  of  the  brush  and  water-colours,  either  by  India  ink  alone,  or  by  various 
tints,  or  by  the  union  of  both.  (For  preparing  colours  for  tints  and  their  ap- 
plication, see  page  .) 

The  most  important  colours  for  conventional  tints  are,  besides  India  ink, 
indigo,  carmine  or  crimson  lake,  and  gamboge,  used  separately  or  compounded, 
and  burnt  sienna,  yellow  ochre,  and  vermilion,  generally  used  alone. 

The  following  conventional  colours  are  used  by  the  French  military  engineers 
in  their  coloured  topography :  Woods,  yellow,  using  gamboge  and  a  very  little 
indigo ;  grass  land,  green,  made  of  gamboge  and  indigo ;  cultivated  land,  brown, 
made  of  lake,  gamboge,  and  a  little  India  ink  or  burnt  sienna  will  answer. 
Adjoining  fields  should  be  slightly  varied  in  tint.  Sometimes  furrows  are  in- 
dicated by  strips  of  various  colours.  Gardens  are  represented  by  small  rec- 
tangular patches  of  brighter  green  and  brown;  uncultivated  land,  marbled 
green  and  light  brown  ;  brush,  brambles,  etc.,  marbled  green  and  yellow  ;  heath, 
furze,  etc.,  marbled  green  and  pink  ;  vineyards,  purple,  composed  of  lake  and 
indigo ;  sands,  light  brown,  made  of  gamboge  and  lake,  or  yellow  ochre  will  do ; 
lakes  and  rivers,  light  blue,  with  a  darker  tint  on  their  upper  and  left-hand  sides ; 
seas,  dark  blue,  with  a  little  yellow  added ;  marshes,  the  blue  of  water,  with 
spots  of  grass  green,  the  touches  all  lying  horizontally  ;  roads,  brown,  between 
the  tints  for. sand  and  cultivated  ground,  with  more  India  ink  ;  hills,  greenish 
brown,  made  of  gamboge,  indigo,  lake,  and  India  ink.  Woods  may  be  finished 
up  by  drawing  the  trees  and  colouring  them  green,  with  touches  of  gamboge 


TOPOGRAPHICAL   DRAWING. 


in 


toward  the  light  (the  upper  and  left-hand  side),  and  of  indigo  on  the  opposite 
side. 

In  addition  to  the  conventional  colours,  an  imitation  of  the  conventional 
signs  is  introduced  in  colour  with  the  brush,  and  shadows  are  almost  invaria- 
bly introduced.  The  light  is  usually  supposed  to  come  from  the  upper  left- 
hand  corner,  and  to  fall  sufficiently  oblique  to  allow  of  a  decided  light  and 
shade  to  the  slopes  of  hills,  trees,  etc.  After  the  shadow  has  been  painted,  the 
outline  of  the  object  is  strengthened  by  a  heavy  black  line  on  the  side  opposite 
the  light.  The  flat  tints  are  first  laid  on  as  above,  and  then  the  conventional 
signs  are  drawn  in  with  a  pencil  and  coloured  in  with  appropriate  and  more 
intense  tints ;  the  shadows  are  generally  represented  in  India  ink. 

For  the  shading  of  hills,  wash  the  surface  first  with  the  proper  flat  tint, 
trace  in  with  a  pencil  the  outlines,  then  lay  on  in  India  ink  tints  proportioned 
in  intensity  to  the  height  of  the  hills  and  steepness  of  the  slopes.  To  soften  the 
tints,  a  water  brush  is  used  ;  the  tints  are  laid  on  with  the  colour  brush,  and 
softened  by  passing  the  water  brush  rapidly  along  the  edges.  The  water  brush 
must  not  have  too  much  water,  as  it  would  in  that  case  lighten  the  tint  more 
than  is  intended,  and  leave  a  ragged,  harsh  edge.  Tints  may  be  applied  in 
very  light  shades,  one  over  another,  with  the  boundary  of  the  upper  tint  not 
reaching  the  extreme  limit  of  the  tint  below  it. 
When  depth  of  shade  is  required,  it  is  best  produced 
by  application  of  several  light  tints  in  succession ; 
no  tint  is  to  be  laid  over  the  other  until  the  first  is 
dry. 

In  shading  by  contours  it  is  usual  to  increase  the 
intensity  of  the  shade  beyond  that  .of  the  mere  super- 
position of  one  shade  on  another;  where  there  are 

high  altitudes  and  numerous  contours,  the  lower  ones  should  be  put  in  with 
a  different  tint,  as  burnt  sienna  or  sepia,  with  increasing  shades,  and  above 
these  graduated  shades  of  India  ink,  beginning  at  the  same  intensity  as  that  of 
the  colour  last  put  on  (Plate  IX). 

When  woods  have  to  be  represented,  the  shading  used  for  the  trees,  instead 
of  interfering  with  the  shadows  due  to  the  slopes,  may  be  made  to  harmonize 
with  them,  and  contribute  to  the  general  effect  by  presenting  greater  or  less 
depth,  according  to  the  position  of  the  woods  on  the  sides  or  summits  of  the 
hills. 

An  expeditious  and  effective  way  of  representing  hills  with  a  brush,  imitat- 
ing hills  drawn  with  a  pen  on  the  vertical  system,  is  effected  by  pressing  out 
the  brush  flat  to  a  comb-like  edge,  drawing  this  over  a  nearly  dry  surface  of 
India  ink,  and  then  brushing  lightly  or  more  heavily  between  the  contours, 
according  to  the  steepness  of  the  slope,  each  of  the  comb- like  teeth  making  its 
mark  (Plate  VII). 

Kivers  and  masses  of  water  may  be  shaded  in  with  a  colour  and  water  brush ; 
or,  by  superposition  of  light  tints,  a  shadow  may  be  thrown  from  the  bank 
toward  the  light,  and  the  outline  of  this  bank  strengthened  with  a  heavy  black 
line ;  the  tints  are  to  be  in  indigo. 

Topographical  drawings  may  be  made  in  water-colour  with  but  one  tint,  as 
India  ink,  or  ink  mixed  with  a  little  sepia.  The  conventional  signs  are  made 


TOPOGRAPHICAL  DRAWING. 

in  imitation  of  pen  drawings,  the  hills  in  softened  tint,  or  drawn  with  the  comb- 
edged  brush. 

Artistic  and  effective  drawings  are  made  of  hills  as  they  would  appear  in 
nature  under  an  oblique  light,  the  sides  of  the  hills  next  the  light  receiving  it 
more  brilliantly  according  as  they  are  inclined  nearer  to  right  angles  with  its 
rays,  and  the  shades  on  the  sides  removed  from  the  light  increasing  in  intensity 
as  the  slopes  increase  in  steepness. 

Having  damp-stretched  the  paper  upon  the  drawing-board,  first  draw  in  the 
lines  in  pencil,  and  afterward  repeat  them  with  a  very  light  ink-line ;  a  soft 
sponge,  well  saturated,  should  then  be  passed  quickly  over  the  surface  of  the 
drawing  in  order  to  remove  any  ink  that  would  be  liable  to  mix  with  the  tint 
and  mar  its  uniformity. 

The  moistened  surface  will  prevent  the  tint  from  drying  too  rapidly  at  the 
edges.  In  tinting,  never  allow  the  edge  to  dry  until  the  whole  surface  is  cov- 
ered ;  leave  a  little  superfluous  colour  along  the  edge  while  filling  the  brush.  In 
applying  a  flax  tint  to  large  surfaces,  let  the  drawing-board  be  inclined  at  an 
angle  of  five  or  six  degrees,  to  allow  the  colour  to  flow  downward  over  the  sur- 
face. With  a  moderately  full  brush,  commence  at  the  upper  outline,  and  carry 
the  colour  along  uniformly  from  left  to  right  and  from  right  to  left  in  horizon- 
tal bands,  taking  care  not  to  overrun  the  outlines,  in  approaching  which  the 
point  of  the  brush  should  be  used,  and  at  the  lower  outline  let  there  be  only 
sufficient  colour  in  the  brush  to  complete  the  tinting. 

The  colour  should  not  be  allowed  to  accumulate  in  inequalities  of  the  paper, 
but  should  be  evenly  distributed  over  the  whole  surface. 

Too  much  care  can  not  be  given  to  the  first  application  of  colour ;  attempt- 
ing to  remedy  a  defect  by  washing  or  applying  fresh  tints  generally  makes  bad 
worse. 

Erasers  should  never  be  used  on  a  tinted  drawing,  as  the  paper,  when 
scratched,  receives  the  tint  more  readily,  and  retains  a  larger  portion  of  colour 
than  other  parts,  thereby  causing  a  darker  tint. 

Marbling  is  done  by  using  two  separate  tints,  and  blending  them  at  their 
edges.  A  separate  brush  is  required  for  each  tint ;  before  the  edge  of  the  first 
is  dry,  pass  the  second  tint  along  the  edge,  blending  one  tint  into  the  other,  and 
continue  with  each  tint  alternately. 

In  reference  to  general  effect  in  tinted  topographical  drawings,  intensity  and 
everything  else  should  be  subordinate  to  clearness.  No  tint  should  be  prom- 
inent or  obtrusive.  Tints  that  are  of  small  extent  must  be  a  little  more  intense 
than  large  surfaces,  or  they  will  appear  lighter  in  shade.  Keep  a  general  tone 
throughout  the  whole  drawing.  Beginners  will  find  it  best  to  keep  rather  low 
in  tone,  strengthening  their  tints  as  they  acquire  boldness  of  touch. 

Plate  VIII  gives  an  example  of  coloured  topography. 

The  plan  is  usually  so  drawn  that  the  top  may  represent  the  north ;  the 
upper  left-hand  corner  is  then  the  northwest. 

In  inking  in,  commence  first  with  the  light  lines,  since  a  mistake  in  these 
lines  may  be  covered  by  the  shade-lines.  Describe  all  curves  before  drawing 
the  straight  lines,  for  it  is  easier  to  join  neatly  a  straight  line  to  a  curve  than 
the  opposite.  Ink  in  with  system,  commencing,  say,  at  the  top  ;  ink  in  all  light 
lines  running  easterly  and  westerly,  then  all  light  lines  running  northerly  and 


TOPOGRAPHICAL  DRAWING. 

southerly,  then  commence  in  the  same  way  and  draw  in  the  shade  lines.  Ele- 
vated objects  have  their  southern  and  eastern  outline  shaded,  while  depressions 
have  the  northern  and  western ;  thus,  in  conventional  signs,  roads  and  canals 
are  shaded  on  opposite  sides.  Having  inked  in  all  lines  that  are  drawn  with  a 
ruler  or  described  with  compasses,  commence  again  at  one  corner  to  fill  in  the 
detail,  keeping  all  parts  of  the  plan  except  what  you  are  actually  at  work 
upon  covered  with  paper  to  preserve  it  from  being  soiled.  The  curved  lines  of 
brooks,  fences,  etc.,  are  sometimes  drawn  with  a  drawing-pen,  sometimes  with 
a  steel  pen  or  goose-quill. 

Boundary  lines  of  private  properties,  of  townships,  of  counties,  of  States, 
etc.,  are  indicated  by  various  combinations  of  short  lines  and  dots,  thus  : 


All  plans  should  have  meridian  lines  drawn  on  them ;  also  scales,  and  the 
dates  on  which  the  plans  were  finished.  Page  120  gives  several  designs  for 
meridians  and  borders.  In  these  diagrams  it  will  be  observed  that  both  true 
and  magnetic  -meridians  are  drawn ;  this  is  desirable  when  the  variation  is 
known,  but  in  many  surveys  merely  the  magnetic  meridian  is  taken ;  in  these 
cases  this  line  is  simply  represented  with  half  of  the  barb  of  the  arrow  at 
the  north  point,  and  on  the  opposite  side  of  the  line  from  the  true  meridian. 

Scales  on  drawings  which  are  to  be  reproduced  by  photography  should 
always  be  drawn  in  ;  on  others,  the  proportion  of  the  plan  to  the  ground  should 
be  expressed  decimally,  as  ?oW»  TUOW  or  ^J  stating  the  number  of  feet, 
chains,  etc.,  to  the  inch. 


120 


TOPOGRAPHICAL  DRAWING. 


ORTHOGRAPHIC    PROJECTION. 


ARCHITECTURAL  and  mechanical  drawings  are  usually  the  delineation  of 
bodies  by  orthographic  projection,  which  is  the  representation  on  a  sheet  of 
paper,  having  only  two  dimensions,  length  and  breadth,  of  solids,  having  three, 
length,  breadth,  and  thickness,  on  such  scales  that  dimensions  can  be  taken 
from  the  parts,  and  structures  and  machines  constructed  therefrom. 

Place  any  surface,  for  instance,  a  sheet  of  paper  or  a  drawing-board,  at 
right  angles  to  the  sun's  rays.  This  may  be  readily  done  by  inserting  a  pin 
into  the  surface,  and  making  it  vertical  to  the  surface  in  every  direction  by  a 
right-angled  triangle ;  then  place  the  surface  in  the  direct  rays  of  the  sun,  and 
in  such  a  position  that  there  will  be  no  shadow  on  the  surface  from  the  pin ; 
the  sun's  rays  are  then  perpendicular  to  the  surface.  Take  a  wafer  or  a  circu- 
lar bit  of  paper  and  hold  it  over  the  paper  by  means  of  a  long  pin  or  wire,  and 
we  obtain  shadows,  as  above,  varying  with  the  inclination  of  the  wafer  to  the 
plane  of  the  paper.  When  parallel  with  the  plane,  the  shadow  is  a  complete 
circle  ;  when  at  right  angles,  a  line ;  and  it  varies  between  them  as  the  wafer  is 
inclined.  These  shadows  are  the  orthographic  projections  of  the  wafer;  no 
line  can  be  longer  than  it  is  naturally,  but,  if  inclined  or  vertical,  it  is  reduced 
in  length  till  it  becomes  a  point  only.  The  orthographic  projection  of  the  pin 
which  has  determined  the  position  of  the  surface  is  merely  the  shadow  of  the 
head.  If  the  pin  be  inclined  at  all,  the  body  of  the  pin  is  projected  as  a 
shadow  by  a  line ;  if  the  pin  be  laid  on  the  surface,  its  projection  is  the  whole 
length  of  the  pin..  The  sun's  rays  act  as  perpendiculars,  which  will  be  here- 
after spoken  of  as  projecting  the  points  of  an  object  upon  a  surface  which 
will  represent  the  object  itself  in  drawing;  and,  should  any  confusion  occur  to 
the  draughtsman  of  how  an  object  is  to  be  projected  or  drawn,  if  he  can  make 
the  outline  of  the  object  on  any  convenient  scale  in  wire  and  get  its  shadows 
by  the  sun's  vertical  rays  on  a  plane,  he  can  readily  see  how  the  object  should 
be  drawn. 

Since  the  surfaces  of  all  bodies  may  be  considered  as  composed  of  points, 
the  first  step  is  to  represent  the  position  in  space  of  a  point,  by  referring  it  to 
planes  whose  position  is  established.  The  projection  of  a  point  upon  a  plane 
is  the  foot  of  the  perpendicular  let  fall  from  the  point  to  the  plane. 

If  on  two  planes  not  parallel  to  each  other,  whose  positions  are  known,  we 


121 


ORTHOGRAPHIC  PROJECTION. 


have  the  projection  of  a  point,  the  position  of  this  point  is  determined  by  erect- 
ing perpendiculars  from  each  plane  at  the  projected  points  :  their  intersection 
will  be  the  point. 

If  from  every  point  of  an  indefinite  straight  line,  A  B  (Fig.  252),  placed  in 
any  manner  in  space,  perpendiculars  be  let  fall  on  a  plane,  L  M  N  0,  whose 
position  is  given,  then  all  the  points  in  which  these  perpendiculars  meet  the 
plane    will    form     another     indefinite 
straight  line,  a  I :  this  line  is  called  the 
projection   of    the    line    A  B    on    this 
plane.     It  is  only  necessary  to  project 
two  points  of  the  line,  and  the  straight 
line  drawn  through  the  two  projected 
points  will   be   the  projection   of    the 


FIG.  252. 


Fio.  253. 


given  line.  The  projection  of  a  straight  line,  itself  perpendicular  to  the  plane, 
is  the  point  in  which  it  meets  the  plane. 

If  the  projections  a  b  and  a'  V  of  a  straight  line  on  the  two  planes  L  M  N  0 
and  L  M  P  Q  (Fig.  253)  are  known,  this  line  A  B  i&  determined ;  for  if,  through 
one  of  its  projections,  a  #,  a  plane  be  drawn  perpendicularly  to  L  M  N  0,  and 
if  through  a'  b'  another  plane  be  drawn  perpendicular  to  L  M  P  Q,  the  inter- 
section of  the  two  planes  will  be  the  line  A  B. 

To  delineate  a  solid,  it  must  be  referred  to  three  planes,  at  right  angles  to 
each  other. 

Thus,  let  a  b  c  (Fig.  254)  be  a  parallelepiped  in  an  upright  position,  of 
which  the  plane  a  b  is  horizontal,  and  the  planes  a  c  and  c  b  vertical.  Let  d  e, 
df,  and  d  g  be  the  planes  of  projection.  The  sides  of  the  body  being  parallel 
to  these  planes,  each  to  each,  let  the  figure  of  the  parallelepiped  be  projected 
on  them.  Draw  parallel  lines  from  the  angles  of  the  body  perpendicular  to  the 
planes,  as  indicated  by  the  dotted  lines ;  then  upon  the  plane  d  e,  a'  b'  is  the 
projection  of  the  surface  a  b,  the  plan  of  the  object;  upon  the  plane  df,  a'  c', 
the  projection  of  the  surface  a  c,  the  front  elevation;  and  upon  the  plane  d  g, 
the  projection  b'  c'  of  the  surface  b  c,  the  side  elevation.  Thus,  three  distinct 
views  of  the  regular  solid  a  b  c  are  delineated  on  plane  surfaces,  any  two  of 
which  are  a  sufficient  description  of  the  object.  From  the  two  figures  a'  c',  V  c\ 
for  example,  the  third  figure  a'  b'  may  be  compounded,  by  drawing  the  vertical 
lines  c'  h  b'  i  and  a'  k,  c'  I  to  meet  the  plane  d  e,  and  by  producing  them  hori- 
zontally till  they  meet  and  form  the  figure  a'  b'.  Similarly,  the  figure  b'  c'  may 


ORTHOGRAPHIC  PROJECTION. 


123 


be  deduced  from  the  other  two  by  the  aid  of  the  lines  h,  i,  from  a!  V  and  the 
lines  m,  n,  from  a'  c' . 

It  is  in  this  way  that  a  third  view  of  any  piece  of  machinery  is  to  be  found 
from  two  given  views ;  and  in  many  cases  two  elevations,  or  one  elevation  and 


FIG.  254. 


FIG.  255. 


a  plan,  may  afford  a  sufficiently  complete  idea  of  the  construction  of  a  machine. 
When  parts  are  inclosed  by  others,  views  of  the  interior  are  required,  in  which 
case  the  machine  is  supposed  to  be  cut  across  by  planes,  vertical,  horizontal,  or 
inclined,  to  reveal  its  structure.  Such  views  are  termed  sections,  and  distin- 
guished, with  reference  to  the  planes  of  section,  as  vertical  or  horizontal  or 
inclined  sections. 

In  practice,  the  drawings  are  done  upon  one  common  surface,  the  plane  of 
paper.  Suppose  the  plane  d  g  (Fig.  254)  revolved  back  into  the  position  d  a', 
and  d  e  also  moved  to  d  e',  both  of  these  positions  being  in  the  plane  of  d  f. 
This  done,  the  three  views  are  depicted  on  one  plane  surface  (Fig.  255) ;  d  I 
and  d  m  are  the  ground  and  vertical  lines  ;  the  positions  of  the  same  points  in 
a'  c'  and  a1  V  are  in  the  same  perpendicular  from  the  ground-line ;  and  the 
position  of  a  point  in  the  plane  may  be  found  by  applying  the  edge  of  the 
square  to  the  same  point  as  represented  in  the  elevation.  The  same  is  true  as 
between  the  two  elevations,  and  establishes  a  method  of  drawing  several  views  of 
one  machine  upon  the  same  surface  of  paper  in  strict  agreement  with  each  other. 

PKOJECTIONS   OF    SIMPLE    BODIES. 

Right  projections  of  a  regular  hexagonal  pyramid  (Fig.  256). — Two  distinct 
geometrical  views  are  necessary  to  convey  a  complete  idea  of  the  form  of  the 
object:  an  elevation  to  represent  the  sides  of  the  body,  and  to  express  its 
height ;  and  a  plan  to  express  the  form  horizontally. 


124 


ORTHOGRAPHIC   PROJECTION. 


Draw  a  horizontal  line  L  T  through  the  centre  of  the  sheet  to  represent  the 
ground  line.  Then  draw  a  perpendicular  to  the  ground  line,  S  S',  to  represent 
the  axis  of  the  pyramid. 

To  construct  the  plan,  from  any  point,  S',  on  the  line  S  S',  as  a  centre,  con- 
struct the  hexagonal  base ;  the  lines  A'  S',  B'  S',  etc.,  represent  the  projections 
of  its  edges  in  the  plan. 

Since  the  base  of  the  pyramid  rests  upon  the  horizontal  plane,  it  must 


be  projected  vertically  upon  the  ground  line.  From  each  of  the  angles  at 
A',  B',  C',  and  D'  erect  perpendiculars  to  that  line.  The  points  of  intersec- 
tion, A,  B,  C,  and  D,  are  the  true  positions  of  all  the  angles  of  the  base ;  and 
it  only  remains  to  lay  off  the  height  of  the  pyramid,  from  the  point  G  to  S,  and 
to  draw  S  A,  S  B,  S  C,  and  S  D,  which  are  the  only  edges  of  the  pyramid  visi- 
ble in  the  elevation  ;  S  A  and  S  D,  being  in  the  vertical  plane,  are  seen  in  their 
true  length  ;  the  points  F'  and  E'  being  situated  in  the  lines  B  B'  and  C  C',  the 
lines  S  B  and  S  C  are  each  the  projections  of  two  edges  of  the  pyramid. 

To  construct  the  projections  of  the  same  pyramid,  having  its  base  set  in  an 
inclined  position,  but  with  its  edges  S  A  and  S  D  still  in  the  vertical  plane 
(Fig.  257). 

With  the  exception  of  the  inclination,  the  vertical  projection  of  this  solid  is 


ORTHOGRAPHIC   PROJECTION. 


125 


precisely  the  same  as  in  the  preceding  example,  and  it  is  only  necessary  to  copy 
that  elevation.  To  do  this,  fix  the  position  of  the  point  D  upon  the  ground 
line,  through  which  draw  D  A,  making  with  L  T  the  desired  inclination  of  the 
base  of  the  pyramid.  Make  D  A  equal  to  the  A  D  of  the  preceding  figure,  and 
on  this  erect  the  vertical  projection  S  A  D  of  that  figure. 

Since  the  edges  S  A  and  S  D  are  still  in  the  vertical  plane,  and  the  point 
D  remains  unaltered,  the  projection  A'  of  the  point  A  will  still  be  in  the  line 
A'  S'.  The  remaining  points,  B',  C',  etc.,  in  the  projection  of  the  base,  are 
found  by  the  intersections  of  perpendiculars  let  fall  from  the  corresponding 
points  in  the  elevation,  with  lines  drawn  parallel  to  A'  S',  at  a  distance  equal  to 
the  width  of  the  base.  Joining  all  the  contiguous  points,  we  obtain  A'  B'  C'  D' 
E'  F',  the  horizontal  projection  of  the  base,  two  of  its  sides  being  concealed  by 
the  body  of  the  pyramid.  The  vertex  S  having  been  similarly  projected  to  S', 
and  joined  by  straight  lines  to  the  several  an- 
gles of  the  base,  the  projection  of  the  solid 
is  completed. 

To  find  the  horizontal  projection  of  a  trans- 
verse section  of  the  same  pyramid,  made  by  a 
plane  perpendicular  to  the  vertical,  but  in- 
clined at  an  angle  to  the  horizontal  plane  of 
projection,  letting  all  the  sides  of  the  base  be 
inclined  to  the  ground  line  (Fig.  258). 

Since  none  of  the  sides  of  the  base  are  to 
be  parallel  with  the  ground  line,  draw  a  line 
A'  D'  making  the  required  angle  with  that 
line,  and  from  the  points  A'  and  D'  set  out  the 
angular  points  of  the  hexagon.  To  obtain  the 
projections  of  the  edges  of  the  pyramid,  join 
the  angular  points  which  are  diametrically 
opposite  and  project  the  figure  thus  obtained 
upon  the  vertical  plane,  as  shown  in  the  eleva- 
tion. 

If  the  cutting  plane  be  represented  by  the 
line  a  d  in  the  elevation,  it  will  expose,  as  the 
section  of  the  pyramid,  a  polygon  whose  an- 
gular points,  being  the  intersections  of  the  va- 
rious edges  with  the  cutting  plane,  will  be 
projected  in  perpendiculars  drawn  from  the 
points  where  it  meets  these  edges  respective- 
ly ;  from  the  points  a,  f,  b,  etc.,  let  fall  the 
perpendiculars  a  a',  //',  b  b',  etc. ;  join  their 
contiguous  points  of  intersection  with  the 
lines  A'  D',  F'  C',  B'  E',  etc. ;  and  the  resulting 
six-sided  figure  represents  the  section  required.  The  edges  F  S  and  E  S,  being 
concealed  in  the  elevation,  but  necessary  for  the  construction  of  the  plan,  are 
expressed  by  dotted  lines,  as  also  is  the  portion  of  the  pyramid  situated  above 
the  cutting  plane,  supposed  to  be  removed,  but  necessary  in  order  to  draw  the 
lines  representing  the  edges.  The  ordinary  method  of  expressing  sections  in 


Fio.  258. 


126 


ORTHOGRAPHIC  PROJECTION. 


purely  line  drawings  is  by  filling  up  the  spaces  comprised  within  their  outlines 
with  a  number  of  parallel  straight  lines  drawn  at  equal  distances,  called  section 
lines. 

To  represent  in  plan  and  elevation  a  regular  six-sided  prism  in  an  upright 
position  (Fig.  259). 

Lay  down  the  ground  line  Gr  K  and  draw  the  axis  of  the  prism  S  S'.  De- 
scribe the  hexagonal  plan  A'  B'  C'  D'  E'  F',  as  in  the  previous  example.  From 
each  of  the  angular  points,  A',  B',  etc.,  erect  perpendiculars,  and  on  one  of  these 
perpendiculars  set  off  A  G,  the  height  of  the  prism,  and  draw  a  parallel  to  the 
ground  line,  A  D,  which  completes  the  vertical  projection.  The  face,  B  C  H  I, 
being  parallel  to  the  vertical  plane,  is  seen  in  its  true  size,  while  Gr  H  and  I  K 


are  each  equal  to  one  half  of  H  I,  which  enables  us  to  draw  the  elevation  with- 
out constructing  the  plan— a  fact  to  be  remembered  in  the  drawing  of  nuts, 
bolt-heads,  etc.,  in  machine  drawing. 

To  form  the  projections  of  the  same  prism,  supposing  it  to  have  been  moved 
round  the  point  G  in  a  plane  parallel  to  the  vertical  plane  (Fig.  260). 


ORTHOGRAPHIC  PROJECTION. 


127 


Copy  the  elevation  (Fig.  259)  on  the  inclined  base  G  K ;  let  fall  perpen- 
diculars from  all  the  angles  in  the  elevation ;  and  join  the  contiguous  points  of 
intersection  with  the  horizontal  lines  appropriate  to  these  points  respectively. 
The  plan  remaining  the  same  width  as  before,  the  polygon  A'  B'  C'  D'  E'  F'  is 
the  projection  of  the  upper  surface, 
and  G'  H'  I'  K'  L'  M'  that  of  the  base 
of  the  prism.  All  the  edges  are  rep- 
resented in  the  horizontal  projection 
by  equal  straight  lines,  as  D'  K',  A'  G', 
etc.,  and  the  sides  A'  B  ',  G'  H',  etc., 
remain  still  parallel  to  each  other, 
which  affords  the  means  of  verifying 
the  accuracy  of  the  drawings.  The 
upper  surface  and  the  base,  seen  ob- 
liquely in  this  projection,  do  not  ap- 
pear as  true  hexagons  in  the  plan. 

Required  the  projections  of  the 
same  prism  set  into  a  position  in- 
clined to  loth  planes  of  projection 
(Fig.  261). 

Assuming  the  inclination  of  the 
prism  upon  the  horizontal  plane  to  be 
as  in  the  preceding  figures,  copy  the 
plan  of  Fig.  260  on  an  axis  A'  K'  in- 
clined to  the  vertical  plane  of  projec-  * 
tion.  Since  the  prism  preserves  its 
former  inclination  to  the  horizontal 
plane,  every  point  in  it,  as  A,  in  as- 
suming its  new  position,  simply  moves 
in  a  horizontal  plane,  and  will  there- 
fore be  at  the  same  distance  above  the 
ground  line  that  it  was  in  the  eleva- 
tion (Fig.  260),  and  it  will  also  be  in 
the  perpendicular  A'  A ;  the  point  of 
intersection  A  is,  therefore,  its  projec- 
tion in  the  elevation.  Determine  the 
remaining  angular  points  in  this  view  and  join  the  contiguous  points  and  the 
corresponding  angles  of  the  upper  and  lower  surface  and  the  figure  is  complete. 

CONIC    SECTIONS. 

The  plan  of  the  cone  (Fig.  262)  is  simply  a  circle,  described  from  the  centre 
S',  with  a  diameter  equal  to  that  of  the  base.  Its  elevation  is  an  isosceles 
triangle,  obtained  by  drawing  tangents  A'  A,  B'  B,  perpendicular  to  and 
intersecting  the  ground  line;  then  set  off  upon  the  centre  line  the  height 
C  S,  and  join  S  A,  S  B.  These  lines  are  called  the  exterior  elements  of  the 
cone. 

Given  the  projections  of  a  cone,  and  the  direction  of  a  plane  X  X,  cutting  it 
perpendicularly  to  the  vertical,  and  obliquely  to  the  horizontal  plane ;  required 


FIG.  261. 


128 


ORTHOGRAPHIC   PROJECTION. 


to  find,  first,  the  horizontal  projection  of  this  section;  and,  secondly,  the  out- 
line of  the  ellipse  thus  formed  (Figs.  262,  263). 

Through  the  vertex  of  the  cone  draw  a  line  S  E  to  any  point  within  the 
base  A  B  ;  let  fall  a  perpendicular  from  E,  cutting  the  circumference  of  the  base 


in  E',  and  join  E'  S' ;  then 
another  perpendicular  let 
fall  from  e  will  intersect 
E'  S'  in  a  point  e',  which 
will  be  the  horizontal  pro- 
jection of  a  point  in  the 
curve  required  ;  and  so  on 
for  any  number  of  points. 

The  exterior  genera- 
trices A  S  and  B  S  being 
both  projected  upon  the 
line  A'  B',  the  extreme  lim- 
its of  the  curve  sought  will 
be  at  the  points  a'  and  V  on  that  line,  which  are  the  projections  of  the  points 
of  intersection  a  and  b  of  the  cutting  plane  with  the  outlines  of  the  cone. 
And  since  the  line  a'  V  divides  the  curve  symmetrically  into  two  equal  parts, 
the  points/',  g',  h',  etc.,  will  be  obtained  by  setting  off  above  that  line,  and  on 
their  respective  perpendiculars,  the  distances  d'  d3,  e'  ez,  etc.  A  sufficient  num- 
ber of  points  having  thus  been  determined,  the  curve  drawn  through  them 
(which  will  be  found  to  be  an  ellipse)  will  be  the  outline  of  the  section  re- 
quired. 

This  curve  may  be  obtained  by  another  method,  depending  on  the  principle 
that  all  sections  of  a  cone  by  planes  parallel  to  the  base  are  circles.  Thus,  let 
the  line  F  G  represent  such  a  cutting  plane ;  the  section  which  it  makes  with 
the  cone  will  be  denoted  on  the  horizontal  projection  by  a  circle  drawn  from 


ORTHOGRAPHIC   PROJECTION. 


129 


the  centre  S',  with  a  radius  equal  to  half  the  line  P  G ;  and  by  projecting  the 
point  of  intersection  H  of  the  horizontal  and  oblique  planes  by  a  perpendicular 
H  H',  and  noting  where  this  line  cuts  the  circle  above  referred  to,  two  points 
H'  and  I'  are  determined  in  the  curve.  Additional  points  are  obtained  similarly. 
The  preceding  methods  exhibit  the  section  as  fore-shortened.  To  solve  the 
second  question  proposed,  let  the  cutting  plane  X  X  be  conceived  to  turn 
upon  the  point  b,  so  as  to  coincide  with  the  vertical  line  b  k,  and  (to  avoid  con- 


fusion  of  lines)  let  b  Tc  be  trans- 
ferred to  a'  b'j  which  will  repre- 
sent, as  before,  the  extreme  limits 
of  the  curve  required ;  take  any 
point,  as  d,  in  this  new  position 
of  the  cutting  plane,  it  will  be  -  B\ 
represented  by  d",  and,  if  the  cut- 
ting plane  were  turned  upon  a'  V 
(Fig.  263)  as  an  axis  till  it  is 
parallel  to  the  vertical  plane,  the 
point  which  had  been  projected 
at  d"  would  then  have  described 
round  a'  V  an  arc  of  a  circle, 
whose  radius  is  the  distance  d'  d* 

(Fig.  262).  This  distance,  therefore,  set  off  at  d'  and/'  on  each  side  of  a'  V  ^ 
gives  two  points  in  the  curve  sought.  The  curve  drawn  through  any  number 
of  points  thus  obtained  will  be  an  ellipse  of  the  true  form  and  dimensions  of 
the  section. 

To  find  the  horizontal  projection  and  actual  outline  of  the  section  of  a  cone, 
made  ~by  a  plane  Y  Y  parallel  to  one  side  or  element,  and  perpendicular  to  the 
vertical  plane  (Figs.  264,  265). 

Determine  by  the  second  method  laid  down  in  the  preceding  problem  any 
10 


FIG.  264. 


130 


ORTHOGRAPHIC   PROJECTION. 


number  of  points,  as  F',  G',  J',  K',  etc.,  in  the  curve  representing  the  horizon- 
tal projection  of  the  section  specified.  The  horizontal  plane  passing  through 
M  gives  only  one  point  M',  which  is  the  vertex  of  the  curve  sought. 

To  determine  the  actual  outline  of  this  curve,  suppose  the  plane  Y  Y  to  turn 
as  upon  a  pivot  at  M,  until  it  has  assumed  the  position  M  B,  and  transfer  M  B 
to  the  parallel  M9  B"  (Fig.  265).  The  point  F  will  thus  have  first  described 
the  arc  F  E  till  it  reaches  the  point  E,  which  is  then  projected  to  E4 ;  suppose 
the  given  plane,  now  represented  by  M"  B',  to  turn  upon  that  line  as  an  axis, 
until  it  assumes  a  position  parallel  to  the  vertical  plane,  the  point  E9,  which  is 
distant  from  the  axis  M'  B'  by  the  distance  F'  S'  (Fig.  264),  will  now  be  pro- 
jected to  Fa  and  G",  two  points  in  the  curve  required,  which  is  a,  parabola. 

To  draw  the  vertical  projection  of  the  sections  of  two  opposite  cones  made  by 
a  plane  parallel  to  their  axis  (Fig.  266). 


D 


Let  C  E  D  and  C  B  A  be  the  two  cones,  and  X  X  the  position  of  the 
cutting  plane.  Project  in  plan  either  of  the  cones,  as  b  E'  D' ;  from  its  centre, 
with  a  radius  equal  to  L  H,  describe  a  circle,  and  draw  the  tangent  1)  a  ;  b  a 
will  be  the  horizontal  projection  of  the  cutting  plane.  Draw  the  line  H'  M' 
parallel  to  the  cutting  plane ;  H',  M'  corresponding  in  position  to  the  inter- 
sections H,  M,  of  the  plane  with  the  cones.  From  H'  and  M'  lay  off  distances 
equal  to  L  K,  K  I,  and  the  length  of  the  cone,  and  through  these  points  draw 
perpendiculars,  as/V,  d"  c',  b'  a',  etc.,  which  must  be  made  equal  to  the  chords 
/  e,  d  c,  b  a,  made  by  the  cutting  plane  a  5,  with  circles  whose  radii  are  G  K, 
I  F,  and  the  radius  of  the  base  of  the  cone.  Through  the  points  «',  c',  e',  H',/', 
d',  b',  draw  the  curve  for  the  projection  required.  A  similar  construction  will 
give  the  sectional  projection  of  the  opposite  cone  at  M'.  The  curve  thus  found 
is  the  hyperbola. 

PENETRATIONS    OR   INTERSECTIONS    OF    SOLIDS. 

Represent  the  projections  of  two  cylinders  of  unequal  diameters  meeting 
each  other  at  right  angles  (Fig.  267).  The  one,  the  rectangle  ABED  for  its 
vertical,  and  the  circle  A'  H'  B'  T'  for  its  horizontal  projection  ;  the  other,  being 


ORTHOGRAPHIC  PROJECTION. 


131 


horizontal,  is  indicated  in  the  former  by  the  circle  L  P  I  N,  and  in  the  latter  by 
the  rectangle  L'  I'  K'  M'.  From  the  position  of  these  two  solids  the  curves 
formed  by  their  junction  will  be  projected  horizontally  in  the  curves  0'  H'  P', 
B'  T'  S',  and  vertically  in  L  P  I  N. 

But,  if  the  position  of  these  bodies  be  changed  into  that  represented  by  Fig. 
268,  the  lines  of  their  intersection  will  assume  in  the  vertical  projection  a 
totally  different  aspect,  and  may  be  determined  as  follows : 

Through  any  point  taken  upon  the  plan  of  Fig.  268  draw  a  horizontal  line 
a'  #',  indicating  a  plane  cutting  both  cylinders  parallel  to  their  axes;  this 


B 


FIG.  267. 


FIG.  268. 


plane  would  cut  the  vertical  cylinder  in  lines  drawn  perpendicularly  through 
the  points  c'  d'.  To  find  the  vertical  projection  of  its  intersection  with  the 
other  cylinder,  conceive  its  base  I'  L',  after  being  transferred  to  I2  L",  to  be 
revolved  about  I*  La  as  an  axis  parallel  to  the  horizontal  plane ;  this  is  expressed 
in  part  by  simply  drawing  a  semicircle  of  the  diameter  I*  La.  Produce  the 
line  a'  b'  to  a' ;  then  set  off  the  distance  a"  e'  on  each  side  of  the  axis  I  K,  and 
draw  straight  lines  through  these  points  parallel  to  it.  These  lines  a  b,  g  li, 


132 


ORTHOGRAPHIC   PROJECTION. 


denote  the  intersection  of  the  plane  a'  V  with  the  horizontal  cylinder,  and 
therefore  the  points  c,  d,  m,  o,  where  they  cut  the  perpendiculars  c  c' ',  d  d',  are 
points  in  the  curve  required.  By  passing  other  horizontal  planes  similar  to  a'  b' 
through  both  cylinders,  and  operating  as  before,  any  number  of  points  may  be 
obtained.  The  vertices  i  and  k  of  the  curves  are  projected  directly  from  i'  and 
&',  the  intersections  of  the  outlines  of  both  cylinders.  When  the  cylinders  are 
of  unequal  diameters,  as  in  the  present  case,  the  curves  of  penetration  are  hy- 
perbolas. 

When  the  diameters  of  the  cylinders  are  equal  (Fig.  269),  and  when  they 


r 


FIG.  269. 


FIG.  270. 


cut  each  other  at  right  angles,  the  curves  of  penetration  are  projected  vertically 
in  straight  lines  perpendicular  to  each  other. 

To  delineate  the  intersections  of  two  cylinders  of  equal  diameters  at  right 
angles,  when  one  of  the  cylinders  is  inclined  to  the  vertical  plane  (Fig.  270). 

Suppose  the  two  preceding  figures  to  be  drawn,  the  projection  c  of  any 
point,  as  <?',  must  be  situated  in  the  perpendicular  c'  c.  Since  the  distance  of 


ORTHOGRAPHIC  PROJECTION. 


133 


this  point  (projected  at  c  in  Fig.  269)  from  the  horizontal  plane  remains  un- 
altered, it  must  also  be  in  the  horizontal  line  c  c.  Upon  these  principles  all 
the  points  indicated  by  literal  references  in  Fig.  270  are  determined ;  the 
curves  of  penetration  resulting  therefrom  intersect  each  other  at  two  points 
projected  upon  the  axial  line  L  K,  of  which  that  marked  q  alone  is  seen.  The 
ends  of  the  horizontal  cylinder  are  ellipses. 

To  find  the  curves  resulting  from  the  intersection  of  two  cylinders  of  un- 
equal diameters,  meeting  at  any  angle  (Fig.  271). 

Suppose  the  axes  of  both  cylinders  to  be  parallel  to  the  vertical  plane,  and 
let  A  B  E  D  and  N  0  Q  P  be  their  projections  upon  that  plane.  In  construct- 
ing, in  the  first  place,  their 
horizontal  projection,  ob- 
serve that  the  upper  end 
A  B  of  the  larger  cylinder  is 
represented  by  an  ellipse 
A'  K'  B'  M',  which  may  easi- 
ly be  drawn  by  the  help  of 
the  major  axis  K'  M'  equal 
to  the  diameter  of  the  cylin- 
der, and  of  the  minor  A'  B', 
the  projection  of  the  diame- 
ter. The  visible  portion  of 
the  base  of  the  cylinder  be- 
ing similarly  represented  by 
the  semi-ellipse  L'  D'  H',  its 
entire  outline  will  be  com- 
pleted by  drawing  tangents 
L'  M'  and  H'  K'.  The  up- 
per extremity  P  N  of  the 
smaller  cylinder  will  also  be 
projected  in  the  ellipse  p'  N'. 
Conceive  a  plane,  as 
a'  g',  to  pass  through  both 
cylinders  parallel  to  their 
axes  ;  it  will  cut  the  surface 
of  the  larger  cylinder  in 
two  straight  lines,  passing 
through  the  points  /'  and  g' 
on  the  upper  end  of  the  cyl- 
inder ;  these  lines  will  be 
represented  in  the  elevation 
by  projecting  the  points/' 
and  g'  to  /,  g,  and  drawing 
a  f  and  c  g  parallel  to  the  axis. 


V-s       ^"^ 

ff?--:^, 


K 


FIG.  271. 


The  plane  a'  g'  will  in  like  manner  cut  the 

smaller  cylinder  in  two  straight  lines,  which  will  be  represented  in  the  verti- 
cal projection  by  d  h  and  e  t,  and  the  intersections  of  these  lines  with  a/ 
and  c  g  will  give  four  points  I,  &,  m,  and  n,  in  the  curves  of  penetration 
these  points,  one  only,  I,  is  visible,  /',  in  the  plan. 


Of 


134 


ORTHOGRAPHIC   PROJECTION. 


To  find  the  curves  of  penetration  in  the  elevation  without  the  aid  of  the  plan 
(Fig.  271). 

Let  the  bases  D  E  and  Q  0  of  both  cylinders  be  revolved  parallel  to  the 
vertical  plane  after  being  transferred  to  any  convenient  distance,  as  Da  Ea  and 
Qa  Oa,  from  the  principal  figure ;  they  will  then  be  vertically  projected  in  the 

circles  Da  Ha  Ea  and  Qa  G'  Oa.  Draw 
«a  ca  parallel  to  D  E,  and  at  any  suitable 
distance  from  the  centre  I ;  this  line 
will  represent  the  intersection  of  the 
base  of  the  cylinder  with  a  plane  parallel 
to  the  axes  of  both,  as  before.  The  in- 
tersection of  this  plane  with  the  base  of 
the  smaller  cylinder  will  be  found  by 
setting  off  from  R  a  distance  R  p,  equal 
to  I  o,  and  drawing  through  the  point  p 
a  straight  line  parallel  to  Q  0.  The 
intersection  of  the  supposed  plane  with 
the  convex  surfaces  of  the  cylinders  will 
be  represented  by  the  lines  af,  eg,  and 
d  A,  e  i;  and,  consequently,  the  inter- 
sections of  these  lines  indicate  points  in 
the  curves  sought.  These  points  may 
be  multiplied  by  conceiving  other  planes 
to  pass  through  the  cylinders. 

To  find  the  curves  of  penetration  of 
a  cone  and  sphere  (Fig.  272). 

Let  D  S  be  the  axis  of  the  cone, 
A'  L'  B'  the  circle  of  its  base,  and  the 
triangle  A  B  S  its  projection  on  the  ver- 
tical plane ;  and  let  C,  C',  be  the  projec- 
tions of  the  centre,  and  the  equal  circles 
E'  K'  F'  and  E  G  F  those  of  the  cir- 
cumferences of  the  sphere. 

This  problem  can  be  solved  only  by 
the  aid  of  imaginary  intersecting  planes. 
Let  a  b  represent  the  projection  of  a 
horizontal  plane ;  it  will  cut  the  sphere 
in  a  circle  whose  diameter  is  a  b,  and 

which  is  partially  drawn  from  the  centre  C'  in  the  plan,  as  a'  f  b'.  Its  in- 
tersection with  the  cone  is  also  a  circle  described  from  the  centre  S'  with  the 
diameter  c  d  as  c'  f  d' ;  the  points  e'  and  /"',  where  these  two  circles  cut  each 
other,  are  the  horizontal  projections  of  two  points  in  the  lower  curve,  which 
is  entirely  hidden  by  the  sphere.  The  points  referred  to  are  projected  ver- 
tically upon  the  line  a  b  at  e  and/.  The  upper  curve,  which  is  seen  in  both 
projections,  is  obtained  by  a  similar  process ;  but  it  is  to  be  observed  that  the 
horizontal  cutting  planes  must  be  taken  in  such  positions  as  to  pass  through 
both  solids  in  circles  which  shall  intersect  each  other.  In  this  respect  it 
will  be  necessary,  first,  to  determine  the  vertices  m  and  n  of  the  curves  of 


FIG.  272. 


ORTHOGRAPHIC  PROJECTION. 


135 


penetration.  For  this  purpose,  conceive  a  vertical  plane  passing  through  the 
axis  of  the  cone  and  the  centre  of  the  sphere ;  its  horizontal  projection  will 
be  the  straight  line  C'  L',  joining  the  centres  of  the  two  bodies.  Suppose 
this  plane  to  be  turned  upon  the  line  C  C'  as  on  an  axis,  until  it  becomes 
parallel  to  the  vertical  plane ;  the  points  S'  and  L'  will  now  have  assumed 
the  positions  S3  and  L2,  and  consequently  the  axis  of  the  cone  will  be  projected 
vertically  in  the  line  D'  S8,  and  its  side  in  S*  L8,  cutting  the  sphere  at  the 
points  p  and  r.  Conceive  the  solids  to  have  resumed  their  original  relative 
positions,  the  vertices  or  adjacent  limiting  points  of  the  curves  of  penetration 
must  be  in  the  horizontal  lines  p  o  and  r  q,  drawn  through  the  points  deter- 
mined as  above ;  their  exact  positions  on  these  lines  may  be  ascertained  by  pro- 
jecting vertically  the  points  m'  and  n',  where  the  arcs  described  by  the  points  p 
and  r,  in  restoring  the  cone  to  its  first  position,  intersect  the  line  S'  L'. 

It  is  of  importance,  further,  to  ascertain  the  points  at  which  the  curves  of 
penetration  meet  the 
outlines  A  S  and  S  B 
of  the  cone.  The  plane 
which  passes  through 
these  lines,  being  pro- 
jected horizontally  in 
A'  B',  will  cut  the  sphere 
in  a  circle  whose  diame- 
ter is  i'  j' ;  this  circle, 
described  in  the  eleva- 
tion from  the  centre  C, 
will  cut  the  sides  A  S 
and  S  B  in  four  points, 
at  which  the  curves  of 
penetration  are  tangent 
to  the  outlines  of  the 
cone. 

To  find  the  lines  of 
penetration  of  a  cylin- 
der and  a  cylindrical 
ring,  or  annular  torus 
(Fig.  273). 

Let  the  circles  A'  E' 
B',  F'  G'  K',  represent 
the  horizontal,  and  the 
figure  A  C  B  D  the  ver- 
tical projection  of  the 
torus,  and  let  the  circle 
II' /'  L',.and  the  rectan- 
gle H  I  M  L  be  the 
analogous  projections  of 
the  cylinder,  which 

passes  perpendicularly  through  it.     Conceive,  as  before,  a  plane,  a  5,  to 
horizontally  through  both  solids ;  it  will  cut  the  cylinder  in  a  circle  which 


pass 
will 


136  ORTHOGRAPHIC   PROJECTION. 

be  projected  in  the  base  H'/'  L'  itself,  and  the  ring  in  two  other  circles,  of 
which  one  only,  part  of  which  is  represented  by  the  arc/'  b*  b' ',  will  intersect 
the  cylinder  at  the  points/'  and  is,  which,  being  projected  vertically,  will  give 
two  points /and  b9  in  the  upper  curve  of  penetration. 

Another  horizontal  plane,  taken  at  the  same  distance  below  the  centre  line 
A  B  as  that  marked  a  b  is  above  it,  will  cut  the  ring  in  circles  coinciding  with 
those  already  obtained  ;  consequently  the  points/'  and  b9  indicate  points  in  the 
lower  as  well  as  in  the  upper  curves  of  penetration,  and  are  projected  vertically 
at  d  and  e.  Thus,  by  laying  down  two  planes  at  equal  distances  on  each  side 
of  A  B,  four  points  in  the  curves  required  are  determined. 

To  determine  the  vertices  m  and  n,  following  the  method  explained  in  the 
preceding  problem,  draw  a  plane  0  n ,  passing  through  the  axis  of  the  cylinder 
and  the  centre  of  the  ring,  and  conceive  this  plane  to  be  revolved  about  the 
point  0  until  it  has  assumed  the  position  0  B',  parallel  to  the  vertical  plane ; 
the  point  n',  representing  the  extreme  outline  of  the  cylinder  in  plan,  will  now 
be  at  r',  and,  being  projected  vertically,  that  outline  will  cut  the  ring  in  two 
points  p  and  r,  which  would  be  the  limits  of  the  curves  of  penetration  in  the 
supposed  relative  position  of  the  two  solids ;  and  by  drawing  the  two  horizontal 
lines  r  n  and  p  m,  and  projecting  the  point  n'  vertically,  the  intersections  of 
these  lines,  m  and  n,  are  the  vertices  of  the  curves  in  the  actual  position  of  the 
penetrating  bodies. 

The  points  at  which  the  curves  are  tangents  to  the  outlines  H  I  and  L  M  of 
the  cylinder  may  readily  be  found  by  describing  arcs  of  circles  from  the  centre 
0  through  the  points  H'  and  L',  which  represent  these  lines  in  the  plan,  and 
then  proceeding,  as  above,  to  project  the  points  thus  obtained  upon  the  eleva- 
tion. Lastly,  to  determine  the  points,  as  j,  z,  etc.,  where  the  curves  are  tan- 
gents to  the  horizontal  outlines  of  the  ring,  draw  a  circle  P'  s'  j'  with  a  radius 
equal  to  that  of  the  centre  line  of  the  ring,  namely,  P  D  ;  the  points  of  inter- 
section z'  and/  are  the  horizontal  projections  of  the  points  sought. 

Required  to  represent  the  section  which  would  be  made  in  this  ring  by  a 
plane,  N'  T',  parallel  to  the  vertical  plane. 

Such  a  section  will  be  represented  in  its  actual  form  and  dimensions  in  the 
elevation.  To  determine  its  outlines,  let  two  horizontal  planes,  g  q  and  i  k, 
equidistant  from  the  centre  line  A  B,  be  supposed  to  cut  the  ring ;  their  lines 
of  intersection  with  it  will  have  their  horizontal  projections  in  the  two  circles 
g'  o'  and  h1  q',  which  cut  the  given  plane  N'  T'  in  o'  and  q'.  These  points  being 
projected  vertically  to  0,  <?,  &,  etc.,  give  four  points  in  the  curve  required.  The 
line  N'  T'  cutting  the  circle  A'  E'  B'  at  N',  the  projection  N  of  this  point  is 
the  extreme  limit  of  the  curve. 

The  circle  P'  s'f,  the  centre  line  of  the  rim  of  the  torus,  is  cut  by  the  planes 
N'  T'  at  the  point  *•',  which,  being  projected  vertically  upon  the  lines  D  P  and 
C  I,  determines  s  and  I,  the  points  of  contact  of  the  curve  with  the  horizontal 
outlines  of  the  ring.  Finally,  the  points  t  and  u  are  obtained  by  drawing  from 
the  centre  0  a  circle,  T'  v',  tangent  to  the  given  plane,  and  projecting  the  point 
of  intersection  v'  to  the  points  v  and  x,  which  are  then  to  be  replaced  upon  C  D 
by  drawing  the  horizontals  v  t  and  x  u. 

Required  to  delineate  the  lines  of  penetration  of  a  sphere  and  a  regular  hex- 
agonal prism  whose  axis  passes  through  the  centre  of  the  sphere  (Fig.  274). 


ORTHOGRAPHIC   PROJECTION. 


137 


The  centres  of  the  circles  forming,  the  two  projections  of  the  sphere  being 
upon  the  axis  C  C'  of  the  upright  prism,  which  is  projected  horizontally  in  the 
regular  hexagon  D'  E'  F'  G'  H'  I',  and  all  the  lateral  faces  of  the  prism  being 
equidistant  from  the  centre  of  the  sphere,  their  lines  of  intersection  with  it  will 
be  circles  of  equal  diameters.  The  perpendicular  face,  represented  by  the  line 
E'  F'  in  the  plan,  will  meet  the  surface  of  the  sphere  in  two  circular  arcs,  E  F 
and  L  M,  described  from  the  centre  0,  with  a  radius  equal  to  c'  b'  or  a1  c'. 
And  the  intersections  of  the  two  oblique  faces  D'  E'  and  F'  G'  will  obviously 
be  each  projected  in  two  arcs  of  an  ellipse,  whose  major  axis  dg  is  equal  to 
e'/',  and  minor  axis  the  vertical  projection  of  e'  f.  As  it  is  necessary  to 
draw  small  portions  only  of  these  curves,  the  following  method  may  be  em- 
ployed :  Draw  D  G  through  the  points  E,  F;  divide  the  portions  E  F  and 
F  G  respectively  into  the  same  number  of  equal  parts,  and,  drawing  perpen- 
diculars through  the  points  of  division,  set  off  from  F  G  the  distances  from 


FIQ.  274. 


FIG.  275. 


the  corresponding  points  in  E  F  to  the  circular  arc  E  C  F,  as  points  in  the 
elliptical  arc  required.  The  remaining  elliptical  arcs  can  be  traced  by  the 
same  method. 


138 


ORTHOGRAPHIC   PROJECTION. 


Required  to  draw  the  lines  of  penetration  of  a  cylinder  and  a  sphere,  the 
centre  of  the  sphere  being  without  the  axis  of  the  cylinder  (Fig.  275). 

Let  the  circle  D'  E'  L'  be  the  projection  of  the  base  of  the  given  cylinder, 
and  let  A  B  be  the  diameter  of  the  given  sphere.  If  a  plane,  as  c'  d',  be  drawn 
parallel  to  the  vertical  plane,  it  will  cut  the  cylinder  in  two  straight  lines, 

G  G',  H  H'.  This  plane  will  also  cut 
the  sphere  in  a  circle  described  from 
the  centre  C  with  a  radius  of  half  the 
line  c'  d' ;  its  intersection  with  the  lines 
G  G'  and  H  H'  will  give  so  many  points 
in  the  curves  sought,  viz.,  G,  H,  I,  K. 

The  planes  a'  V  and  e'  f,  which  are 
tangents  to  the  cylinder,  furnish  respect- 
ively only  two  points  in  the  curves ;  of 
these  points,  E  and  F  alone  are  visible, 
the  other  two,  L  and  M,  being  concealed 
by  the  solid  ;  therefore  the  planes  drawn 
for  the  construction  of  the  curves  must 
be  all  taken  between  a'  b1  and  e'f.  The 
plane  which  passes  through  the  axis  of 
the  cylinder  cuts  the  sphere  in  a  circle 
whose  projection  upon  the  vertical  plane 
will  meet  at  the  points  D,  N,  and  g,  h, 
the  outlines  of  the  cylinder,  to  which 
the  curves  of  penetration  are  tangents. 

To  find  the  lines  of  penetration  of 
a  frustum  of  a  cone  and  a  prism  (Fig. 
276). 

The  frustum  is  represented  in  the 
plan  by  two  circles  described  from  the 
centre  C' ;  and  the  horizontal  lines  M  N 
and  M'  N'  are  the  projections  of  the 
axis  of  a  prism  of  which  the  base  is 
square,  and  the  faces  respectively  par- 
allel and  perpendicular  to  the  planes  of 
projection. 

In  laying  down  the  plan  of  this  solid,  it  is  supposed  to  be  inverted,  in  order 
that  the  smaller  end  of  the  cone  and  the  lines  of  intersection  of  the  lower  sur- 
face, F  G,  of  the  prism  may  be  exhibited.  According  to  this  arrangement,  the 
letters  A'  and  B'  ought,  strictly  speaking,  to  be  marked  at  the  points  I'  and  H', 
and  conversely ;  but,  as  the  part  above  M'  N'  is  exactly  symmetrical  with  that 
below  it,  the  distribution  of  the  letters  of  reference  in  the  figures  can  lead  to  no 
confusion. 

The  intersection  of  the  plane  F  G  with  the  cone  is  projected  horizontally 
in  a  circle  described  from  the  centre  C',  with  the  diameter  F'  G'.  The  arcs 
I'  F'  A'  and  H'  G'  B'  are  the  only  parts  of  this  circle  which  require  to  be 
drawn.  In  the  vertical  projection  the  extreme  points  K,  L,  A,  B  need  only 
be  found,  for  the  lines  of  intersection  are  here  projected  straight. 


Fio.  276. 


ORTHOGRAPHIC  PROJECTION. 


139 


To  describe  the  curves  formed  by  the  intersection  of  a  cylinder  with  the 
frustum  of  a  cone,  the  axes  of  the  two  solids  cutting  each  other  at  right  angles 
(Fig.  277). 

The  projections  of  the  solids  are  laid  down  in  the  figure  precisely  as  in  the 
preceding  example.  The  intersections  of  the  outlines  in  elevation  furnish  four 
points  in  the  curves  of  penetration. 
These  points  are  all  projected  horizontal- 
ly upon  the  line  A'  B'.  Now  pass  a 
plane,  as  a  b,  horizontally  through  both 
solids  ;  its  intersection  with  the  cone  will 
be  a  circle  of  the  diameter  c  d,  while  the 
cylinder  will  be  cut  in  two  parallel 
straight  lines,  represented  in  the  eleva- 
tion by  a  b,  and  whose  horizontal  projec- 
tion may  be  determined  in  the  following 
manner:  Conceive  a  vertical  plane, f g, 
cutting  the  cylinder  at  right  angles  to 
its  axis,  and  let  the  circle  g  ef  thereby 
formed  be  described  from  the  intersec- 
tion of  the  axes  of  the  two  solids;  the 
line  j  h  will  now  represent,  in  this  posi- 
tion of  the  section,  the  distance  of  one  of 
the  lines  sought  from  the  axis  of  the  cyl- 
inder. Set  off  this  distance  on  both  sides 
of  the  point  A',  and  through  the  points 
k  and  a'  thus  obtained,  draw  straight 
lines  parallel  to  A'  B' ;  the  intersections 
of  these  lines  with  the  circle  drawn  from 
the  centre  C'  of  the  diameter  c'  d'  will 
give  four  points  m',p',  n,  and  o,  which, 
being  projected  vertically  upon  a  b,  deter- 
mine two  points,  m  and  p,  in  the  curves 
required. 

In  order  to  obtain  the  vertices  or  ad- 
jacent limiting  points  of  the  curves,  draw 
from  the  vertex  of  the  cone  a  straight 
line,  t  e,  touching  the  circle  g  ef,  and  let  a  horizontal  plane  be  supposed  to 
pass  through  the  point  of  contact  e.  Proceed  according  to  the  method  given 
above  to  determine  the  intersections  of  this  plane  with  each  of  the  solids  in 
question  •  the  four  points  i',  r',  q,  and  s,  projected  vertically  upon  the  line  e  r, 
determine  the  vertices  i  and  r  required. 

THE    HELIX. 

A  helix  is  the  curve  described  upon  the  surface  of  a  cylinder  by  a  point  re- 
volving round  it,  and  at  the  same  time  moving  parallel  to  its  axis  by  a  certain 
invariable  distance  during  each  revolution.  This  distance  is  called  the  pitch  of 
the  helix  or  screw. 

Required  to  construct  the  helical  curve  described  by  the  point  A1  upon  a  cyl- 


r-US * JB 


FIG  277. 


140 


ORTHOGRAPHIC  PROJECTION. 


inder  projected  horizontally  in  the  circle  A'  C'  F',  the  pitch  being  represented 
by  the  line  A1  A3  (Fig.  278). 

Divide  the  pitch  A1  A3  into  any  number  of  equal  parts,  say  eight ;  and 
through  each  point  of  division,  1,  2,  3,  etc.,  draw  straight  lines  parallel  to  the 
ground  line.  Then  divide  the  circumference  A'  C'  F'  into  the  same  number  of 
equal  parts ;  the  points  of  division,  A',  B',  C',  E',  F',  etc.,  will  be  the  horizontal 

projections  of  the  differ- 
ent positions  of  the  given 
point  during  its  motion 
round  the  cylinder.  Thus, 
when  the  point  is  at  B'  in 
the  plan,  its  vertical  pro- 
jection will  be  the  point  of 
intersection  B  of  the  per- 
pendicular drawn  through 
B'  and  the  horizontal 
drawn  through  the  first 
point  of  division.  'Also, 
when  the  point  arrives  at 
C'  in  the  plan,  its  vertical 
projection  is  the  point  C, 
where  the  perpendicular 
drawn  from  C'  cuts  the 
horizontal  passing  through 
the  second  point  of  divis- 
ion, and  so  on  for  all  the 
remaining  points.  The 
curve  A1  B  C  E  F  A3, 
drawn  through  all  the 
points  thus  obtained,  is 
the  helix  required. 

To  draw  the  vertical 
elevation  of  the  solid  con- 
tained between  two  helical 
surfaces  and  two  concen- 
tric cylinders  (Fig.  278). 

A    helical    surface    is 
generated   by   the  revolu- 
Fro  278.  tion    of    a    straight    line 

round  the  axis  of  a  cylin- 
der, its  outer  end  moving  in  a  helix,  and  the  line  itself  forming  with  the  axis 
a  constant  and  invariable  angle. 

Let  A'  C'  1^'  and  K'  M'  0'  represent  the  concentric  bases  of  the  cylinders, 
whose  common  axis  S  T  is  vertical ;  the  curve  of  the  exterior  helix  A1  C  E  F  A3 
is  the  first  to  be  drawn  according  to  the  method  above  shown.  Then,  having  set 
off  from  A1  to  A"  the  thickness  of  the  required  solid,  draw  through  A"  another 
helix  equal  and  similar  to  the  former.  Now  construct,  as  above,  similar  helices, 
K  C  0  and  Ka  C9  0s,  of  the  same  pitch  as  the  last,  but  on  the  interior  cylinder. 


ORTHOGRAPHIC  PROJECTION. 


141 


The  lines  A'  K',  B'  L',  C'  M',  etc.,  represent  the  horizontal  projections  of  the 
various  positions  of  the  generating  straight  line,  which,  in  the  present  example, 
has    been    supposed   to  be 
horizontal ;    and  these  lines 
are   projected  vertically  at 
A1  K,  B  L,  etc. 

In  the  position  A1  K 
the  generating  line  is  pro- 
jected in  its  actual  length, 
and  at  the  position  C'  M' 
its  vertical  projection  is  the 
point  C.  The  same  re- 
mark applies  to  the  genera- 
trix of  the  second  helix. 

To  determine  the  verti- 
cal projection  of  the  solid 
formed  by  a  sphere  moving 
in  a  •  helical  curve  (Fig. 
279). 

Let  A'  C'  E'  be  the  base 
of  a  cylinder,  upon  which 
the  centre  point  C'  of  a 
sphere  whose  radius  is  a'  C' 
describes  a  helix,  which  is 
projected  on  the  vertical 
plane  in  the  curve  A  C  E  J, 
determined  as  before.  From 
the  various  points  A,  B, 

C,  D ,  in  this  curve, 

as  centres,  describe   circles 

with  the  radius  a'  C' ;  these 

denote  the  various  positions 

of   the    sphere    during   its 

helical  motion ;  and,  if  lines 

be   drawn   touching   them, 

the  curves  thereby  formed  will  constitute  the  figure  required.     One  of  these 

curves  disappears  at  0,  but  reappears  again  at  I.     The  exterior  and  interior 

circles  of  the  plan  represent  the  horizontal  projection  of  the  solid  in  question. 

The  conical  helix  differs  from  the  cylindrical  one  in  that  it  is  described  on 
the  surface  of  a  cone  instead  of  on  that  of  a  cylinder ;  but  the  construction 
differs  but  slightly  from  the  one  described.  By  following  out  the  same  prin- 
ciples, helices  may  be  represented  as  lying  upon  spheres  or  upon  any  other 
surfaces  of  revolution. 


FIG.  279. 


DEVELOPMENT   OF   SURFACES. 


The  development  of  the  surface  of  a  solid  is  the  drawing  or  unrolling  on  a 
plane  the  form  of  its  covering,  the  form  that  cut  out  of  paper  would  exactly  fit 
and  cover  the  surface  of  the  solid.  Frequently,  in  practice,  the  form  of  the 


142 


ORTHOGRAPHIC   PROJECTION. 


surface  of  a  solid  is  found  by  applying  paper  or  thin  sheet-brass  directly  to  the 
solid  and  cutting  it  to  fit. 

To  develop  the  surface  of  a  cylinder  formed  ly  the  intersection  of  another 
equal  cylinder,  as  the  knee  of  a  stove-pipe  (Fig.  280). 

Let  A  B  C  D  be  the  elevation  of  the  pipe  or  cylinder.  Above  A.  B  describe 
the  semicircle  A'  4'  B'  of  the  same  diameter  as  the  pipe ;  divide  this  semicircle 


^ 

V 

^ 

^ 

^\ 

2 

*X^ 

r> 


into  any  number  of  equal  parts, 
eight  for  instance ;  through  these 
points,  1',  2',  3',  etc.,  draw  lines 
parallel  to  the  side  A  C  of  the  pipe, 
and  cutting  the  line  C  D  of  the  in- 
tersection of  the  two  cylinders. 
Lay  off  A*  B"  equal  to  the  semicir- 
cle A'  4'  B',  and  divided  into  the 
same  number  of  equal  parts ; 
through  these  points  of  division 
erect  perpendiculars  to  A"  B",  and 
on  these  perpendiculars  lay  off  the 
distances  A"  C",  1"  1",  2"  2",  3"  3", 
and  so  on,  corresponding  to  A  C, 

1  1, 2  2,  3  3,  etc.,  in  preceding  figure.     Through  the  points  C",  1",  2" ,  D", 

draw  connecting  lines,  which  gives  but  one  half  of  the  surface  of  the  pipe,  the 

other  being  exactly  similar  to  it. 

To  develop  the  surface  of  a  cylinder  intersected  ly  another  cylinder,  as  in 

the  formation  of  a  T-pipe  (Fig.  281). 

The  construction  is  similar  to  the  preceding. 

To  develop  the  surface  of  a  right  cone  (Fig.  282). 

From  C'  as  a  centre,  with  a  radius,  C'  A',  equal  to  the  inclined  side  A  C  of 


FIG.  280. 


ORTHOGRAPHIC   PROJECTION. 


143 


the  cone,  describe  an  arc  of  a  circle,  and  on  this  arc  lay  off  the  distance 
A'  B'  A",  equal  to  the  circumference  of  the  base  of  the  cone ;  connect  A'  C'  and 
C'  A",  and  A'  B'  A'  C'  is  the  developed  surface  required. 

To  develop  the  surface  of  the  frustum  of  a  cone,  D  A  B  E  (Fig.  282). 
D'  E'  D"  is  the  development  of  the  cut-off  cone  0  D  E  as  shown  by  the 

preceding  construction,  and  A'  B'  A' 
D"  E'  D'  the  developed  surface  of  the 
frustum. 

To  develop  the  surface  of  a  frus- 
tum of  a  cone,  when  the  cutting  plane 
a  b  is  inclined  to  the  base  (Fig.  282). 

On  A  B,  the  base,  describe  the 
semicircle  A  3'  B  ;  divide  the  semicir- 
cle into  any  number  of  equal  parts, 
six  for  instance;  from  each  point  of 
division,  1',  2',  3',  4',  5',  let  fall  perpen- 
diculars to  the  base  at  1,  2,  3,  4,  5  ; 
connect  each  of  these  last  points  with 


B' 

FIG.  282. 

the  apex  C.  Divide  now  the  arc  A'  B'  A",  equal  to  the  circumference  of  the 
base  A  3  B,  into  twelve  equal  parts ;  each  of  these  parts  by  the  construction  is 
equal  to  the  arc  A  1',  1'  2' ;  connect  these  points  of  division  with  the  point  C' ; 
on  C'  A'  take  C'  a'  equal  to  C  a,  a  being  the  point  at  which  the  plane  cuts  the 
inclined  side  of  the  cone ;  in  the  same  way  on  C'  B',  lay  off  C'  b'  equal  to  C  b. 

All  the  lines  connecting  the  apex  C  with  the  base,  included  within  the  two 
inclined  sides,  are  represented  as  less  than  their  actual  length,  and  must  be 
projected  on  the  inclined  sides  to  determine  their  absolute  dimensions ;  project, 
therefore,  the  points  1*,  2*,  3*,  4',  5*,  at  which  the  cutting  plane  intersects  the 
lines  01,  02,  C  3,  C  4,  C  5,  by  drawing  parallels  to  the  base  through  these 
points  to  the  inclined  side  C  B.  Now  lay  off  C'  1",  C'  2"",  etc.,  equal  to  C  1' ', 
C  2' ',  etc.  ;  connect  the  points  a',  1',  2',  ....  J',  .  •  •  •  a',  and  a'  A'  B'  A"  a"  b' 
is  the  developed  surface. 


144 


ORTHOGRAPHIC   PROJECTION. 


To  develop  the  surface  of  a  sphere  or  ball  (Figs.  283,  284). 

The  surface  can  not  be  accurately  represented  on  a  plane,  but  only  approxi- 
mately by  gores.     Let  CAB  (Fig.  284)  be  the  eighth  of  a  hemisphere  ;  on  C  D 
describe  the  quarter  circle  D  A  c ;  divide  this  arc  into  any  number  of 
equal  parts,  six  for   instance;   from  the  points  of   division 
1,  2,  3,  ...  let  fall  perpendiculars  on  C  D,  and  from  the 
intersections  with  this  line  describe  arcs  1'  1",  2'  2", 
3'  3', ...  cutting  the  line  C  B  at  1",  2",  3*,  .... 
on   the   straight  line   C' D'    (Fig.    283),   lay   off 
C'  D'  equal  to  the  arc  D  A  c,  with  as  many 

A' 

\ 

i 
i 

I 


II 


FIG.  283. 


Fio.  284. 


equal  divisions;  then  from  either  side  of  this  line  lay  off  1'"  1"",  2'"  2""  .... 
D'  B'  equal  to  the  arcs  1'  1",  2'  2"  ....  D  B  (Fig.  284).  Connect  the  points 
C',  1"",  2/|r",  ....  and  C'  A'  B'  is  approximately  the  developed  surface. 

In  the  preceding  demonstrations  the  forms  are  described  to  cover  the  sur- 

face only  ;  in  construction,  allowance  is  to 
be  made  for  lap  by  the  addition  of  mar- 
gins on  each  side.  And  on  account  of  the 
difficulty,  in  the  formation  of  hemispheri- 
cal ends  of  boilers,  of  bringing  all  the 
gores  together  at  the  apex,  it  is  usual  to 
make  them,  as  shown  (Fig.  285),  by  cut- 
ting short  the  gores,  and  surmounting  the 
centre  with  a  cap-piece. 

For  small  boilers  and  air  chambers  the 
spherical  ends  are  dished. 

SHADE    LINES. 

The  effectiveness  of  outline  drawings  is 
increased  by  the  use  of  shade  lines  ;  the 
method  is  wholly  conventional.  The  rule 
used  in  preparing  drawings  for  the  United 

States  Patent  Office  is  the  simplest  and  the  one  generally  used  in  this  country. 
In  this  the  light  falls  from  the  upper  left-hand  corner  of  the  sheet  of  drawing- 
paper,  and  at  an  angle  of  45°  ;  hence,  the  right-hand  and  lower  edge  of  a 
projection  (Fig.  286)  and  the  left-hand  and  upper  edge  of  a  recess  appear  in 
heavy  lines  (Fig.  287).  In  the  case  of  a  circular  object  the  shade  is  ter- 


FlQ 


ORTHOGRAPHIC   PROJECTION. 


145 


]        I 


LJ 


FIG.  286. 


FIG.  288. 


FIG.  289. 


11 


146 


ORTHOGRAPHIC   PROJECTION. 


initiated  by  a  diameter  inclined  at  an  angle  of  45°,  the  shade  being  a  graduated 
one,  as  shown  in  Fig.  288. 

Fig.  289  is  an  example  of  this  method. 

In  a  second  method  the  elevation  is  shaded,  as  in  the  foregoing,  but  in  the 
plan  the  light  falls  from  the  lower  left-hand  corner  of  the  drawing,  making  the 
upper  and  right-hand  edges  of  projections  and  the  lower  and  left-hand  side  of 

Elevation. 


FIG.  290. 

recesses  shaded.  Examples  of  this  method  are  shown  in  Fig.  290.  In  the 
orthographic  projection  of  solids  the  boundary  lines  between  surfaces  in  the 
light  and  shadow  are  made  heavy. 

Still  another  method  is  described  in  the  following  chapter  on  "  Shades  and 
Shadows,"  where  the  light  falls  over  the  left  shoulder,  and  this  is  the  one  gen- 
erally used  in  the  casting  of  shadows  and  often  in  topographical  drawings. 


SHADES   AND    SHADOWS. 

RAYS  of  light  are  diffused  through  space  in  straight  lines,  and  the  direct 
rays  of  the  sun  may  be  regarded  as  parallel.  The  light  on  an  object  may  come 
directly  from  the  source  of  light,  or  by  reflection  from  other  objects  or  surfaces 
exposed  to  light.  The  surfaces  of  an  object  under  direct  light  are  the  most 
strongly  illuminated,  while  other  surfaces,  from  their  form  or  position  receiv- 
ing less  light,  are  in  shade  or  direct  shadow.  Shadows  are  cast  by  an  object 
upon  another  object  by  the  interception  of  light,  or  upon  any  surface  by  pro- 
jections or  undercutting.  The  limit  of  the  line  of  direct  shadow  is  called  the 
line  of  shade. 

In  the  delineation  of  shadows,  the  most  convenient  mode  of  regarding  the 
rays  of  light  is,  in  all  cases,  as  falling  in  the  direction  of  the  diagonal  of  a  cube, 
of  which  the  sides  are  parallel  to  the  planes  of  projection.  The  projections  of 
the  ray  form  each  an  angle  of  45°  with  the  ground  line.  This  is  not  true  of 
the  ray  itself  in  space,  for  that  forms  an  angle  of  54°  44'  with  the  ground  line, 
and  an  angle  of  35°  16'  with  each  of  the  planes  of  projection. 

To  find  the  shadow  of  a  point,  as  A,  A'  (Fig.  291),  on  either  plane  of  pro- 
jection, the  vertical,  for  instance,  draw  a  line  through  the  horizontal  projection 


FIG.  291. 


FIG.  292. 


of  the  point  A'  at  an  angle  of  45°  with  the  ground  line,  L  T,  and  at  the  point 
of  intersection  of  those  lines,  a',  erect  a  perpendicular  to  intersect  the  vertical 
projection  of  the  ray  through  A,  which  will  be  at  the  point  a,  the  shadow  in 
question. 

The  converse  of  this  method  determines  the  shadow  of  the  point  on  the 

147 


148 


SHADES  AND   SHADOWS. 


horizontal  plane.    The  shadow  thrown  by  B  of  the  given  line  falls  at  J,  and  the 
straight  line  a  b,  which  joins  these  two  points,  is  the  shadow  required. 

The  line  a  b  is  equal  and  parallel  to  the  given  line  A  B  ;  this  results  from 
the  circumstance  that  the  latter  is  parallel  to  the  vertical  plane. 


tn-  ^///y\  7      /A 


FIG.  293. 


The  shadows  of  a  rectangular  slip  of  paper  or  wood,  A  B  C  D,  cast  upon  the 
same  vertical  plane  and  parallel  to  it,  is  the  rectangle  A  B  C  D  (Pig.  291). 

When  the  object  is  not  parallel  to  the  given  plane,  the  shadow  cast  is  no 
longer  a  figure  equal  and  similarly  placed,  but  the  method  of  determining  it  is 
similar  (Fig.  292). 

By  a  combination  of  the  foregoing  principles,  the  shadow  of  a  slip  of  mould- 
ing placed  on  the  vertical  plane  (Fig.  293)  is  determined. 


FIG.  295. 


Fig.  294  shows  the  shadow  cast  by  a  rectangular  slip  of  cardboard  at  right 
angles  to  the  vertical  plane ;  Fig.  295,  the  shadow  cast  by  a  slip  parallel  to  the 
ground  plane  and  at  right  angles  to  the  vertical  plane,  which  is  itself  set  at  a 


SHADES  AND  SHADOWS. 


149 


horizontal  angle ;  Fig.  296,  the  shadow  of  the  slip  cast  on  a  concave  surface ; 
Fig.  297,  the  shadow  cast  on  a  vertical  plane  by  a  circle  parallel  to  it ;  Figs. 
298,  299,  301,  the  shadows  on  a  vertical  plane  by  circles  in  various  positions 


A'      <f   B' 


FIG.  297. 


^  /    // 


FIG.  298. 


relative  to  this  plane,  in  all  which  the  shadow  assumes  the  form  of  an  ellipse ; 
Fig.  300,  the  shadow  cast  by  a  circle  horizontal  to  the  ground  plane  on  a  verti- 
cal convex  surface ;  Fig.  302,  the  shadow  cast  by  a  circle  parallel  to  the  vertical 


! — 
\ 

^'-^a 


/  '    ~]\t*/       .      * 


J) 


m 


FIG.  299, 


FIG.  300. 


plane  of  the  projection,  the  shadow  being  thrown  upon  two  plane  surfaces  at 
an  angle  to  each  other. 


150 


SHADES  AND  SHADOWS. 


In  every  drawing  where  the  shadows  are  to  be  inserted,  it  is  of  the  utmost 
importance  that  the  projections  which  represent  the  object  whose  shadow  is 
required,  and  the  surface  upon  which  this  shadow  is  cast,  should  be  exactly  de- 


FIG.  301. 


FIG.  302. 


fined  by  lines  drawn  lightly  in  India  ink,  and,  to  prevent  mistakes,  erase  all 
pencil  marks  before  proceeding  to  the  operations  determining  the  lines  of 
shadow. 


MEN 


FIG.  303. 


FIG.  304. 


In  Fig.  303  the  three  sides  of  the  hexagonal  pyramid,  A'  B'  F',  A'  B'  C',  and 
A'  C'  D',  alone  receive  the  light ;  consequently  the  edges  A'  F'  and  A'  D'  are 
the  lines  of  shade.  To  determine  the  shadow  cast  by  these  two  lines,  draw 
from  the  projections  of  the  vertex  of  the  pyramid  the  lines  A  b  and  A'  a'  paral- 


SHADES  AND   SHADOWS. 


151 


FIG.  305. 


lei  to  the  ray  of  light ;  then  erect  at  the  point  J  a  perpendicular  to  the  ground 
line,  which  gives  at  a'  the  shadow  of  the  vertex  on  the  horizontal  plane  on  the 
other  side  of  the  ground  line ;  and  finally  join  this  last  point,  a',  with  the  points 

D'  and  F' ;  the  lines  D'  a'  and  F'  a'  are  the   

outlines  of  the  required  shadow  on  the 
horizontal  plane.  But,  as  the  pyramid  is 
sufficiently  near  the  vertical  plane  to  throw 
a  portion  of  its  shadow  upon  it,  this  por- 
tion may  be  found  by  erecting  at  the  point 
c,  where  the  line  A'  a'  cuts  the  ground 
line,  a  perpendicular  c  a,  intersecting  the 
line  AZ>  in  a;  the  lines  ad  and  ae  join- 
ing this  point  with  those  where  the  hori- 
zontal part  of  the  shadow  meets  the  ground 
line,  will  be  its  outline  upon  the  vertical 
plane. 

Fig.  304  represents  the  shade  on  a  cyl- 
inder placed  vertically,  and  its  shadow  cast 
on  two  planes  of  projection. 

Draw  the  tangents  D'  d'  and  C'  c1  parallel  to  the  rays  of  light ;  these  are  the 
outlines  of  the  shadow  cast  upon  the  horizontal  plane.  Through  the  point  of 
contact  C'  draw  the  vertical  line  C  C' ;  this  line  denotes  the  line  of  shade  upon 
the  surface  of  the  cylinder. 

If  the  shadow  of  this  cylinder  were  entirely  cast  upon  the  horizontal  plane, 
it  would  terminate  in  a  semicircle  drawn  from  the  centre  0',  with  a  radius  equal 
to  that  of  the  base ;  but  a  part  of  the  shadow  of  the  upper  part  is  thrown  upon 
the  vertical  plane,  and  its  outline  is  defined  by  an  ellipse  drawn  in  the  manner 
indicated  in  Fig.  298. 

Fig.  305  represents  the  line  of  shade  and  the  shadow  of  a  horizontal  cylinder 
inclined  to  the  vertical  plane.  The  construction  in  this  case  is  the  same  as  that 
explained  by  Fig.  304.  Of  the  horizontal  lines  of  shade,  C  D  alone  is  visible 
in  the  elevation,  while  A  B  alone  is  seen  in  the  plan,  where  it  may  be  found 
by  drawing  a  perpendicular  from  A  meeting  the  base  F'  G'  in  A'.  The  line 
A'  E',  drawn  parallel  to  the  axis  of  the  cylinder,  is  the  line  of  shade  required. 
Project  the  shadow  of  the  line  A  B  on  the  vertical  plane,  as  in  previous  exam- 
ples, to  define  the  outline  of  the  shadow  of  the  cylinder. 

The  example  here  given  presents  the  particular  case  in  which  the  bases  of 
the  cylinder  are  parallel  to  the  direction  of  the  rays  of  light.  In  this  case,  to 
determine  the  line  A'  E'  lay  off  the  angle  A'  L  A\  equal  to  35°  16',  so  that  the 
side  A2  L  shall  be  tangent  to  the  circle  F'  A"  G',  representing  the  base  of  the 
cylinder  laid  down  on  the  horizontal  plane ;  through  the  point  of  tangency, 
A",  draw  a  line,  A'  E',  parallel  to  the  axis  of  the  cylinder,  for  the  line  of 
shade. 

Fig.  306  represents  a  cylinder  upon  which  a  shadow  is  thrown  by  a  rec- 
tangular cap,  of  which  the  sides  are  parallel  to  the  planes  of  projection.  The 
shadow  in  this  case  is  derived  from  the  edges  A'  D'  and  A'  E',  the  first  of  which, 
being  perpendicular  to  the  plane  of  projection,  gives  a  straight  line  at  an  angle 
of  45°  for  the  outline  of  its  shadow,  whereas  the  side  A'  E'  being  parallel  to 


152 


SHADES  AND  SHADOWS. 


that  plane,  its  shadow  is  determined  by  a  portion  of  a  circle,  a  b  c,  described 
from  the  centre,  0. 

If  the  cap  be  hexagonal  (Fig.  307),  or  circular  (Fig.  308),  the  mode  of  con- 
struction is  similar.     Commence  by  finding  the  points  which  indicate  the  main 


FIG.  306. 


FIG.  307. 


FIG.  308. 


direction  of  the  outline.  To  ascertain  the  point  a  at  which  the  shadow  com- 
mences, draw  from  a'  the  line  a'  A'  at  an  angle  of  45°,  and  projected  vertically 
to  a  A.  Then  the  highest  point  b  (Fig.  308)  is  determined  by  the  intersection 
of  the  radius  0'  B',  drawn  parallel  to  the  ray,  with  the  circumference  of  the 
base  of  the  cylinder  on  which  the  shadow  is  cast ;  the  point  c,  where  the  outline 
of  the  cast  shadow  intersects  the  line  of  shade,  is  determined  by  a  like  process. 
In  Figs.  309,310,  and  311  a  hexagonal  prism  is  substituted  for  the  cylinder. 


c" Si 


FIG.  309. 


FIG.  310. 


FIG.  311. 


Fig.  312  shows  the  section  of  a  steam-cylinder  by  a  plane  passing  through 
its  axis,  with  its  piston  and  rod  in  full.  To  define  its  shadows,  conceive  the 
piston  P  to  be  removed ;  the  shadow  cast  into  the  interior  of  the  cylinder  will 
then  consist  of  that  projected  bjf  the  vertical  edge  B  C,  and  by  a  portion  of  the 
horizontal  edge  B  A.  To  find  the  first,  draw  through  B'  a  line,  B'  #',  at  an 
angle  of  45°  with  B'  A' ;  the  point  b',  where  this  line  meets  the  interior  surface 
of  the  cylinder,  being  projected  vertically,  gives  the  line  bf  as  the  outline  of 


SHADES  AND   SHADOWS. 


153 


SEF 


k  A 


the  shadow  sought.  Then,  parallel  to  the  direction  of  the  light,  draw  a  tangent 
at  F'  to  the  inner  circle  of  the  base ;  its  point  of  contact,  being  projected  to  F 
in  the  elevation,  marks  the  commencement  of  the  outline 
of  the  shadow  cast  by  the  upper  edge  of  the  cylinder. 
The  point  #,  where  it  terminates,  will  be  the  intersection 
of  the  straight  line  fb,  already  determined,  with  a  ray, 
B  b,  from  the  upper  extremity  of  the  edge  B  C  ;  and  any 
intermediate  point  in  the  curve,  as  e,  may  be  found  in  the 
same  way.  The  outline  of  the  shadow  required  will  then 
be  the  curve  F  e  b  and  the  straight  line  b  f.  Insert  the 
piston  P  and  its  rod  T  into  the  cylinder,  as  shown.  The 
lower  surface  of  the  piston  will  then  cast  a  shadow  upon 
the  interior  surface  of  the  cylinder,  of  which  the  outline 
D  d  h  o  may  be  formed  as  above.  The  piston-rod  T, 
being  cylindrical  and  vertical,  casts  a  shadow  into  the  in- 
terior of  the  cylinder,  consisting  of  the  rectangle  ij  I  Tc 
drawn  parallel  to  the  axis. 

In  Fig.  313  is  shown  the  interior  of  a  cylinder  closed 
at  the  top  with  the  exception  of  a  central  apertur.e 
through  which  the  light  is  admitted.  Follow  previous  construction,  but  to 
determine  what  parts  of  the  upper  and  lower  edges  of  the  central  aperture 
cast  their  shadows  into  the  interior  of  the  cylinder,  establish  the  position  of 
the  point  of  intersection,  c,  of  the  two  curves  b  c  /and  ace,  shadows  of  these 
edges,  which  is  the  cast  shadow  of  the  lowest  point,  C,  in  the  curve  D  C,  pre- 
viously laid  down  in  the  circular  opening  of  the  cover. 

For  the  shadow  cast  in  the  interior  of  a  cylinder,  in  section,  inclined  to  the 
horizontal  plane  (Fig.  314),  on  a  convenient  part  of  the  paper  draw  the  diag- 


FIG.  312. 


FIG.  313. 


FIG.  314. 


FIG.  315. 


onal  m  o,  parallel  to  the  line  of  light  A'  E,  and  construct  a  square,  mnop  (Fig. 
315) ;  from  one  of  the  extremities,  o,  draw  the  line  o  r,  parallel  to  A'  B',  and 
through  the  opposite  extremity,  m,  draw  a  perpendicular,  r  s,  to  this  line,  and 
set  off  on  the  perpendicular  the  distance  r  s  equal  to  the  side  of  the  square,  and 
join  s  o.  Now,  draw  through  the  point  A',  in  the  original  figure,  a  line,  A'  a', 


154: 


SHADES  AND   SHADOWS. 


FIG.  316. 


parallel  to  s  o,  intersecting  the  cir- 
cle A'  a'  B'  in  the  point  a',  which, 
being  projected  by  a  line  parallel  to 
the  axis  of  the  cylinder,  and  meet- 
ing the  line  drawn  from  A  at  an 
angle  of  45?,  gives  the  first  point 
a  in  the  curve  C  d  a.  The  other 
points  are  obtained  in  like  manner, 
by  drawing  at  pleasure  other  lines, 
such  as  D'  d',  parallel  to  A'  a'. 

For  the  shadow  cast  into  the  in- 
terior of  a  hollow  hemisphere  (Fig. 
316),  let  A  B  C  D  represent  the 
horizontal  projection  of  a  concave 
hemisphere.  Draw  through  the 
centre  a  line,  A  C,  perpendicular  to 
the  ray  of  light ;  the  points  B  and 

D  will  at  once  give  the  extremities  of  the  curves  sought.     On  any  point  of  B  D 
produced,  as  0',  construct  the  semicircle  A'  a'  C'  with  a  radius,  A'  0',  equal  to 

A  0.     At  A'   draw   the  line 
B*  A'  #',  making  an  angle  of  35° 

f/'^g  16'   with   A'  C'.      The '  angle 

made  by  the  ray  of  light  in 
space  with  the  planes  of  pro- 
jection, a',  the  point  of  inter- 
section  of   the   line  with   the 
semicircle,  projected  to  «,  gives 
a  point  of  the  outline  of  the 
shadow.  Similar  sections,  as  EF 
parallel  to  A  C,  will  give  other  points.     As  this 
outline  is  an  ellipse  whose  axes  are  B  D  and  twice 
0  a,  it  may  be  constructed,  when  the  point  a  is 
determined,  by  the  ordinary  methods  for  ellipses. 
In  a  niche  (Fig.  317)  the  shadow  of  the  cir- 
cular outline  upon  the  spherical  portion  is  part 
of  an  ellipse,  e  c  D,  found  as  in  the  previous 
example.     The  point  e,  where  this  ellipse  cuts 
the  horizontal  diameter  A  F,  limits  the  cast 
shadow  upon  the  spherical  surface ;  therefore 
all  the  points  beneath  it  must  be  determined 
upon  the  cylindrical  part.     Through  A'  in  the 
plan  draw  the  line  A'  a'  parallel  to  the  ray  of 
light;  project  a'  till  it  intersects  the  line  of 
light  A  a  in  the  elevation  at  a.     The  line  of 
shadow  below  a  is  the  shadow  of  the  edge  of 
the  cylinder,  and  is  a  straight  line.     The  line 
of  shadow  between  a  and  e  is  the  outline  of  the 
317-  circular  part  falling  on  a  cylindrical  surface. 


0' 


>E 


SHADES   AND   SHADOWS. 


157 


exterior  of  the  ring.     Draw  rays  of  Alight  through  E*  F4,  draw  a  diagonal  ray 
tangent  at  <?,  transfer  e1  C1  to  C*  e* ;  C3  e*  will  be  half  the  minor  axis,  and  Ea  Fa 
the  major  axis  of  the  ellipse  which  defines 
the  limit  of  shadow  for  the  interior  of  the 
ring. 

The  shadow  on  the  surface  of  a  grooved 
pulley  (Fig.  320)  is  cast  by  the  circumfer- 
ence of  the  edge  A'  B'.  Draw  central  lines 
through  C  of  the  plan  and  describe  a  circle 
C  b  with  the  radius  of  the  least  diameter  of 
the  pulley ;  from  b  draw  a  line  b  a  at  an 
angle  of  45° ;  project  a  to  a',  and  from  a' 
draw  a'  b'  as  a  limiting  point  in  the  line  of 
shade,  for  another  point  draw  a  horizontal 
line  from  b'  intersecting  the  centre  line  at 
b* ;  project  c  and  d  on  the  plan  to  the  ele- 
vation, and  intersect  the  projection  of  d  at 
d'  by  a  ray  of  light  from  c' ;  d1  is  the  high- 
est point  in  the  curve.  Take  any  horizon- 
tal line  E  F  in  the  elevation  and  describe 
from  C  on  the  plan  an  arc  with  a  radius 

equal  to  one  half  this  line ;  draw  from  C'  a  ray  intersecting  E  F  at  e,  which 
project  to  e',  and  from  e'  as  a  centre  describe  an  arc  with  a  radius  equal  to  C  B ; 
the  point  of  intersection  of  this  arc  with  the  circumference  of  the  plan  E  F  is 
projected  to/'.  The  limit  of  shade  is  then  drawn  through  the  points  #',  d',  #*, 
/',  and  g. 


FIG.  320. 


FIG 


Fig.  321  represents  the  projections  of  a  screw  with  a  single  square  thread, 
and  placed  in  a  horizontal  position,  A'  a'  being  the  direction  of  the  ray  of 
light.  The  shadow  is  simply  that  cast  by  the  outer  edge,  A  B,  of  the  thread 
upon  the  surface  of  the  inner  cylinder ;  its  outline  is  delineated  in  the  same 


158 


SHADES  AND  SHADOWS. 


manner  as  in  treating  of  a  cylinder  surmounting  another  of  smaller  diameter 
(Fig.  308). 

The  shadow  cast  by  the  helix  ABC  upon  the  concave  surface  of  the  square- 
threaded  nut  is  a  curve,  a  C  (Fig.  322),  determined  in  the  same  way  as  that 
in  the  interior  of  a  hollow  cylinder.  The  same  rule  applies  to  the  edges  A  A2 


/ 


V\^\\ 

;<  ^V  \ 


«K— -^ 


A- 

!    '    J  \  I 

L     f\— /— 

#—"-    \  / 
)^'- 


kx 


/ 


FIG.  32a. 


and  A"  E,  as  well  as  to  those  of  the  helix  F  G  H  and  the  edge  H  I.  The  shadow 
of  the  two  edges  J  K  and  K  L,  thrown  upon  an  inclined  helical  surface,  of 
which  A  L  is  the  generatrix,  follows  the  rules  given  in  Fig.  323. 


FIG.  323. 


SHADES  AND   SHADOWS. 


159 


-  In  the  case  of  a  triangular-threaded  screw  (Fig.  323)  the  outer  edge,  A'  C  D, 
of  the  thread  projects  its  shadow  upon  a  helical  surface  inclining  to  the  left,  of 
which  the  generatrix  is  known. 

Describe  from  the  centre  0  a  number  of  circles  representing  the  bases  of  so 
many  cylinders,  on  the  surfaces  of  which  suppose  helical  lines  to  be  traced  of 
the  same  pitch  as  those  which  form  the  exterior  edges  of  the  screw.  Draw  any 
line  parallel  to  the  ray  of  light,  as  B'  E',  cutting  the  circles  described  in  the 
plan  in  the  points  B',  F',  G',  E',  which  are  projected  to  their  corresponding 
helical  lines  in  the  elevation  at  B3,  F,  G,  and  E.  Transferring  the  point  B'  to 
its  appropriate  position  B  on  the  edge  A'  C  D,and  drawing  through  the  latter  a 
line,  B  i,  at  an  angle  of  45°,  its  intersection  with  the  curve  B3  G  E  will  give  one 
point  in  the  curve  of  the  shadow  required.  By  constructing  other  curves,  as 
H  J  K,  the  remaining  points  in  the  curve,  as  h,  may  be  found. 


C- 


•—          x  \ 


J) 


L 


FIG.  324. 


The  same  processes  are  requisite  to  determine  the  outlines  of  the  shadows 
cast  into  the  interior  surfaces  of  the  corresponding  nut  (Fig.  324).  These 
shadows  are  derived  not  only  from  the  helical  edge,  A  B  D,  but  also  from  that 
of  the  generatrix,  A  C. 

The  principles  here  laid  down  and  illustrated  are  a  sufficient  guide  for  the 
delineation  of  the  shades  and  shadows  of  nearly  all  ordinary  forms  and  com- 
binations of  machinery  and  architecture.  Students  should  not  copy  the  figures 
as  here  represented,  but  should  adopt  some  convenient  scale  somewhat  larger, 
and  construct  drawings  according  to  the  description. 

MANIPULATION"    OF   SHADING    AND    SHADOWS,    AND    METHODS    OF   TINTING. 

The  intensity  of  a  shade  or  shadow  is  regulated  by  the  forms  of  bodies,  the 
position  that  they  occupy  in  relation  to  the  light,  and  the  distance  from 
the  eye. 


160  SHADES  AND  SHADOWS. 

Surfaces  in  the  Light. — Flat  surfaces  wholly  exposed  to  the  light,  and  at 
all  points  equidistant  from  the  eye,  receive  a  uniform  tint. 

Of  two  parallel  surfaces,  the  one  nearer  the  eye  receives  a  lighter  tint.  Every 
surface  exposed  to  the  light,  but  not  parallel  to  the  plane  of  projection,  having 
no  two  points  equally  distant  from  the  eye,  receives  unequal  tints,  gradually 
increasing  in  depth  as  the  parts  recede  from  the  eye.  Of  two  surfaces  un- 
equally exposed  to  the  light,  the  one  more  nearly  perpendicular  to  the  rays  re- 
ceives the  fainter  tint. 

Surfaces  in  Shade. — When  a  surface  entirely  in  the  shade  is  parallel  to  the 
plane  of  projection,  it  receives  a  uniform  dark  tint.  Of  two  objects  in  the 
shade  parallel  to  each  other,  the  one  nearer  the  eye  receives  the  darker  tint. 
On  a  surface  in  the  shade,  inclined  to  the  plane  of  projection,  the  parts  nearest 
the  eye  receive  the  deepest  tint. 

If  two  surfaces  exposed  to  the  light,  but  unequally  inclined  to  its  rays,  have 
a  shadow  cast  upon  them,  the  part  of  it  which  falls  upon  the  more  lighted  sur- 
face should  be  darker  than  where  it  falls  upon  the  other  surface. 

The  methods  of  shading  generally  adopted  are  either  by  the  superposition 
of  any  number  of  flat  tints,  or  by  tints  softened  off  at  their  edges. 

(See  Plates  I,  II,  III,  IV,  V,  XI,  XII,  and  XV.) 

In  the  shading  of  a  prism  by  flat  tints  (Plate  I,  Fig.  4),  the  face,  a  b  c  d, 
being  parallel  to  the  plane  of  projection,  receives  a  uniform  tint  usually  of  India 
ink  or  sepia.  When  the  surface  to  be  tinted  is  large,  put  on  a  very  light  tint 
first,  and  then  go  over  the  surface  with  a  tint  sufficiently  dark  to  give  the 
desired  tone.  The  face,  b  g  h  c,  being  inclined  to  the  plane  of  projection,  re- 
ceives a  graduated  tint  from  the  line  b  c  to  the  line  g  h.  This  is  obtained  by 
laying  on  a  succession  of  flat  tints.  Divide  the  plan  V  g'  into  equal  parts,  as  at 
the  points  1',  2',  and  from  these  points  project  lines  upon,  and  parallel  to  the 
sides  of,  the  face  b  g  h  c.  These  lines  should  be  drawn  very  lightly  in  pencil, 
as  they  merely  serve  to  circumscribe  the  tints.  A  grayish  tint  is  then  spread 
over  the  portion  of  the  face  between  the  lines  b  c  and  1,  1  (Fig.  2).  When  this 
is  dry,  the  same  tint  is  laid  on  again,  and  extended  over  the  space  comprised 
within  the  lines  b  c  and  2,  2  (Fig.  3).  A  third  tint,  covering  the  whole  surface 
be  Tig  (Fig.  4),  imparts  the  desired  graduated  shade  to  that  side  of  the  prism. 
The  number  of  tints  in  the  graduated  shade  depends  upon  the  size  of  the  sur- 
face, and  the  depth  of  tint  must  vary  according  to  the  number  used.  The 
greater  the  number,  the  softer  the  appearance  and  the  less  harsh  the  lines  which 
border  the  different  tints.  This  method  is  preferable  to  that  sometimes  em- 
ployed of  first  covering  the  whole  surface  b  g  h  c  with  a  faint  tint,  then  putting 
on  a  second  tint  b  2  2  c,  followed  by  a  narrow  wash  Z>  1  1  c,  because  the  outline 
of  each  wash  remains  untouched  and  presents  a  prominence  and  harshness. 

The  face  a  dfe,  also  inclined  to  the  plane  of  projection,  should,  as  it  is  en- 
tirely in  the  light,  be  covered  by  a  series  of  much  fainter  tints  than  the  surface 
b  g  h  C,  which  is  in  the  shade,  darkening,  however,  toward  the  line  ef.  The 
gradation  of  tint  is  effected  as  on  the  face  b  g  h  c. 

In  shading  a  cylinder  by  means  of  flat  tints  (Figs.  5-12),  the  line  of  separa- 
tion between  the  light  and  shade,  a  b  (Fig.  6),  is  determined  by  the  radius  0  a' 
(Fig.  5),  drawn  perpendicular  to  the  rays  of  light  R  0.  The  part  of  the  eleva- 
tion of  the  cylinder  which  is  in  the  shade  is  comprised  between  the  lines  a  b 


SHADES  AND  SHADOWS. 

and  c  d.  This  portion,  then,  should  be  shaded  as  a  surface  in  the  shade  in- 
clined to  the  plane  of  projection.  All  the  remaining  part  that  is  visible  of  the 
cylinder  presents  itself  to  the  light ;  but,  in  consequence  of  its  curvature,  the 
rays  of  light  form  angles  varying  at  every  part  of  its  surface,  which  should  re- 
ceive a  graduated  tint.  Determine  the  part  of  the  surface  that  is  most  directly 
affected  by  the  light,  situated  about  the  line  ei  (Fig.  12).  The  visual  rays  are 
perpendicular  to  the  vertical  plane  and  parallel  to  V  0  ;  the  part  which  ap- 
pears clearest  to  the  eye  may  be  limited  by  the  line  T  0,  which  bisects  the 
angle  V  0  R.  Project  the  points  e'  and  w',  and  draw  the  lines  e  i  and  m  n 
(Fig.  12) ;  the  surface  comprised  between  these  lines  will  represent  the  lightest 
part  of  the  cylinder. 

This  part  should  have  no  tint  upon  it  whatever  if  the  cylinder  is  polished 
— as  a  turned  iron  shaft  or  a  marble  column ;  but  if  the  surface  of  the  cylinder 
be  rough,  as  a  cast-iron  pipe,  then  a  very  light  tint,  considerably  lighter  than 
on  any  other  part,  may  be  given'  it. 

Divide  the  half- plan  of  the  cylinder/'  m'  a'  c'  into  any  number  of  equal 
parts  by  faint  pencil-lines,  and  begin  the  shading  by  laying  a  tint  over  a  c  d  b 
(Fig.  6).  When  this  is  dry,  put  on  a  second  tint  covering  the  line  a  b  of  sepa- 
ration of  light  and  shade,  and  extending  over  one  division  (Fig.  7).  Proceed 
in  this  way,  as  shown  in  Figs.  6-12,  until  the  whole  of  that  part  of  the  cylinder 
which  is  in  the  shade  is  covered.  Treat  in  a  similar  manner  the  part  feig 
(Fig.  12),  and  complete  the  operation  by  covering  the  whole  surface  of  the  cyl- 
inder, excepting  the  surface  e  m  n  *',  with  a  very  light  tint. 

In  shading  the  frustum  of  a  hexagonal  pyramid  (Plate  II),  the  face  abed 
should  receive  a  uniform  flat  tint,  as  in  Plate  I,  or  the  tint  may  be  slightly  deep- 
ened toward  the  top  of  the  pyramid,  as  that  surface  is  not  quite  parallel  to  the 
vertical  plane. 

The  face  b  g  h  c,  being  inclined  and  in  the  shade,  should  receive  a  dark  tint ; 
darkest  where  it  meets  the  line  b  c,  and  gradually  becoming  lighter  as  it  ap- 
proaches the  line  g  h.  To  produce  this  effect,  apply  a  narrow  strip  of  tint  at 
be  (Fig.  6),  and  then,  qualifying  the  tint  in  the  brush  with  a  little  water,  join 
another  strip  to  this,  and  finally,  by  means  of  another  brush  moistened  with 
water,  soften  off  this  second  strip  toward  the  line  1,  1,  which  may  be  taken  as 

the  limit  of  the  first  tint. 

\ 

When  the  first  tint  is  dry,  cover  it  with  a  second,  which  must  be  similarly 
treated,  and  should  extend  up  to  the  line  2,2  (Fig.  7).  Proceed  in  this  manner 
with  other  tints,  until  the  whole  face  b  g  li  c  is  shaded  (Fig. '8).  In  the  same 
way  the  face  e  a  dfis  to  be  covered,  though  with  a  considerably  lighter  tint,  for 
the  rays  of  light  fall  upon  it  almost  perpendicularly. 

The  tint  on  these  two  faces  should  be  slightly  graduated  from  ea  tofd,  and 
from  cli  to  b  g ;  but  this  graduation  may  be  disregarded  until  some  proficiency 
in  shading  has  been  acquired. 

In  shading  a  cylinder  by  means  of  softened  tints  (Plate  II),  the  boundary 
of  each  tint  being  indicated, 'as  in  Plate  I,  the  first  strip  of  tint  must  cover  the 
line  of  extreme  shade  a  b,  and  then  be  softened  off  on  each  side.  Other  succes- 
sively wider  strips  of  tint  follow,  and  receive  the  same  treatment  as  the  one  first 
put  on. 

If,  after  shading  a  figure  by  the  foregoing  method,  any  very  apparent  iue- 
12 


162  SHADES  AND   SHADOWS. 

qualities  present  themselves  in  the  shades,  such  defects  may  be  remedied,  in 
some  measure,  by  washing  off  excesses  of  tint  with  a  brush  or  a  damp  sponge, 
and  by  supplying  a  little  colour  to  those  parts  which  are  too  light. 

Dexterity  in  shading  figures  by  softened  tints  is  facilitated  by  practising 
upon  large  surfaces. 

Whatman's  best  rough-grained  drawing-paper  is  better  adapted  for  receiving 
colour  than  any  other.  Of  this  paper,  the  double-elephant  size  is  preferable,  as 
it  possesses  a  peculiar  consistence  and  grain.  The  face  of  the  paper  to  be  used 
is  the  one  on  which  the  water-mark  is  read. correctly. 

The  paper  for  a  coloured  drawing  ought  always  to  be  damp-stretched 
(page  54). 

The  size  of  the  brushes  used  depends  upon  the  scale  to  which  the  drawing 
is  made.  Long,  thin  brushes,  however,  should  be  avoided.  Those  possessing 
corpulent  bodies  and  fine  points  are  to  be  preferred,  as  they  retain  a  greater 
quantity  of  colour,  and  are  more  manageable. 

Sable  brushes  are  more  durable  and  better  than  camel's  hair,  but  more  ex- 
pensive. Economy  may  be  practised  by  using  camel's  hair  for  the  larger  sizes 
and  red  or  black  sable  for  the  smaller. 

During  the  process  of  laying  on  a  flat  tint,  if  the  surface  be  large,  the  draw- 
ing may  be  slightly  inclined,  and  the  brush  well  charged  with  colour,  so  that 
the  lower  edge  of  the  tint  may  be  kept  moist  until  the  whole  surface  is  covered. 
In  tinting  a  small  surface,  the  brush  should  never  have  much  colour  in  it,  other- 
wise the  surface  will  unavoidably  present  coarse,  ragged  edges,  and  an  uneven 
appearance  throughout. 

All  objects  with  curved  outlines  have  a  certain  amount  of  reflected  light 
imparted  to  them.  Bodies,  whatever  may  be  their  form,  are  affected  by  re- 
flected light;  but,  with  a  few  exceptions,  this  light  is  only  appreciable  on 
curved  surfaces. 

In  proportion  to  its  degree  of  polish  or  brightness  is  the  amount  of  reflected 
light  which  a  body  spreads  over  adjacent  objects,  and  also  its  own  susceptibility 
of  illumination  under  the  reflection  from  other  bodies.  A  polished  steam- 
cylinder  or  a  white  porcelain  vase  both  receives  and  imparts  more  reflected  light 
than  a  rough  casting  or  a  stone  pitcher. 

Shade,  even  the  most  inconsiderable,  ought  never  to  extend  to  the  outline 
of  any  smooth  circular  body.  On  a  polished  sphere  the  shade  should  be  deli- 
cately softened  off  just  before  it  meets  the  circumference,  and,  when  the  shad- 
ing is  completed,  the  body-colour  intended  for  the  sphere  may  be  carried  on  to 
its  outline.  This  will  give  a  clearness  to  the  part  of  the  sphere  influenced  by 
reflected  light  which  it  could  not  have  possessed  if  the  shade-tint  had  been  ex- 
tended to  its  circumference.  Very  little  shade  should  be  suffered  to  reach  the 
outlines  even  of  rough  circular  bodies,  lest  the  colouring  present  a  harsh, 
unreal  appearance. 

Shadows  become  lighter  as  they  recede  from  the  bodies  which  cast  them, 
and  appear  to  increase  in  depth  as  their  distance  from  the  spectator  diminishes. 
In  Nature  this  increase  is  only  appreciable  at  considerable  distances.  But  it  is 
important  for  the  effective  representation  of  machinery  that  the  variation  in 
the  distance  of  each  part  from  the  spectator  should  strike  the  eye,  and  an  exag- 
geration in  expressing  the  varying  depths  of  the  shadows  is  one  means  of  effect- 


SHADES  AND  SHADOWS.  163 

ing  that  object.  The  shadows  on  the  nearest  and  most  prominent  parts  of  a 
machine  should  be  made  as  dark  as  colour  can  render  them,  the  colourist  being 
thus  enabled  to  exhibit  a  marked  difference  in  the  shadows  on  the  other  parts 
of  the  machine  as  they  recede  from  the  eye.  The  same  direction  is  applicable 
to  shades.  The  shade  on  a  cylinder,  situated  near  the  spectator,  ought  to  be 
darker  than  on  one  more  remote.  As  a  general  rule,  the  colour  on  a  machine 
should  become  lighter  as  the  parts  on  which  it  is  placed  recede  from  the  eye. 

Plates  III  and  IV  present  some  examples  of  finished  shading  and  shadows 
of  the  solids  given  «under  the  head  of  "  Orthographic  Projection." 

The  direction  of  the  shades  and  shadows  in  the  elevation  is  from  the  upper 
left-hand  corner,  and  in  the  plan  from  the  lower  left-hand  corner. 

The  shadow  on  a  concave  surface  is  darkest  toward  its  outline,  and  becomes 
lighter  as  it  nears  the  edge  of  the  object.  Reflection  from  the  part  of  the  sur- 
face on  which  the  light  falls  causes  this  gradual  diminution  in  the  depth  of 
the  shadow,  the  greatest  amount  of  reflection  being  opposite  the  greatest 
amount  of  light.  No  brilliant  or  extreme  light  should  be  left  on  concave  sur- 
faces, as  such  lights  tend  to  render  it  doubtful  whether  the  objects  presented 
are  concave  or  convex.  After  the  body-colour  has  been  put  on,  a  faint  wash 
should  be  passed  very  lightly  over  the  whole  concavity.  This  will  not  only 
modify  and  subdue  the  light,  but  soften  asperities  in  the  tinting,  which  are 
particularly  unsightly  on  a  concave  surface. 

The  lightest  part  of  a  sphere  is  confined  to  a  mere  point,  around  which  the 
shade  gradually  increases  as  it  recedes.  This  point  is  not  indicated  on  the 
figure  because  the  shade-tint  on  a  sphere  ought  not  to  be  spread  over  a  greater 
portion  of  its  surface  than  is  shown  there.  The  very  delicate  and  hardly  per- 
ceptible progression  of  the  shade  in  the  immediate  vicinity  of  the  light-point 
should  be  effected  by  means  of  the  body-colour,  either  by  lightening  it  toward 
the  light  point  for  polished  or  light-coloured  curved  surfaces,  or  deepening  the 
body-colour  for  unpolished  surfaces  from  the  light  point  until  it  meets  the 
shade  tint  over  which  it  is  spread  uniformly. 

To  shade  a  sphere  effectively,  put  on  two  or  three  softened-off  tints  in  the 
form  of  crescents  converging  toward  the  light-point,  the  first  one  being  carried 
over  the  point  of  deepest  shade. 

A  ring  (Plate  IV,  Fig.  7)  is  a  difficult  object  to  shade.  To  change  with  ac- 
curate and  effective  gradation  the  shade  from  the  inside  to  the  outside  of  the 
ring,  to  leave  with  regularity  a  line  of  light  upon  its  surface,  and  to  project  its 
shadow  with  precision,  requires  attention  and  care. 

It  should  be  noted  that  the  depth  of  a  shadow  on  any  object  is  in  propor- 
tion to  the  degree  of  light  which  it  encounters  on  the  surface  of  that  object. 
In  the  plan  (Fig.  6)  the  shadow  of  the  apex  of  the  cone  falls  upon  the  lightest 
point  of  the  sphere  and  is  the  darkest  part  of  the  shadow.  The  deepest  portion 
of  the  shadow  of  the  cone  on  the  cylinder  in  the  plan  (Fig.  4)  is  where  it  coin- 
cides with  the  line  of  extreme  light.  Flat  surfaces  are  similarly  affected,  the 
shadows  thrown  on  them  being  less  darkly  expressed  according  as  their  inclina- 
tion to  the  plane  of  projection  increases.  The  body-colour  on  a  flat  surface 
should,  on  the  contrary,  increase  in  depth  as  the  surface  becomes  more  inclined 
to  this  plane. 

Reflected  lisrht  is  incident  to  shadows  as  well  as  to  shades.     This  is  observ- 


164  SHADES  AND   SHADOWS. 

able  where  the  shadow  of  the  cone  falls  upon  the  cylinder,  though  to  a  less  ex- 
tent, on  other  parts  of  these  figures.  The  reflected  light  on  the  cone  from  the 
sphere  or  cylinder  adds  greatly  to  the  effect  of  the  shadows  and  to  the  appear- 
ance of  the  objects  themselves. 

The  peculiarities  and  effects  of  light,  shade,  and  shadow  may  be  seen  in  the 
examples  of  screws  (Plate  V). 

In  topographical  and  architectural  drawing  artistic  effect  may  often  be  in- 
troduced, but  in  mechanical  drawing  distinctness  of  outline  and  accuracy  of 
expression  are  essential ;  though,  to  maintain  harmony  in  the  colouring  and  to 
equalize  the  appearance  of  the  drawing,  large  shades  should  be  coloured  less 
dark  than  small  ones,  at  equal  distances  from  the  eye,  and  no  very  dark  shad- 
ing is  permissible. 

In  preparing  colours  for  tints,  great  care  should  be  used  in  grinding.  The 
end  of  the  cake  should  be  slightly  wetted  and  rubbed  on  a  porcelain  palette, 
then  transferred  by  a  wet  brush  to  another  saucer,  and  water  added  to  bring 
to  the  required  tint.  Mixed  colours  should  be  intimately  blended  by  the  brush. 
Grind  more  than  enough  of  the  tint  required,  and  let  it  stand  in  the  saucer 
till  the  grosser  particles  have  settled  and  the  liquid  is  of  clear,  uniform  tint. 
It  is  common  to  make  little  boxes  or  bags  of  waste  drawing-paper  to  hold  the 
colours  instead  of  saucers ;  the  gross  matters,  settling  on  the  bottom,  are  not 
then  so  readily  disturbed. 

Instead  of  hard  cakes  of  colour,  moist  colours  are  used,  either  in  pans  or 
tubes,  which  saves  the  trouble  of  grinding.  For  flat  tints  or  washes,  aniline 
colours,  dissolved  in  water  and  kept  bottled,  are  the  readiest  means  of  colour- 
ing, but  are  not  applicable  to  finished  work. 

If  the  surface  of  the  paper  is  greasy  and  resists  colours,  dissolve  a  piece  of 
ox-gall,  the  size  of  a  pea,  in  a  tumbler  of  water,  and  use  this  solution  with  the 
colours  instead  of  plain  water. 

When  the  brush  is  too  full,  as  it  comes  toward  the  limit  of  the  tint,  take  up 
the  surplus  moisture  on  a  wet  sponge  or  piece  of  cloth  or  blotting-paper. 

An  expeditious  way  of  shading  a  cylinder,  or  of  delineating  the  shores  of  a 
stream  or  lake,  is  by  drawing  with  a  brush  full  of  the  darkest  tint  along  the 
sides,  and  then,  with  a  wet  brush,  modifying  this  tint  toward  the  light  from 
the  sides,  so  as  to  give  a  shaded  appearance.  For  this  purpose,  two  brushes 
will  be  necessary — one  with  colour,  the  other  with  water ;  also,  a  tumbler  of 
water,  and  a  piece  of  blotting-paper,  to  take  up  the  excess  of  moisture  from 
paper  or  brush.  Often  a  single  line  of  dark  colour  blended  this  way  will  ex- 
press all  that  is  necessary,  but  the  effect  may  be  improved  by  a  sort  of  stippling 
with  the  colour-brush  and  by  extending  the  line  of  shade. 

The  same  effect  is  obtained  better  by  drawing  two  faint  pencil-lines  on  the 
elevation  of  the  cylinder,  for  instance,  to  indicate  the  extremes  of  light  and 
shade  on  its  surface  and  passing  the  brush,  moderately  full  of  the  darkest  tint, 
down  the  line  of  deepest  shade,  spreading  the  colour  more  or  less  on  either  side, 
according  to  the  diameter  of  the  cylinder ;  then,  before  this  layer  of  tint  is  dry, 
if  possible,  toward  the  line  of  extreme  light,  beginning  at  the  top,  and  encroach- 
ing slightly  over  the  edge  of  the  first  tint,  lay  on  another  not  quite  so  dark,  but 
about  double  its  width.  Put  on  the  second  tint  before  the  first  is  thoroughly 
dry,  that  its  edges  may  be  softened  by  the  application  of  the  second.  While 


SHADES  AND   SHADOWS. 


165 


this  second  tint  is  still  damp,  with  a  much  lighter  colour  in  the  brush,  pro- 
ceed in  the  same  manner  with  a  third  tint,  and  so  on  to  nearly  the  line  of  ex- 
treme light.  Eepeat  this  process  on  the  other  side  of  the  first  tint,  approach- 
ing the  outline  of  the  cylinder  with  a  very  faint  wash,  so  as  to  represent  the 
reflected  light  which  progressively  modifies  the  shade  as  it  nears  that  line. 
Then  let  a  darkish  narrow  strip  of  tint  meet  and  pass  along  the  outline  of 
the  cylinder  on  the  other  side  of  the  extreme  line  of  light,  after  which  gradu- 
ally fainter  tints  should  follow,  treated  in  the  manner  already  described,  and 
becoming  almost  imperceptible  just  before  arriving  at  the  line  of  light. 

But  it  is  not  possible,  by  the  above-described  means  alone,  to  impart  a  suf- 
ficient degree  of  well-regulated  rotundity  to  the  appearance  of  such  an  object. 
It  may  be  necessary  to  equalize  the  superfluities  and  deficiencies  of  colour  to 
some  extent  by  a  species  of  gross  stippling.  This  is  done  by  spreading  a  little 
colour  over  the  parts  where  it  is  deficient,  and  then  passing  the  brush;  supplied 
with  a  very  light  wash,  very  lightly  over  nearly  the  whole  width  of  the  shade. 
This  process  may  be  repeated  to  suit  the  degree  of  finish  which  it  is  desired  to 
give  the  drawing.  The  shading  of  all  curved  surfaces  is  treated  in  the  same 
manner. 

The  shades  having  been  put  in,  the  shadows  follow.  Draw  the  outline  of 
the  shadow  in  pencil,  and  along  its  inner  line,  the  line  which  forms  a  portion 
of  the  figure  of  the  object  whose  shadow  is  to  be  represented,  lay  on  a  strip  of 
the  darkest  tint,  wide  or  narrow,  according  to  the  width  of  the  shadow,  and 
then,  before  it  is  dry,  soften  off  its  outer  edge. 

The  finish  is  made  by  a  light  wash  or  two  of  the  body-colour,  and  in  pass- 
ing over  the  shades  and  shadows  care  must  be  taken  to  manoeuvre  the  brush  at 
such  parts  quickly  and  lightly. 

The  shades  and  shadows  of  a  machine  being  modified  in  intensity  as  their 
distance  from  the  eye  increases,  its  body-colour  should  be  treated  in  a  similar 
manner,  becoming  less  bright  as  the  parts  of  the  machine  which  it  covers  recede 
from  the  spectator. 

When  the  large  circular  members  of  a  machine  have  been  shaded,  the  shad- 
ows, and  even  the  body-colour  on  those  parts  farthest  removed  from  the  eye,  are 
to  follow,  and  the  proportion  of  India  ink  in  the  tint  used  should  increase  as 
the  part  to  be  coloured  becomes  more  remote.  A  little  washing,  moreover,  of 
the  most  distant  parts  is  allowable,  as  it  gives  a  pleasing  appearance  of  atmos- 
pheric remoteness,  or  depth,  to  the  colour  thus  treated. 

The  amount  of  light  and  reflection  on  the  members  of  a  machine  should 
diminish  in  intensity  as  the  distance  of  such  objects  from  the  spectator  in- 
creases. As  it  is  necessary,  for  effect,  to  render  on  the  parts  of  a  machine  near- 
est the  eye  the  contrast  of  light  and  shade  as  intense  as  possible,  so,  for  the 
same  object,  the  light  and  shade  on  the  remotest  parts  should  be  subdued  and 
blended  according  to  the  extent  or  size  of  the  machine. 

To  add  to  the  definiteness  of  a  coloured  mechanical  drawing,  it  is  well  to 
make  the  lines  of  light  and  shade  distinct. 

After  having  marked  in  pencil  the  position  of  the  extreme  light,  take  #ie 
drawing-pen,  filled  with  a  just  perceptible  tint,  and  draw  a  line  of  colour  on 
one  side  of  the  line  of  light,  almost  touching  it ;  then  with  the  brush,  filled 
with  similar  light  tint,  join  this  line  of  colour  while  still  wet,  and  fill 'up  the 


166  SHADES  AND  SHADOWS. 

space  unoccupied  by  the  shade-tint,  within  which  the  very  light  colour  in  the 
brush  will  disappear.  Treat  the  part  of  the  object  on  the  other  side  of  the  line 
of  light  in  the  same  way.  The  extreme  depth  of  shade  may,  with  great  effect, 
be  indicated  by  filling  the  pen  with  dark  shade-tint,  and  drawing  it  exactly 
over  the  line  representing  the  deepest  part  of  the  shade.  On  either  side,  join- 
ing this  strip  of  dark  colour,  another,  of  lighter  tint,  is  to  be  drawn.  Others 
successively  lighter  follow,  until,  on  one  side,  the  line  of  the  body  is  joined,  and 
on  the  other  the  lightest  part  of  the  body  is  nearly  reached.  The  line  of  light 
is  then  to  be  shown,  and  the  faint  tint  used  for  this  to  be  spread  with  the  brush 
lightly  over  the  whole  of  the  part  of  the  body  that  is  situated  on  either  side  of 
this  line,  thus  blending  into  smooth  rotundity  the  graduated  strips  of  tint  drawn 
by  the  pen. 

In  all  tinted  drawings  the  important  parts  should  be  more  conspicuously 
expressed  than  the  mere  adjuncts.  Thus,  if  the  drawing  be  to  explain  the 
construction  of  the  machine,  the  tint  of  the  edifice  may  be  more  subdued  than 
those  of  the  machine ;  and  if  the  machine  be  unimportant,  it  may  be  repre- 
sented in  mere  outline,  while  the  edifice  is  brought  out  conspicuously. 

With  regard  to  washings,  the  soft  sponge  is  an  excellent  means  of  correct- 
ing great  errors  in  drawing  or  colouring,  but  care  must  be  taken  not  to  rub 
the  surface.  In  removing  or  softening  colour,  for  large  surfaces,  use  the  sponge ; 
for  small  spots,  the  brush.  While  colouring,  keep  a  clean,  moist  brush  by  you 
to  remove  or  modify  a  colour. 

The  immediate  effect  of  washing  is  to  soften  a  drawing,  an  effect  often  very 
desirable  in  architectural  and  mechanical  drawings,  and  the  process  is  simple 
and  easily  acquired ;  keep  the  sponge  or  brush  and  the  water  clean ;  after  the 
washing  is  complete,  take  up  the  excess  of  moisture  with  the  sponge  or  brush 
or  with  a  piece  of  clean  blotting-paper.  Where  vigour  is  required,  let  the 
borders  of  the  different  tints  be  distinct. 

There  are  no  conventional  tints  that  draughtsmen  have  agreed  upon  to  be 
uniformly  used  to  represent  different  materials.  India  ink  is  not  a  black,  but 
a  brown,  making  with  a  blue  a  greenish  cast,  and  with  gamboge  a  smear.  A 
coloured  drawing  is  better  without  the  use  of  any  India  ink  at  all ;  any  depth  of 
colour  may  be  as  well  obtained  with  blue  as  with  black.  There  is  the  objection 
to  gamboge  that  it  is  gummy,  and  does  not  wash  well,  and  a  better  effect  is  ob- 
tained with  yellow  ochre.  For  the  reds,  the  madder  colours  are  the  best,  as 
they  stand  washing.  For  the  shade-tint  of  almost  any  substance  a  neutral  tint 
is  required,  such  as  Payne's  gray,  or  madder  brown  subdued  with  indigo. 


MATERIALS. 


VARIED  materials  enter  into  the  composition  of  structures  and  machines,  or  form 
their  supports,  which  are  to  be  represented  by  the  draughtsman.  That  of  the  earths  and 
rocks,  in  their  natural  position,  are 
shown  under  the  head  of  "  Topo- 
graphical Drawing,"  or  by  a  closer 
imitation  of  Nature,  with  or  without 
colour. 

Fig.  325  represents  a  plan  and 
section  of  an  earth-bank  of  a  canal, 
with  a  paved  rock- slope. 

A  base  of  rock  may  be  represented 
by  stratifications  (Fig.  326). 

Rocks,  gravels,  sands,  muds,  etc., 
either  in  their  natural  or  structural 
positions,  are  shown  in  "Engineering 
Drawing." 

Earth,  when  first  dug,  occupies 
more  space  than  when  in  its  natural 
condition,  but,  after  a  time,  it  shrinks 
and  becomes  more  compact.  The 
earth  dug  out  of  a  hole,  when  settled, 
will  not  fill  the  hole.  Sand,  gravel, 
loam,  and  clay,  will  occupy  from  8  to  12  per  cent  less  space  than  when  in  the  natural 
cut. 

Loose,  dry  sand  weighs  from  90  to  100  pounds  per  cubic  foot;  compacted,   110; 
gravel,  about  the  same ;  clay,  in  the  bank,  120  pounds.     Sands  and  gravels  are  excellent 
material  for  embankments  and  fills.     The  slopes  in  cuts  and  fills  are  usually  H  horizon- 
tal to  1  perpendicular.     Sands  and  gravels  are  readily  drained,  and,  when  dry,  are  but 
little  affected  by  frost.     The  clays  are  hard  to  drain,  heave  with  the 
frost  when  wet,  and,  under  the  influence  of  a  thaw  or  excess  of 
water,  become  fluid,  but  well  rammed  they  are  used  as  puddle  walls 
in  the  centre  of  reservoir  embankments  for  stanchness.      In  these 
positions .  it   is   recommended  that   the   clay  should  be  compacted 
dry.     Very  fine  sand,  with  gravel,  and  perhaps  some  admixture  of 
clay,  a  glacier  till,  is  known  as  hard-pan  by  engineers,  very  difficult 
to  be  moved  with  the  pick,  and  often  requiring  blasting.     The  same 
material  wet,  but  without  gravel,  forms  a  quicksand— a  jelly-like 
material— from  which,  if  a  spadeful  be  taken  out,  the  hole  closes  up 
at  once,   and  excavation  shows  but  little  visible  sign  of  a  depression,  the  space  being 
made  good  from  the  entire  mass.     There  is  another  material,  called  quicksand,  which  is 
rather  a  running  sand — even  when  not  wet,  it  rests  with  a  very  flat  slope;  the  particles 
are  very  fine,  and  flow  like  the  sands  in  an  hour-glass. 

107 


FIG.  325. 


FIG.  326. 


168 


MATERIALS. 


Sands  and  gravels  are  large  components  of  mortars,  letons,  and  concrete ;  and  burnt 
with  clay,  of  brick,  tile,  and  pottery. 

BUILDING   MATERIALS.  ,    - 

The  natural  building  materials  of  civilized  communities  are  wood  and  stone,  which 
are  to  be  worked  or  fashioned  to  the  purposes  to  which  they  are  to  be  applied. 


FIG.  327. 


FIG.  328. 


Fig.  327  shows  various  sections  of  timber  in  which  the  rings  or  yearly  growth  are 
very  strongly  shown,  and  the  effect  of  shrinkage  by  black  margins  and  distortion,  accord- 
ing to  the  form  of  cut. 

The  strongest  timber  lies  about  one  third  the  radius  from  the  pith  in  the  butt  log ; 
in  the  top  log  the  heart  position  seems  strongest;  but  in  important  bridge  and  floor  tim- 
bers the  heart  should  be  excluded  (Fig.  328) ;  exterior  rings  or  sap  are  soft  and  liable  to 
decay. 

For  beams  or  girders,  the  timber  should  be  cut  so  that  the  stress  will  be  parallel  with, 

and  not  across,  grain.  For  posts  in 


compression,  and  lengthwise  of  the 
fibre,  the  section  may  be  from  any 
part. 

Figs.  329,  330,  and  331  are  draw- 
ings of  wood,  longitudinal  and  sec- 
tional, in  which  the  grain  of  the 
wood  is  imitated,  but  wood  is  more 
often  represented  in  plain  outline, 
and  the  cross-section  of  a  timber 
thus  (Fig.  332),  or  by  mere  hatch- 
ing. When  distinguished  by  col- 
our, burnt  sienna  is  used  commonly 


FIG.  329. 


Fm.  330. 


Fia.  331. 


FIG.  332. 
for  wood,  but  sometimes  the  colour  and  grain  of  the  wood  is  imitated. 

The  draughtsman,  for  his  designs,  will  probably  have  to  confine  himself  to  the  timber 
within  his  reach.  But  he  should  know  what  is  best  for  his  purpose,  reference  being  had 
to  economy  in  cost  and  maintenance.  For  most  purposes,  wood  should  be  seasoned,  so 
that  joints  may  not  open  under  this  operation  after  the  material  is  in  the  structure.  But, 
for  work  under  water,  wood  should  be  but  slightly  seasoned,  as  a  swelling  of  the  wood 
may  be  disastrous.  Seasoning  of  timber  may  be  done  by  exposure  for  a  time  to  outer 


MATERIALS.  169 

air-currents;  if  in  a  kiln,  it  can  be  done  speedily  with  heated  air,  or  by  steam.  For 
beams,  girders,  and  the  like,  there  should  be  few  knots,  especially  on  the  outer  edges — 
for  posts,  small  ones  are  not  objectionable ;  while  for  sidings  and  under-floors,  firm,  large 
knots  do  not  impair  the  work ;  but  no  smooth  work  can  be  made  with  knotty  lumber.  In 
most  specifications,  lumber  is  "to  be  square-edged,  without  sap,  and  large  or  loose  knots." 

In  selecting  lumber  for  a  permanent  structure,  the  life  and  endurance  of  the  material 
are  to  be  considered.  Most  of  the  woods,  sheltered  from  the  wet  and  exposed  to  air- 
currents,  will  last  for  a  very  long  time ;  but  many  will  check  and  warp  and  become  dis- 
torted. All  lumber  in  earth  beneath  the  level  of  water  will  last  indefinitely.  In  salt 
water,  above  the  earth,  all  are  subject  to  the  attacks  of  the  worm — the  Teredo  and  Lim- 
noria — and,  where  the  water  is  pure,  the  destruction  is  very  rapid.  Sewer-water  and 
fresh  water  are  both  destructive  to  the  worm.  Green  or  wet  timber,  in  positions  from 
which  the  air  is  excluded,  soon  fail  through  dry  rot,  and  even  seasoned  timber  under  un- 
favourable conditions. 

The  life  of  timber  exposed  to  wet  or  dry  rot  can  be  prolonged  by  filling  the  pores 
with  creosote,  pyrolignite  of  iron,  solutions  of  chlorides  of  mercury  or  zinc  and  various 
other  antiseptics.  There  are  works  in  which  the  timber  is  first  steamed  in  close  cylinders 
to  remove  the  sap  and  rarefy  the  air  in  the  pores,  and  then  injecting  the  preserving 
fluids.  Open  tanks  of  plank  can  be  readily  constructed,  in  which  the  soaking  of  lumber 
in  cold  solution,  especially  that  of  corrosive  sublimate,  is  effective. 

CHARACTERISTICS   AND   USE. 

White  Pine. — A  wood  of  the  most  general  application  in  the  market;  is  light,  stiff, 
easily  worked,  nails  are  easily  driven  into  it,  and  takes  paint  well,  warps  and  checks  but 
little  in  seasoning,  endures  well  in  exposed  situations ;  clear  stuff,  of  best  quality,  useful 
for  patterns  and  models,  for  interior  finish  of  houses,  doors,  window  sashes,  furniture.  It 
forms  the  base  or  inner  core  of  the  best  veneered  work,  holds  glue  well,  and  the  composite 
structure  is  better  than  single  solid  wood.  The  cheaper  kinds  of  pine  are  used  for  frames 
of  buildings,  posts,  girders,  and  beams.  Even  with  large  knots  is  well  adapted  for  board- 
ings, and  is  extensively  used  for  goods-boxes. 

Southern  Pine. — A  heavy,  strong,  resinous,  lasting  wood,  clear  and  mostly  without 
knots,  hard  to  be  worked  by  hand-tools,  and  when  seasoned  difficult  to  nail.  The  sur- 
faces, from  their  resinous  character,  do  not  hold  paint  well.  It  is  used  very  largely  for 
girders,  beams,  and  posts  of  mills  and  warehouses,  and  for  floors  of  the  same,  when  ex- 
posed to  heavy  work  or  travel.  For  the  first,  it  can  be  obtained  of  almost  any  dimension 
to  suit ;  for  floors,  it  is  sold  in  long  strips,  from  two  to  six  inches  wide,  of  varied  lengths, 
tongued  and  grooved,  and  when  laid  is  blind-nailed,  toeing  the  nail  through  the  tongue, 
so  that  the  nail-head  does  not  show. 

Experiments  of  the  Forestry  Division  of  the  United  States  Department  of  Agriculture 
prove  that  the  extracting  of  the  turpentine  from  the  long-leaf  yellow-pine  trees  does  not 
in  any  material  sense  injure  them  for  use  as  lumber.  The  bled  timber  is  heavier  in  the 
bottom  cuts  by  about  two  pounds  per  cubic  foot. 

Canadian  Red,  Norway,  and  Silver  Pines  are  resinous  woods,  like  the  Southern  pine, 
and  are  used  for  similar  purposes,  but  are  not  as  valuable — woods  less  straight  in  the 
grain,  and  with  more  knots. 

Spruce.  —  A  light,  straight-grained  wood,  with  but  few  knots,  which  are  small  and 
often  decayed.  It  does  not  last  well  exposed  to  the  weather,  and  checks  and  warps 
badly  in  seasoning.  It  is  the  most  common  wood  here  for  floor-beams  and  common 
floors,  but  it  must  be  well  braced  and  nailed,  and  is  not  fitted  for  joiner- work. 

Hemlock  is  similar  to  the  spruce,  and,  when  selected,  is  less  liable  to  check  and  twist 
in  seasoning.  It  is  often  of  a  very  poor  quality,  Irash  and  shaky.  Exposed,  it  is  but 
little  better,  if  any,  than  the  spruce.  For  stables,  it  is  well  adapted  for  grain-boxes,  as 
the  fibre  prevents  the  gnawing  of  rats. 


MATERIALS. 

Ash. — Some  of  the  ashes  are  of  exceeding  toughness.  A  straight,  close-grained  wood. 
It  is  used  for  carriage  and  machine  frames,  and  for  interiors,  doors,  wainscot,  floors, 
when  no  paint  is  used. 

Chestnut. — Somewhat  like  the  ash  in  appearance,  but  coarser-grained,  and  very  en- 
during in  exposed  positions.  It  is  most  largely  used  for  cross-ties  of  railways.  As  a 
roof-frame  exposed  in  the  inside,  and  in  general  interior  finish  without  paint,  the  effect 
is  very  good.  The  closer-grained  woods  are  very  often  thus  used. 

Black  Walnut  is,  in  the  trunk,  a  straight-grained,  gummy  wood,  clogging  the  plane 
a  little  in  its  working;  the  knots  are  useful  for  veneer.  Were  the  wood  'cheap  enough, 
it  would  undoubtedly  make  a  good  frame.  It  is  used  here  for  desks  and  counters,  for 
furniture  and  interior  finish,  as  an  ornamental  wood. 

Butternut. — Similar  to  the  black  walnut,  less  commonly  used,  but  fully  equal  as  an 
ornamental  wood. 

Hickory. — A  strong,  tough  wood;  is  used  for  cogs  of  mortise-wheels,  handspikes,  axe- 
helves,  and  wheelwrights'  work. 

Beech. — A  close-grained  wood,  but  of  little  application  in  this  market.  Sometimes 
used  for  cogs  of  wheels,  for  small  tool-handles,  and  in  marquetry. 

Oak,  Live. — A  very  strong,  tough,  enduring  wood,  used  industrially  almost  entirely 
for  ship-building.  Ornamentally,  in  marquetry  and  panels. 

Oak,  White. — A  very  valuable,  strong,  tough  wood,  with  great  endurance.  It  is 
heavy,  and  hard  to  work,  and  was  formerly  used  largely  for  the  frames  of  houses,  but 
has  been  superseded  by  the  white  pine.  It  is  used  in  ship-yards  and  in  water-works — 
for  the  frames  of  flumes,  penstocks,  and  dams,  and  for  the  planking  of  the  latter,  for 
dock-buffers  and  piles,  and  for  railway  and  warehouse  platforms.  The  red  and  black 
oaks  may  in  general  be  considered  a  cheaper  and  poorer  quality  of  the  white  oak.  All 
have  a  handsome  grain,  that  adapts  them  to  ornamental  work. 

Bass,  Poplar,  White-wood,  are  light  woods,  mostly  used  in  the  manufacture  of  fur- 
niture, for  drawer-bottoms,  cabinet-backs,  panels;  they  are  very  clear  stock,  easily 
worked,  and  can  be  readily  obtained  in  thin,  wide  boards. 

Cedar. — A  straight-grained,  light  wood,  of  great  endurance,  valuable  for  posts,  sills, 
shingles ;  used  for  pails  and  domestic  utensils.  The  red  variety,  from  its  odour,  is  ad- 
mirable for  drawers  and  chests,  preserving  their  contents  from  moths. 

Locust  is  in  the  market  only  in  small  sticks ;  is  of  extreme  endurance.  It  is  used 
almost  invariably  here  for  the  sills  of  the  lowest  floors  of  buildings,  where  there  can  be 
no  ventilation,  and  for  treenails  of  ship-planks. 

Elm. — Although  a  tree  of  wide  diffusion,  is  but  little  used  as  lumber.  It  is  kept  for 
an  ornamental  tree,  beyond  its  usefulness  for  any  other  purpose  but  fuel.  Well  selected, 
it  is  said  to  be  an  enduring  timber,  useful  for  piles  and  places  exposed  to  wet. 

Maples  are  tough,  close-grained  woods,  rather  to  be  considered  among  the  ornamental 
woods,  for  furniture  and  interior  finish.  The  same  may  be  said  of  the  cherry,  plum,  and 
apple  tree,  of  which  the  denser  woods  are  admirably  adapted  for  the  handles  of  small 
tools,  for  bushings  of  spools  and  bobbins. 

The  list  of  imported  woods  is  extremely  large,  mostly  for  ornamental  purposes;  but 
the  mahogany  is  one  of  the  very  best  of  woods  for  patterns  and  small  models,  as  it 
changes  but  little  in  seasoning;  and  the  lignum-vitae,  a  very  hard  and  heavy  wood,  is 
used  for  pulley-sheaves,  packing-rings  of  pumps,  water-wheel  steps,  and  shaft-bushings. 

Timbers  of  the  same  kind  vary  much  in  their  weight,  strength,  and  endurance,  ac- 
cording to  the  localities  in  which  they  are  grown,  the  season  at  which  they  are  cut,  and 
how  seasoned.  Tables  are  given  in  the  Appendix  in  detail,  their  varied  resistance  under 
stresses  and  their  specific  gravities. 

Of  late  years  paper  in  sheets  and  pulp  has  been  used  instead  of  woods,  and  serves 
well  many  purposes  on  account  of  its  little  shrinkage,  incombustibility,  strength,  and 
endurance. 


MATERIALS. 


171 


Earth. 


„  Concrete. 


Brick. 


^///YA/////^//,. 
y///A//////////// 


////A//. 

' 


Rubble. 


Timber. 


STONES. 

In  selecting  the  form  of  construction,  and  the  stones  of  which  it  is  to  be  composed, 
the  draughtsman  must  be  governed  by  the  fitness  for  the  purpose  and  the  cost.  He  must 
select  from  what  he  can  readily  get,  and  arrange  the  form  to  suit  the  material.  He  must 
know  what  is  to  be  the  exposure,  and  what  the  effect  will  be  on  the  stones.  Almost  any 
stone  will  stand  in  a  protected  wall,  but  many  of  the  sandstones  and  slates  disintegrate 
and  exfoliate  under  the  influence  of  the  weather,  heat,  cold,  frost,  and  moisture.  Even 
the  granites  are  liable  to  serious  decomposition  when  the  feldspars  are  alkaline ;  and  the 
limestones  (dolomites),  of  which  the  English  Houses  of  Parliament  are  composed,  have 
failed  in  the  sulphurous  air  of  London  smoke,  while  at  Southwell  Minster  they  have 
stood  for  over  800  years.  Chemical  tests  of  stone  to  determine  endurance  are  deceptive. 
The  safe  way  is  to  see  how  the  material  has  stood  in  like  situations  to  the  one  in  which 
it  is  to  be  employed,  or  go  to  the  quarry,  and  see  how  the  stones  have  weathered. 

The  strength  of  stones  to  resist  crushing,  as  determined  by  experimental  cubes,  is 
even  in  the  weaker  stones  much  in  excess  of  what  would  be  required  in  structures,  but 
most  stones  are  weak  under  cross-strains,  and  failures  in  construction  are  more  likely  to 
occur  by  faulty  workmanship  or  design,  by  which  the  stones  are  subjected  to  unequal 
strains,  and  for  which  they  are  not  adapted.  The  weight  should  not  be  brought  on  the 
outer  edges  or  arrises,  as  the  faces  will  chip  readily;  nor  should  most  stones  be  used  for 
wide-span  lintels,  unless  relieved  by  the  masonry  above  the  opening. 

TECHNICAL   TERMS   OF  MASONRY. 

Agreeably  to  the  nomenclature  recommended  in  "Transactions  of  the  American 
Society  of  Civil  Engineers,"  November,  1877: 

Rubble  masonry  includes  all  stones  which  are  used  as  they  come  from  the  quarry,  pre- 
pared at  the  work  by  roughly  knocking  off  their  corners.  It  is  called  uncoursed  rul>Ue 
(Fig.  333)  when  it  is  laid  without  any  attempt  at  regular  courses ;  coursed  rubble,  when 
levelled  off  at  specified  heights  to  a  horizontal  surface  (Fig.  334). 

Square-stoned  Masonry. — Square  stones  cover  all  stones  that  are  roughly  squared  and 
roughly  dressed  on  bed  and  joints. 

Quarry-faced  stones  are  those  which  are  left  untouched  as  they  come  from  the  quarry. 

Pitch-faced  stones  are  those  on  which  the  arris  is  clearly  defined  beyond  which  the 
rock  is  cutting  away  by  pitching-tool. 


172 


MATERIALS. 


Drafted  stones  are  those  in  which  the  face  is  surrounded  by  a  chisel-draft. 
If  laid  in  regular  courses  of  about  the  same  rise  throughout,  it  is  range-work  (Fig. 
335).     If  laid  in  courses  that  are  not  continuous,  it  is  broken  range  (Fig.  336). 


FIG.  334. 


Cut  stones  or  ashlar  covers  all  squared  stones  with  smoothly- dressed  bed  and  joints. 
Generally,  all  the  edges  of  cut  stone  are  drafted,  if  the  face  is  not  entirely  fine  cut,  but 


WTfH 


ICT*;£TI 

r^  'ltw»-  -- 


X. 


Fio.  335. 


FIG.  336. 


they  may  be  quarry-faced  or  pitch-faced ;  as  a  rule,  the  courses  are  continuous  (Figs.  337, 
338),  but,  if  broken  by  the  introduction  of  smaller  stones  of  the  same  kind,  it  is  called 
broken  ashlar  (Fig.  336 j.  If  the  courses  are  less  than  one  foot  in  height,  it  is  small  ash- 
lar (Fig.  337). 


3H  akgir'4?^^l^ 


t'"'"-";:tl  v  i  rcrpM^ifeiffrTi'''^^!^')-^ 
,:^-''^H^:;";;"i4hfe:i::^ 

Fio.  337. 


,!!!  J't 


FIG.  338. 


Squared-stoned  Masonry. — The  joints  in  one  course  should  not  come  directly  over 
those  of  another;  there  should  be  a  lap  or  bond,  and,  in  connecting  the  front  or  face  with 
the  backing,  headers  must  be  introduced  for  bond.  Headers  are  stones  extending  into 
the  wall,  stretchers  running  with  the  face. 

The  backing  is  of  rubble,  sometimes  laid  dry,  but  as  from  its  many  and  large  joints  it 
settles  more  than  the  face,  it  should  be  set  in  mortar  to  provide  uniformity  of  support. 

In  addition  there  is  a  class  of  ornamental  stone  work,  specified  as  "close  jointed, 
hammer-dressed  rubble,"  in  which  there  are  no  courses  and  no  pinners.  The  joint  of 
each  stone  is  carefully  fitted  to  those  beneath  it. 

For  rubble-work,  all  varieties  of  sound  stone  are  used,  and  of  almost  any  size.  In  dry 
work,  for  foundations  and  for  heavy  revetment-walls,  the  stones  are  laid  with  derricks, 
but  they  must  have  fair  beds  and  builds.  If  boulders,  they  must  be  split,  and  cobbles 
in  the  filling  are  worse  than  useless,  as  they  are  unstable,  and  in  settlement  act  as  wedge 
to  increase  the  movement. 


Drafted  Quarry  Face. 


MATERIALS. 

Bush  Hammered. 


Axed. 


173 


GRANITIC  STONES. 

Granite  and  syenite  are  by  builders  classed  as  granites.  The  granite  in  general  rifts 
in  any  direction,  and  works  well  under  the  hammer  and  points.  From  these  circum- 
stances it  is  more  desirable  than  the  syenites,  which  are  much  harder  to  be  worked.  Both 
are  admirable  stones  for  heavy  dock-walls,  bridge-abutments,  river-walls,  either  as 
rubble-squared  stones  or  cut  work,  and  are  very  enduring.  They  are  also  used  for  the 
faces  of  important  buildings,  either  as  fine-cut,  quarry,  or  pitched-face.  Ornamental 
work  of  the  simpler  kind  is  readily  produced ;  more  elaborate  is  expensive,  but  it  is  about 
the  only  stone  in  this  climate  in  which  foliage  and  sharp  undercut  work  will  stand  the 
weather  without  exfoliating.  These  stones,  especially  the  syenites,  admit  of  a  high 
polish,  and  are  used  considerably  for  columns  and  panels  in  buildings,  and  in  monumen- 
tal work.  Gneiss  is  of  the  granitic  order,  but  a  cheaper,  poorer  stone.  It  splits  with 
difficulty,  except  parallel  with  line  of  bed.  It  has  a  foliated  structure,  and  is  not  adapted 
for  ashlar,  but  is  very  good  for  squared-stone  masonry  and  rubble-work,  and  often  used 
for  sidewalk-covers  of  vaults. 

ARGILLACEOUS   STONES. 

The  slates  or  stones  thus  designated  by  builders  were  formerly  in  very  common  use 
as  roofing  material,  and  were  almost  entirely  from  Wales,  but  latterly  they  are  taken  from 
Vermont  and  Pennsylvania,  and  other  parts  of  the  United  States.  They  are  also  used, 
in  thicknesses  of  one  inch  and  above,  for  floors,  platforms,  facing  of  walls,  mantels,  and 
for  wash-tubs  by  plumbers.  Soap-stone  maybe  classed  under  the  clay  stones;  also,  used 
for  tubs,  for  stoves,  and  for  the  lining  of  grates  and  furnaces. 

The  Ulster,  or  North  River  blue  stone  of  this  market,  is  a  coarser  slate,  a  very  strong 
and  enduring  stone;  it  can  be  quarried  of  varying  thickness  up  to  twelve  inches,  and  of 
any  dimension  that  can  be  transported.  It  can  be  readily  cut,  hammer-dressed,  axed, 
planed,  and  rubbed.  Is  generally  used  for  sidewalks  under  these  various  forms.  It  is 
used  as  bond-stones  in  brick  piers,  for  caps,  sills,  and  string-courses. 


THE   SANDSTONES. 

Sandstones,  called  also  freestones,  from  the  ease  with  which  they  are  worked;  and 
from  their  colours,  are  very  popular  for  the  fronts  of  edifices.  In  general,  they  are  not 
very  enduring  stones,  and  when  laid  must  be  set  parallel  to  their  natural  beds,  as  other- 
wise they  flake  off  under  the  influence  of  the  weather.  The  sandstones  are  not  all  of  the 
same  quality;  those  in  which  the  cementing  material  is  nearly  pure  silex,  are  strong, 
enduring  stones,  but  not  those  in  which  the  cementing  material  is  alumina,  or  lime.  By 
examining  a  fresh  fracture,  the  character  of  the  stone  can  generally  be  detected.  A  clay, 
shining  surface  with  sharp  grains  indicate  a  good  stone;  while  rounded  grains,  a  dull, 
mealy  surface,  indicate  a  soft,  perishable  stone.  None  of  the  sandstones  in  this  locality 
are  used  for  heavy  pier  or  abutment  work  and  the  like,  but  there  are  sandstones  in  other 
localities  adapted  to  it. 

LIMESTONE. 

The  coarser  calcareous  stones  are  of  great  variety;  some  are  well  adapted  for 
building  stones,  being  hard  and  compact,  while  others  are  soft  and  friable.  They  are 
more  easily  worked  than  granite,  but  are  not  considered  as  enduring.  They  are  well 


174 


MATERIALS. 


adapted  to  the  same  class  of  heavy  work,  and  the  locks  of  the  Erie  and  Northern  Canals 
and  the  dam  across  the  Mohawk,  at  Cohoes,  are  built  from  limestone  on  the  line  of  the 
canals. 

The  finer  kinds  of  limestones  are  classed  under  the  head  of  marbles.  They  are  easily 
worked,  sawed,  turned,  rubbed,  and  polished.  Marble  is  not  popular  as  a  building 
material,  although  more  enduring  than  most  sandstones,  but  is  susceptible  to  the  action 
of  sulphurous  gases  in  the  smoky  air  of  cities ;  and  it  is  said  that  the  Capitol  at  Wash- 
ington, D.  C.,  built  of  marble,  is  suffering  from  disintegration.  But,  for  interior  finish, 
as  tiles,  wainscots,  architraves,  mantels,  linings  of  walls,  it  is  admirably  adapted,  and 
from  its  richness,  cleanliness,  and  variety  of  colour,  it  is  very  ornamental  and  effective. 


ARTIFICIAL    BUILDING    MATERIAL. 


The  most  common  and  useful  are  bricks.  They  are  generally  made  of  clay,  with  an 
admixture  of  sand,  well  incorporated  together,  and  mixed  with  water  to  the  consistence 
of  a  smooth,  strong,  viscous  mud,  pressed  into  moulds,  dried,  and  burned,  the  best  quality 
being  those  in  the  interior  of  the  kiln.  The  exteriors  are  light,  friable  bricks  adapted 
to  walls  supporting  but  little  weight  and  not  exposed  to  wet.  The  brick  forming  the 
arches  are  very  hard-burned,  dark  in  colour,  often  swelled  and  cracked ;  but,  by  proper 
selection,  they  can  be  used  for  foot-walks.  A  good  brick  is  well  burned  throughout; 
when  struck,  it  gives  a  ringing  sound,  and  is  of  uniform  shape. 

Bricks  vary  somewhat  in  size  and  weight  in  different  localities — from  8  to  8J  inches 
long  x  3£  to  4  inches  broad  x  2  to  2£  inches  thick;  in  general,  the  thickness  of  a  wall 
with  the  joints  is  called  some  multiple  of  4",  as  8",  12",  16"  .  .  .  walls,  and  the  num- 
ber of  bricks  in  such  wall  is  estimated  by  multiplying  the  number  of  brick  in  a  square 
foot  of  face  by  2,  3,  4,  ...  In  some  cases  bricks  are  laid  by  the  thousand  and  there  are 
custom  allowances  for  corners,  openings,  and  indents.  The  best  face  or  front  brick  are 
pressed  and  are  of  great  variety  of  colours,  but  uniform  in  tint.  Of  late  there  has  been  a 
class  of  face  brick  of  which  the  edges  are  taken  off  by  a  set,  leaving  the  face  like  rock- 
faced  ashlar  without  draft. 

For  variety,  Pompeian  face  brick  1£"  x  4"  x  12",  Roman  2"  x  4"  x  10",  faces  plain 
glazed  and  enamelled.  Moulded  brick  for  base,  cornices,  caps,  sills,  corners,  and  arches 
are  in  common  use. 

Bricks  are  laid  in  mortar,  of  lime,  lime  and  cement,  or  cement  only — all  with  an  ad- 
mixture of  sand ;  in  common  walls,  in  lime ;  in  walls  of  heavy  buildings,  above-ground, 
in  lime  and  cement;  beneath,  and  in  wet,  exposed  positions,  in  cement  only.  The  com- 
mon bond  of  the  different  courses  of  brick  is  by  header-courses  every  fifth  or  seventh 
course.  When  bricks  are  laid  in  arches  they  are  set  on  edge,  and  turned  in  4-inch  rings, 
without  any  bond  between  the  different  rings;  or  with  a  bond  of  brick  lengthways, 


MATERIALS.  175 

when  two  courses  come  on  the  same  line,  or  with  radial  joints,  or  alternate  4"  and  8" 
courses  of  brick  work  in  masses  laid  header  and  stretcher;  however  laid,  the  strength 
depends  on  full  joints  in  strong  cement  mortar. 

Bricks  set  on  edge,  as  in  arches  or  in  a  level  course,  are  here  termed  rowlocks. 

Arch  brick,  between  iron  beams,  to  reduce  the  weight,  are  often  made  hollow,  and 
laid  in  flat  arches ;  that  is,  the  joints  are  radial,  but  the  upper  and  lower  surfaces  are 
level.  Hollow  brick  are  also  used  for  walls  and  partitions. 

Fire-brick  can  be  made  of  any  size  and  pattern,  but  are  usually  9  x  4^  x  2f .  They 
are  used  for  the  lining  of  furnaces,  flues,  and  chimneys,  exposed  to  the  action  of  flame  or 
great  heat.  Fire-clay,  with  an  admixture  of  sawdust,  which  is  burned  out  in  the  firing, 
leaves  a  light,  porous,  spongy  mass,  which  can  be  sawed  in  sheets  or  strips,  and  is  well 
adapted  for  covering  the  exposed  parts  of  iron  beams  and  girders,  and,  as  it  admits  of 
nailing,  is  convenient  for  partitions. 

Enamelled  Brick. — The  English  size  is  that  of  fire-brick — the  American  is  that  of  com- 
mon brick.  The  brick,  on  the  faces  to  be  exposed,  are  covered  with  glaze  of  varied  colors 
and  designs,  and  fired.  They  make  a  handsome  ornamental  face  for  walls,  do  not  absorb 
moisture,  and  can  be  washed. 

Tile  are  a  species  of  brick,  with  or  without  enamel.  The  latter  were  originally  used 
for  roof-covering,  but  now  are  used  in  flooring  walks  and  the  like.  The  enameled  or 
encaustic  tile  are  generally  in  squares,  4"  x  4",  6"  x  6",  8"  x  8",  but  there  are  smaller 
ones  for  tessellation,  and  rectangular  strips  for  borders.  They  can  be  obtained  of  any 
color  or  design,  forming  beautifully  ornamented  floors  and  wall-panels. 

Terra-cotta,  a  kind  of  brick,  is  now  largely  used  for  exterior  decoration.  It  is  molded 
in  every  variety  of  capitals,  cornices,  caps,  friezes,  and  panels.  It  is  a  good,  strong  brick, 
with  all  the  good  qualities  of  such  a  material. 

Mortars. — Brick  are  never  laid  dry,  except  in  the  under  part  of  drains,  to  admit  of  the 
removal  of  ground- water.  Stone- work,  except  in  rough,  heavy,  rubble-work,  is  also  gen- 
erally laid  in  mortar.  Where  cut-work  is  backed  with  rubble,  the  joints  in  the  latter 
should  be  as  close  as  possible,  and  full  of  mortar,  that  the  settling  of  the  wall  in  itself 
may  not  be  more  in  the  backing  than  in  the  face.  Some  lay  the  rubble  dry,  and  fill  in 
with  cement  grout,  or  cement  mortar  made  liquid  to  flow  into  the  interstices,  but  the  sand 
is  apt  to  separate  and  get  to  the  bottom  of  the  course. 

By  mortar,  is  usually  understood  a  mixture  of  quicklime  and  sand,  but  mortar  may 
have-an  addition  of  cement  to  the  lime,  or  it  may  be  cement  only  with  sand. 

Lime,  or  properly  quicklime,  is  made  by  the  calcination  of  limestone,  shells,  and  sub- 
stances composed  largely  of  carbonate  of  lime,  carbonic-acid  gas,  water  of  crystallization, 
and  organic  coloring-matter.  Quicklime,  brought  in  contact  with  water,  rapidly  absorbs  it, 
with  a  great  elevation  of  temperature,  and  bursting  of  the  lime  into  pieces,  reducing  it  to 
a  fine  powder,  of  from  two  to  three  and  a  half  times  the  volume  of  the  original  lime.  This 
is  slaked  lime.  It  may  be  slaked  slowly  by  exposure  to  the  air,  from  which  it  will  take 
the  moisture.  This  is  air-slaked  lime.  Barrels  of  lime  exposed  to  rain  often  take  fire 
from  the  heat  caused  by  slaking.  The  paste  of  slaked  lime  may  be  kept  uninjured  for  a 
considerable  time,  if  protected  from  the  air,  and  this  may  readily  be  done  by  a  covering  of 
sand,  and  it  is  customary,  in  some  places,  to  hold  it  over  one  season,  as  an  improvement 
to  the  uniformity  of  quality  in  the  paste.  But,  in  general,  the  lime  is  used  soon  after 
slaking,  and  is  thoroughly  mixed  with  sand,  in  various  proportions,  generally  about  two 
of  sand  to  one  of  lime.  The  theory  of  the  mixture  is,  that  the  lime  should  fill  the  void 
spaces  in  the  sand,  and  the  space  occupied  by  the  mortar  is  a  little  in  excess  of  that  occu- 
pied by  the  sand  alone. 

The  sand  should  be  sharp,  clean,  silicious  grains,  from  one  twelfth  to  one  sixtieth  of  an 
inch  in  diameter.  Close  brick -joints  do  not  admit  of  as  coarse  sand  as  those  of cnt  stone 
work,  and,  in  rubble-work,  sand  coarser  than  the  above  can  be  used,  and  there  will  be 
considerable  saving  of  lime  in  using  a  mixture  of  coarse  and  fine  sand. 


176  MATERIALS. 

The  hydraulic  limes  contain  a  small  proportion  of  silica,  alumina,  and  magnesia ;  slake 
with  but  little  heat,  and  small  increase  of  volume ;  are  more  or  less  valuable,  according 
to  the  property  which  they  have  for  hardening  under  water;  but,  in  this  particular,  are 
not  equal  to  the  hydraulic  cements. 

There  are  two  great  distinctions  of  cements — natural,  as  quarried  from  the  rock  and 
burnt,  and  artificial,  like  Portland,  definite  proportions  from  known  materials,  generally 
preferred  from  their  uniformity  of  composition ;  but  in  this  country  the  natural  cements, 
from  old  quarries  and  responsible  makers,  are  satisfactory. 

Cement  is  used  in  all  masonry  in  exposed  and  wet  situations.  With  a  small  admix- 
ture of  lime,  it  works  better  under  the  trowel,  and  for  brick-work  it  does  not  sensibly 
impair  its  value.  Cement  adds  to  the  strength  of  lime-mortar. 

The  value  of  a  cement  depends  very  largely  on  its  fineness;  the  residue  thrown  out 
from  a  2,500-per-inch  mess  should  not  exceed  10  per  cent,  the  diameter  of  the  wire  is 
about  one  half  the  width  of  the  mesh.  This  residue  is  reckoned  as  sand.  The  voids  in 
the  sand  should  be  filled  by  the  cement.  To  determine  the  amount  of  voids  in  the  sand, 
.fill  a  tight  box  of  known  capacity  with  the  sand  and  then  pour  in  all  the  water  that  it 
will  hold.  The  whole  may  be  considered  as  unity,  and  the  quantity  of  water  the  per- 
centage of  voids.  In  the  same  way  the  voids  of  gravel  or  broken  stone  may  be  deter- 
mined for  concrete.  In  mixing  cement  mortar,  it  is  important  that  it  should  be  thorough, 
that  the  sand  should  be  clean  and  damp,  and  that  each  particle  should  be  covered  with 
cement,  and  if  to  be  used  for  concrete  or  leton,  that  the  stone  or  gravel  should  be  clean 
and  damp,  and  their  surfaces  should  be  completely  covered  with  the  mortar.  Suppose 
the  proportions  be  as  below : 

1  part  cement,  without  voids 1.0 

3  parts  sand,  30  per  cent  voids 2.1 

6  parts  broken  stone,  50  per  cent  voids 3.0 

Parts  in  mixture 6.1 

The  parts  of  sand  and  broken  stone  to  cement  are  larger  than  in  common  use,  or,  say : 

Portland 1,  3,  5 

Natural. 1,  2,  5 

But  the  increase  is  rather  as  an  offset  to  coarseness  of  cement  and  defects  in  mixing.  As 
a  rule,  from  the  time  the  water  is  added  to  the  concrete,  it  should  be  kept  damp  for  a 
month  after  it  is  laid. 

The  Danish  patent  sand  cement  is  sand  ground  Math  Portland  cement  to  a  uniform 
fineness,  and  then  used  like  pure  cement  with  great  economy  of  construction  and  without 
impairing  the  strength  of  the  mortar. 

Concrete  is  used  for  the  base  course  or  foundations  of  walls,  and  is  formed  in  situ, 
that  is,  depositing  and  ramming  it  in  the  trench  where  it  is  to  be  left ;  or  by  forming  in 
moulds,  in  immense  blocks,  for  docks  or  break- water,  or  in  the  forms  of  brick. 

The  bituminous  cements  are  formed  of  natural  bitumens,  or  artificial  from  coal-tar 
mixed  with  various  proportions  of  gravel  and  inert  material.  The  mixture  is  usually 
heated,  put  down  in  layers,  and  rolled  or  rammed.  It  is  used  for  roads  and  sidewalks, 
and  for  water-proof  covering  of  vaults.  For  the  covering  of  roofs,  coarse  paper,  sat- 
urated with  bitumen,  is  put  on  in  layers,  one  over  the  other,  breaking  joints,  cemented 
with  the  bitumen,  the  last  coat  being  of  bitumen,  in  which  gravel  is  imbedded.  For 
an  anti-damp  course  in  a  wall,  or  for  the  joints  in  the  bricks  of  a  wet  cellar-floor,  or  on 
top  of  a  roof,  hot  bitumen  is  used  as  a  cementing  material  with  dry  bricks. 

Plastering. — Coarse- stuff  is  nothing  more  than  common  brick-mortar,  with  an  admix- 
ture of  bullock's  hair.  When  time  can  not  be  given  for  the  setting  it  is  ganged,  that  is, 
mixed  with  some  plaster  of  Paris.  Fine-stuff  is  made  of  pure  lump-lime  with  an  admix- 
ture of  fine  sand,  and  perhaps  plaster  of  Paris.  Hard-finish  is  composed  of  fine-stuff  and 


MATERIALS. 


177 


plaster  of  Paris.  One-coat  work  is  of  coarse-stuff,  which  may  be  rendered,  that  is,  put  on 
masonry,  or  laid  on  laths.  Two-coat  work  is  a  coat  of  coarse-stuff,  or  scratch-coat;  that 
is,  after  the  coat  is  partially  dry  it  is  scratched  for  a  back  for  the  fine  coat.  In  three 
coats,  the  first  coat  is  a  scratch  coat,  the  second  the  brown-coat,  and  the  third  hard -finish. 
Keene's  cement,  for  the  last  finish,  gives  a  hard  surface,  which  admits  of  washing. 

A  single  brick  weighs  between  4  and  5  pounds;  but  a  cubic  foot,  well  laid  in  cement, 
with  full  joints,  will  weigh  about  112  pounds.  They  have  resisted,  in  an  experimental 
test,  as  high  as  13,000  pounds  to  the  square  inch,  but  12  tons  should  be  the  limit  to  the 
load  per  square  foot ;  and  the  brick  should  be  uniform,  well  burned,  and  closely  laid  in 
cement.  In  lime  mortar,  the  load  should  not  exceed  3  tons  per  square  foot. 

The  granites  weigh  from  160  to  180  pounds  per  cubic  foot;  the  limestones  from  150 
to  175;  the  sandstones  from  130  to  170;  the  slates  from  160  to  180;  mortar,  set,  about 
100  pounds ;  masonry,  laid  full  in  mortar,  according  to  the  quality  of  the  stone  and  the 
percentage  of  mortar,  from  150  to  170  pounds.  But,  for  practical  purposes,  common 
mortar-rubble  is  not  equal  in  strength  to  a  brick  wall,  as  it  is  seldom  laid  with  equal  care, 
with  joints  not  as  well  filled  or  the  load  as  evenly  distributed ;  but  cut  stones  will  sustain 
more,  and  ashlar,  up  to  50  tons  per  square  foot  for  sound,  strong  stones. 

METALS. 

Metals  are  often  to  be  shown  distinctively  by  the  draughtsman.  If  he  can  use  colour, 
he  will  in  a  measure  imitate  that  of  the  material.  For  cast-iron,  India-ink,  with  indigo, 
and  a  slight  admixture  of  lake ;  for  wrought-iron,  the  same  colours,  with  stronger  pre- 
dominance of  the  blue;  steel,  in  Prussian- blue ;  brass,  in  a  mixture  of  gamboge  and 
burnt  sienna;  copper,  gamboge  and  crimson  lake.  In  drawings  where  no  colour  is  ad- 
missible as  for  photographing,  or  to  be  reproduced  in  printing,  some  conventional 
hatchings  are  used  to  represent  sections  of  metals,  but  none  have  been  so  established  as 
to  have  a  universal  application.  The  following  are  submitted  to  represent  the  most  com- 
mon industrial  metals: 


Brass  or  Bronze. 


Lead.' 


Copper. 


Steel. 


Wrought  Iron. 


Cast  Iron. 


Under  the  term  iron  may  be  included  cast-iron,  wrought-iron,  and  steel,  differing  from 
each  other  in  the  percentage  of  carbon  contained,  and  in  the  uses  to  which  they  are  applied. 
Cast-iron  contains  more  carbon  than  the  others,  say  from  two  to  five  per  cent.    It  can  be 
13 


178 


MATERIALS. 


cast  in  varied  forms  in  moulds,  but  can  not  be  welded  or  tempered.  The  usual  moulds  are 
in  sand  or  loam,  in  which  the  pattern  is  imbedded,  and  when  drawn  out  the  space  is  filled 
with  molten  metal.  The  drawing  of  patterns  for  molding  involves  a  knowledge  of  the  art 
of  founding.  The  shrinkage  of  the  metal,  usually  about  one  per  cent,  for  which  provision 
must  be  made  in  increased  size  of  pattern,  is  provided  for  by  the  pattern-maker,  the 
draughtsman  giving  finished  sizes,  but  the  draughtsman  must  know  whether  the  pattern 
can  be  drawn  from  the  sand,  and  by  what  system  of  cores  voids  can  be  left ;  or  it  may 
often  happen  that  castings,  designed  as  a  whole,  will  have  to  be  made  in  a  number  of 
pieces,  involving  flanges  and  bolts.  In  cooling,  the  shrinkage  takes  place  the  soonest  in 
the  thinnest  parts,  and,  if  great  care  be  not  taken  by  the  molder  in  exposing  the  thicker 
parts  to  the  air  first,  the  parts  will  shrink  unequally,  and  there  will  be  a  strain  induced 
which  will  materially  weaken  the  casting,  and  it  may  even  break  in  the  mold.  The 
draughtsman,  in  his  design,  should  make  the  parts  of  as  uniform  thickness  as  possible. 

Castings  cool  from  the  outside  inward,  in  annular  crystals  perpendicular  to  the  face, 
as  in  Figs.  339  and  340.  Now,  if  the  casting  consist  of  a  right  angle  (Fig.  341),  there  will 
evidently  be  a  weak  place  along  the  line  A  B,  but,  if  the  angle  be  eased  by  a  curve,  the 


FIG.  339. 


FIG.  340. 


FIG.  341. 


Fiq.  342. 


crystallization  takes  place  as  in  Fig.  342,  and  the  line  of  weakness  is  avoided.  This  is 
effected  by  a  very  small  easement  of  the  angle,  and  a  cove  is  almost  invariably  introduced. 
In  castings,  in  almost  all  metals,  the  same  effects  result  from  cooling,  and  therefore  the 
changes  of  direction  should  not  be  abrupt. 

"When  castings  are  ordered  for  important  structures,  iron  of  certain  tensile  strength  is 
called  for,  and  specimens  of  the  metal,  in  small  rectangular  bars,  are  required,  cast  at  the 
same  time  and  under  as  nearly  the  same  conditions  as  the  casting  which  may  be  subjected 
to  test. 

If  the  casting  be  made  in  dry  sand,  it  cools  slowly,  and  the  surface  is  comparatively 
soft ;  if  in  greensand — sand  somewhat  moist — the  surface  becomes  harder ;  but  if  cast 
on  an  iron  plate,  or  chill,  some  irons  become  as  hard  as  the  hardest  steel,  useful  in 
surfaces  exposed  to  heavy  wear,  as  the  treads  of  railway-wheels.  Cast-iron,  in  general, 
is  brittle  under  the  blows  of  a  hammer,  but  some  mixtures,  under  a  process  of  annealing, 
become  malleable  iron,  used  largely  for  steam-fittings,  parts  of  agricultural  machines,  forms 
requiring  the  toughness  of  wrought-iron,  but  difficult  to  forge. 

Wrought-iron  is  produced  from  cast-iron  by  removing  the  carbon  and  impurities  by 
puddling,  squeezing,  heating,  and  rolling.  As  a  material,  it  is  sold  in  all  sizes  of  wire, 
rods,  shafts,  bars,  plates,  shapes— girders  and  beams,  chains  and  anchors.  Its  applica- 
tion industrially  is  well  known.  When  hot,  it  can  be  welded,  forged,  drawn,  and  swaged 
into  almost  any  required  shape.  Under  the  *team-hammer,  the  largest  shafts,  anchors,  and 
cranks  can  be  built,  or  by  hand  or  by  machinery  it  can  be  wrought  into  tacks,  nuts,  bolts, 
nails,  or  drawn  into  the  finest  wire. 

For  shafts  of  mills  it  is  generally  turned  in  a  lathe  and  polished,  but  of  late  it  can  be 
bought,  up  to  six  inches  diameter,  cold-rolled,  which  adds  very  considerably  to  the  strength, 
and  is  ready  for  use. 

Bessemer  and  Siemens-Martin  metals  are  made  by  burning  out  the  carbon  from  a 
melted  iron,  and  then  reintroducing  a  known  quantity,  say  from  0'03  to  0'6  per  cent  of  car- 
bon. There  are  other  patents  covering  somewhat  different  irons,  but  the  above  are  the  best 
known.  All  are  commonly  classed  as  steel,  but  by  many  are  called  homogeneous  metal ; 


MATERIALS. 

first-class  iron,  of  very  uniform  texture  and  great  strength,  but  not  equal  to  that  of  the  best 
steel. 

Steel  is  produced  from  pure  wrought-iron  by  what  is  called  cementation — heating  the 
bars  in  contact  with  charcoal,  by  which  a  certain  amount  of  carbon  is  taken  up.  The  bars, 
when  taken  out,  are  covered  with  blisters,  apparently  from  the  expansion  of  minute  bub- 
bles within  ;  hence  called  Mistered  steel.  From  this  shear-steel  can  be  produced  by  piling, 
heating,  and  hammering,  or  cast-steel  from  melting  in  a  crucible. 

Steel,  when  broken,  does  not  show  the  fibrous  character  of  wrought-iron.  The  frac- 
ture of  shear-steel  is  fine,  with  a  crystalline  appearance.  The  fracture  of  cast-steel  is  very 
fine,  requiring  very  close  inspection  to  show  the  crystals  or  granulations;  its  appearance 
is  that  of  a  fine,  light,  slaty-gray  tint,  almost  without  luster.  Steel  is  stronger  than  any  of 
the  other  iron  products,  and  especially  applicable  for  the  piston-rods  of  steam-engines,  and 
positions  requiring  great  strength  and  stiffness,  with  the  minimum  of  space.  But  it  is  the 
way  in  which  steel  can  be  hardened  and  tempered  which  adapts  it  to  its  peculiar  appli- 
cations. 

When  the  malleable  metals  are  hammered  or  rolled,  they  generally  increase  in  hard- 
ness, elasticity,  and  denseness,  and  some  kinds  of  steel  springs  are  made  by  the  process 
of  hammer  hardening ;  but  the  usual  process  of  hardening  and  tempering  is  by  heating 
the  steel  to  a  degree  required  by  the  use  to  which  it  is  to  be  applied,  and  cooling  it 
more  or  less  suddenly  by  immersing  in  water  or  oil.  The  greater  the  difference  between 
the  heated  steel  and  the  cooling  medium,  the  greater  the  hardness,  but  too  much  heat 
may  burn  the  steel,  and  too  sudden  cooling  make  it  too  brittle.  Steel,  in  tempering,  is 
heated  from  430°  Fahr.  to  630°.  The  temperature  is  shown  by  the  color — from  a  pale 
yellow  to  deeper  yellow,  light  purple  to  a  dark  purple,  dark  blue  to  a  light  blue,  with  a 
greenish  tinge. 

Steel  is  used  for  the  edges  of  all  cutting-tools,  faces  of  hammers  and  anvils,  and  is  gen- 
erally welded  to  bodies  of  wrought-iron,  but  often  composing  the  entire  tool ;  for  saws, 
springs,  railway  tires,  pins,  and  can  be  bought  in  the  form  of  wire,  rods,  bars,  sheets,  and 
plates,  in  varied  forgings  and  castings. 

All  irons  are  very  liable  to  rust,  and  must  be  protected  where  exposed  to  moisture. 
Polished  surfaces  are  kept  wiped  and  oiled,  others  painted,  others  galvanized  or  plated 
with  some  less  oxidizable  metal,  generally  tin,  zinc,  or  nickel.  Of  late,  a  process  has 
been  introduced  of  coating  them  with  black  oxide,  but  is  yet  of  no  general  application. 

Antimony,  bismuth,  copper,  lead,  tin,  and  zinc,  are  used  more  or  less  industrially,  and 
alloys  of  them  are  extremely  useful.  They  may  be  hardened  somewhat  by  the  process 
of  rolling  and  hammering,  but  can  not  be  welded.  Joinings  are  made  by  soldering  or 
brazing  or  burning — that  is,  melting  together. 

Antimony  expands  by  cooling.  With  tin,  in  equal  proportions,  it  makes  speculum- 
metal,  and  is  used,  with  lead,  to  make  type.  Type  metal  makes  a  very  good  bearing  for 
shafts  and  axles. 

Bismuth  is  chiefly  used  as  a  constituent  of  fusible  metal :  3  bismuth,  5  lead,  and  3  tin, 
is  an  alloy  which  melts  at  212°.  Other  mixtures  are  made,  increasing  the  melting-point 
to  adapt  the  metal  for  fusible  plugs  in  boilers,  or  lowering  the  melting-point,  so  that,  in 
case  of  fire  in  a  building,  a  heat  of  say  140°  melts  the  joint  made  by  the  metal,  and  lets 
water  through  sprinklers,  to  automatically  put  out  the  fire. 

Copper  is  very  malleable  and  ductile.  In  sheets,  it  is  used  for  the  cover  of  roofs,  gut- 
ters, leaders,  lining  of  bath-tubs,  kettles,  stills,  and  kitchen  utensils.  It  is  worked  more 
easily  than  iron,  and  is  stronger  than  lead  or  zinc,  but  it  is  much  more  costly  than  either 
of  these  metals,  and  its  oxide  is  so  poisonous  that,  without  great  care  and  cleaning,  it  can 
not  be  used  to  transmit  or  contain  anything  that  may  be  used  as  food,  without  a  cover  of 
tin.  It  oxidizes  slowly,  and  is  used  extensively  for  ships'  fastenings  and  for  bottom-sheath- 
ing. It  is  the  most  important  element  in  all  the  brass  and  bronze  alloys. 


180  MATERIALS. 

Brass,  in  common  use,  covers  most  of  the  copper  alloys,  no  matter  what  the  other 
components  are,  whether  zinc,  tin,  or  lead,  or  all  three. 

Copper  and  zinc  will  mix  in  almost  any  proportions,  The  ordinary  range  of  good 
yellow  brass  is  from  4^  to  9  ounces  of  zinc  to  the  pound  of  copper.  With  more  zinc  it 
becomes  more  crystalline  in  its  structure,  but,  as  zinc  is  very  much  cheaper  than  copper, 
the  founder  is  apt  to  increase  the  percentage  of  zinc,  with  the  addition  of  a  small  per- 
centage of  lead.  Muntz  metal,  in  its  best  proportion,  contains  lOf  ounces  of  'zinc  to  the 
pound  of  copper. 

Copper  and  tin  mix  in  almost  any  proportion.  The  composition  of  ancient  bronzes  is 
from  1  to  3  ounces  of  tin  to  the  pound  of  copper.  Ten  parts  of  tin  to  90  of  copper  is  the 
usual  mixture  for  field-pieces,  and  this  is  used  in  steam-engine  work,  often  under  the 
name  of  composition.  Bell-metal  is  from  4  to  5  ounces  of  tin  to  the  pound  of  copper ;  Bab- 
bit-metal, for  journal-boxes,  90  of  tin  to  10  of  copper. 

Copper  and  lead  mix  in  any  proportion  up  to  nearly  one  half  lead,  when  they  separate 
in  cooling. 

An  addition  of  from  one  quarter  to  one  half  ounce  of  tin  to  the  pound  of  yellow  brass 
renders  it  sensibly  harder.  A  quarter  to  one  half  ounce  of  lead  makes  it  more  malleable. 

German-silver  is  50  copper,  25  zinc,  and  25  nickel. 

Holzapfel  gives  the  following  alloys  : 

1^  ounce  tin,  £  ounce  zinc,  to  16  ounces  copper,  for  works  requiring  great  tenacity. 

1^  to  If  ounces  tin,  2  ounces  brass,  to  16  ounces  copper,  for  cut  wheels. 

2  ounces  tin,  1^  ounce  brass,  to  16  ounces  copper,  for  turning-work. 

2J  ounces  tin,  1-j-  ounce  brass,  to  16  ounces  copper,  for  coarse-threaded  nuts  and  bearings. 

2J  ounces  tin,  2£  ounces  zinc,  to  16  ounces  copper,  Sir  F.  Chantry's  mixture,  from  which 
a  razor  was  made,  nearly  as  hard  as  tempered  steel. 

Professor  R.  H.  Thurston,  at  the  Stevens  Technological  Institute,  tested  various 
alloys  of  copper,  tin,  and  zinc,  and,  by  a  graphic  method  (Fig.  343),  exhibits  the  re- 
sults, enabling  others  to  judge  the  probable  strength  of  other  mixtures.  The  apices  of 
the  triangle  marked  copper,  tin,  and  zinc,  represent  the  points  of  pure  metal,  100  per 
cent.  The  lines  opposite  the  apex  of  any  metal  represent  the  0  of  such  metal — thus  the 
base  opposite  copper  represents  an  alloy  of  tin  and  zinc  only,  without  any  copper,  and 
every  line  drawn  above  this  base,  and  parallel  to  it,  will  contain  a  percentage  of  copper 
increasing  by  regular  scale,  from  th'e  base  to  the  apex,  and  so  with  lines  opposite  tin  and 
zinc ;  the  first  contains  only  copper  and  zinc,  the  latter  tin  and  copper,  and  the  percent- 
ages of  tin  and  zinc  increase  with  the  distance  from  their  opposite  lines  to  their  vertices. 
The  intersections  of  these  percentage  parallels  define  the  percentages  of  each  metal,  their 
sum  always  making  100  per  cent.  If  the  strength  of  such  alloy,  as  obtained  by  test,  rep- 
resent an  ordinate  or  elevation,  on  any  convenient  scale,  at  its  opposite  intersection  of 
percentage,  a  contour  map,  as  in  the  figure,  may  be  drawn  and  a  model  made  from  it. 
The  summit,  65,000  on  the  figure,  represents  the  position  of  the  strongest  alloy  found:  if 
through  the  scales  marked  copper  on  each  side,  we  find  the  parallel  to  the  base,  which 
passes  through  this  summit,  it  will  be  found  to  be  about  55 — that  is,  55  per  cent  copper. 
In  like  manner,  the  parallel  to  the  o  zinc  base,  intersecting  this  summit,  will  be  about  43 
per  cent  zinc ;  and,  in  the  same  way,  tin  is  2  per  cent. 

To  find  the  probable  strength  of  any  mixture,  it  is  only  necessary  to  find  the  contour 
intersected  by  the  triple  parallels  representing  the  percentages.  It  is  said  probable 
strength,  because  the  care  and  manipulation  of  the  founder  are  such  important  factors  in 
the  result. 

Aluminum  is  about  two  and  a  half  times  the  specific  gravity  of  water.  With  the  re- 
duction in  the  cost  of  manufacture,  its  uses  have  become  more  extended,  and  its  alloys 
now  occupy  a  high  position  in  practical  industry.  With  a  few  per  cent  of  silver, 
titanium  or  copper  aluminum  wire  can  be  made  of  a  tensile  strength  of  80,000  pounds  to 
the  square  inch,  and  an  electrical  conductivity,  weight  for  weight  with  copper  wire,  of 


MATERIALS. 


181 


170  to  100.     A  few  per  cent  of  aluminum  added  to  other  metals  gives  valuable  proper- 
ties; with  8  to  12  per  cent  of  copper,  it  makes  one  of  the  finest  and  strongest  metals 


fft  'o'»       •      vt     •       'M>r 


•i       •  06 


FIG.  343. 


known;  a  10-per-cent  aluminum  bronze  can  be  made  to  fill  a  specification  of  180,000 
pounds  tensile  strength  and  5  per  cent  elongation  in  8  inches ;  and  in  the  proportion  of 
one  third  to  three  fourths  of  a  pound  to  a  ton  of  steel  prevents  blow  holes  and  unsound 
tops  of  ingots. 

There  are  various  other  alloys,  as  phosphate  bronze,  aluminum  bronze,  Sterro-metal, 
of  which  the  strength  are  given  hereafter  in  the  appendix. 

Lead  is  a  very  soft  metal,  that  can  be  readily  rolled  into  sheets  and  drawn  into  pipes, 
and  is  so  flexible  that  it  can  be  readily  fitted  in  almost  any  position.  It  is,  therefore, 
especially  adapted  to  the  use  of  plumbers,  for  the  lining  of  cisterns  and  tanks,  and  for  pipes 
for  the  conveyance  of  water  and  waste.  For  pipes  for  conveying  pure  water  for  drinking 
purposes,  or  for  cisterns  containing  it,  it  is  objectionable,  as  it  oxidizes,  and  the  oxide  is  a 
dangerous  and  a  cumulative  poison,  but,  in  common  waters  which  are  more  or  less  hard, 
the  insides  of  the  pipes  become  covered  with  a  deposit  which  protects  them.  It  is  well, 
before  drinking  from  a  lead  pipe  in  which  the  water  has  stood  for  a  time,  to  draw  off  all 
the  water,  and,  in  lead-lined  cisterns  exposed  more  or  less  to  the  air,  to  protect  them  by  a 
coating  of  asphalt  varnish.  Lead  expands  readily,  and  has  so  little  tenacity  that,  in  many 
positions,  if  heated,  it  has  not  strength  in  cooling  to  bring  it  back  to  its  original  position. 
It  remains  in  wrinkles  on  roofs,  and,  for  pipes  conveying  hot  water,  unless  continuously 
supported,  it  will  hang  down  in  loops,  continuously  increasing  under  variations  of  tern- 


182  MATERIALS. 

perature,  to  rupture.     But  it  makes  a  very  good  plating  for  sheet-iron  for  roofs,  and  its 
oxides  are  the  most  valuable  of  all  pigments. 

Tin,  in  a  pure  state,  is  used  for  domestic  utensils,  as  block-tin,  and  has  also  been  used 
for  pipes  in  the  conveyance  of  water  by  parties  who  feared  the  poisonous  qualities  of  lead 
pipe.  But  its  chief  use  is  for  the  covering  of  sheet-iron,  which  is  sold  under  the  name 
of  tin  or  tin-plate,  and  is  of  universal  application  for  architectural,  industrial,  and  do- 
mestic purposes.  It  is  so  little  affected  by  air  and  moisture  that  roofs,  in  many  places, 
covered  with  it,  need  no  painting,  and  oxidization  takes  place  in  the  iron  beneath  only 
from  deficiency  in  the  plating,  or  from  the  abrasion  or  breaks  in  it. 

Zinc,  in  the  pure  form  of  spelter,  is  crystalline  and  brittle,  but  at  a  temperature  be- 
tween 210°  and  300°  it  is  so  ductile  and  malleable  that  it  can  be  readily  rolled  into 
sheets,  and  of  late  has  been  used  as  a  cheap  substitute  for  sheet-copper ;  but,  under  con- 
siderable variations  of  temperature,  as  for  lining  of  bath-tubs,  it  takes  permanent 
wrinkles,  and,  for  coverings  of  roofs,  suitable  provision  must  be  made  for  its  expansion. 
But  as  a  plating  of  iron,  under  the  name  of  galvanizing,  it  affords  an  admirable  protec- 
tion, cheaply,  and  extends  the  use  of  iron  in  sheets,  bolts,  and  castings,  where  it  would 
not  otherwise  be  applicable.  Zinc,  as  a  pigment,  does  not  discolour,  like  lead,  under 
the  action  of  sulphuretted  hydrogen,  but  it  is  objected  toby  painters  for  its  want  of  body 
or  cover. 

Sulphur,  when  used  in  sufficiently  large  masses  as  to  show  on  a  drawing,  may  be  rep- 
resented by  a  reddish-yellow  tint,  or  some  distinctive  hatching.  It  melts  at  248°  Fahr., 
and,  from  its  fluidity,  answers  admirably  for  the  filling  of  joints  between  stones,  beneath 
the  base  plates  of  iron  columns,  between  wood  and  stone,  and  around  anchor-bolts  in  stone, 
forming,  when  cold,  a  strong,  uniform  bearing,  and  adapting  itself  to  the  roughness  of 
the  material,  and  is  detached  with  difficulty.  It  is  used  largely  for  the  bases  of  engines, 
and  for  the  joints  of  the  cap-stones  of  dams.  On  the  dam  across  the  Mohawk,  at  Cohoes, 
N.  Y.,  many  tons  were  used  in  these  joints,  the  depth  of  sulphur  being  about  6  inches,  and 
now,  after  about  twenty  years'  use,  it  has  been  renewed,  and  there  has  been  no  injurious 
effect  from  the  sulphur  on  the  limestone,  of  which  the  apron  or  capping  is  composed. 
It  is  better  for  most  of  the  above  purposes  than  lead,  being  cheaper,  more  fluid  when 
molten,  shrinks  less  in  cooling,  is  less  affected  by  temperature,  does  not  creep  under 
pressure,  and  its  crushing  strength  is  adequate  to  any  of  the  positions  of  use  above,  but 
it  is  brittle  under  blows.  It  sometimes  rusts  the  bolts  or  iron  with  which  it  is  brought 
in  contact,  but  this  is  prevented  by  an  addition  of  about  20  per  cent  of  coal  tar.  This 
mixture  is  used  as  a  cement  to  fasten  lights  in  illuminating  tile  and  vault  covers. 

When  heated  to  about  300°,  sulphur  begins  to  grow  viscid,  and  at  428°  it  has  the 
consistence  of  thick  molasses.  Above  this,  it  begins  to  grow  thin  again.  Heated  to 
518°,  and  thrown  into  cold  water,  it  becomes  for  a  time  plastic,  and  is  used  for  taking 
moulds  or  casts. 

Sulphur,  in  powder,  mixed  in  proportions  of  one  sal-ammoniac,  two  sulphur,  and 
fifty ,of  iron-filings,  makes  a  mastic  which  is  used  for  calking  the  joints  of  iron  pipes, 
especially  gas- pipes.  The  joint  is  called  a  rust-joint. 

Pure  silver  is  too  soft  for  general  purposes ;  it  alloys  readily  with  lead,  zinc,  bismuth, 
gold,  and  copper.  The  last  is  the  most  important  in  an  industrial  point  of  view  in  its 
use  for  plate,  coin,  and  ornaments,  which  invariably  contain  a  certain  amount  of  copper. 

Silver  is  used  for  plating  by  the  electro-plate  process,  or  by  fire  plating,  in  which  the 
sheet  is  soldered  or  sweated  to  some  other  metal,  as  iron,  German  silver,  composition, 
copper,  etc. 

Gold  is  used  industrially  for  chemical  laboratories ;  sometimes  as  plate  or  for  orna- 
ment, but  mostly  for  gilding  the  baser  metals  by  electro-plating  or  by  fire  gilt.  As  gold 
leaf,  it  is  very  largely  employed  for  ornamental  purposes ;  leaf  can  be  beaten  beyond  any 
requirements  in  the  arts ;  a  single  grain  of  gold  was  spread  to  the  extent  of  75  square 
inches,  and  the  same  weight  of  silver  to  98  square  inches.  Platinum  is  used  largely  for 


MATERIALS. 


183 


various  apparatus  in  chemical  laboratories,  as  it  withstands  high  temperatures  and  is  proof 
against  a  large  number  of  chemicals.  It  is  to  be  had  in  wire  sheets,  crucible  and  dishes, 
and  in  stiles  of  large  capacity  for  the  concentration 
of  sulphuric  acid. 

Glass,  in  drawing,  is  represented  by  a  bluish  tint 
or  by  different  shades  or  hatchings,  expressive  of  the 
effect  of  light  upon  it,  whether  the  light  is  reflected 
or  transmitted. 

Fig.  344  represents  a  portion  of  a  mirror  when  the 
light  is  reflected.  The  exterior  of  windows  is  often 
represented  in  the  same  way,  but  with  deeper  shades, 
and  often  with  a  piece  of  curtain  behind  in  white 
with  dim  outline.  A  window  viewed  from  inside 
is  represented  in  shades  less  than  in  the  figure,  or  as 
transparent,  which  is  conveyed  by  the  dimness  6f 
outline  of  figures  or  skies  seen  beyond. 

Fig.  345  represents  a  glass  flask.  #10.  344. 

Fig.  346  represents  a  glass  box  with  glass  sides. 

Fig.  347  represents  a  glass  jar  containing  fluids  of  different  densities. 

Figs.  348  and  349  represent  spars,  which  may  be  taken  for  any  transparent  sub- 
stances, as  glass,  ice,  and  the  like. 

Common  window-glass  is  blown  in  the  form  of  cylinders  (hence  called  cylinder- 
glass),  flatted  out,  and  cut  in  lights  of  varying  dimensions,  from  6x8  up  to  30  x  30 


FIG.  345. 


FIG.  346. 


FIG.  347. 


inches,  and   put  up  in  boxes  containing  about  fifty 
square  feet.      It   is   classed   as  single-thick  (bout  ^ 
inch)  and  double-thick  (i  inch).     When  the  squares 
are  large,  or  used  for  sky-lights,  they  should  be  the 
latter.      Plate-glass — polished  plate  is  used  for  win- 
dows of  stores  and  first-class  buildings.     It  can  be  got  of  almost  any  dimensions,  and  of 
a  thickness  from  -^  to  £  of  an  inch.     Rough  plate  is  largely  used  for  floor-lights  and 
sky-lights.     It  is  cut  to  required  sizes,  and  of  a  thickness  from  f  to  one  inch. 

Single  thick  cylinder-glass  cuts  off  from  about  8  to  15  per  cent  of  the  light. 

Double-cylinder,  from  12  to  20  per  cent  of  the  light. 

Polished  plate,  three  sixteenths  inch  thick,  from  5  to  7  per  cent  of  the  light. 

Rough  plate,  one  half  inch  thick,  from  20  to  30  per  cent  of  the  light. 

Rough  plate,  one  inch  thick,  from  30  to  40  per  cent  of  the  light. 

Ribbed  glass,  one  eighth  inch  thick,  known  as  "factory  glass,"  gives  by  diffusion  a 
more  effective  illumination  than  clear,  plain  glass  or  the  crystal-ribbed  glass  when  either 
is  screened  with  shades.  On  any  exposure  but  the  southern,  the  crystal-ribbed  glass 
may  be  used  without  window-shades. 


184  MATERIALS. 

This  is  when  the  glass  is  clean ;  but  there  is  always  a  film  of  moisture  on  its  surface, 
which  attracts  dust,  and  impairs  very  much  the  transmitted  light.  Rough  plate  more 
readily  retains  the  dirt,  and,  when  it  is  used  as  floor-lights,  becomes  scratched.  It  is 
therefore  usual,  in  the  better  class  of  buildings,  to  use  a  cast  white  glass,  set  in  iron 
frames.  In  outer,  or  platform  lights,  these  lights  are  in  the  form  of  lenses,  set  in  cast- 
iron  frames  with  an  asphalt  putty,  or  resting  on  iron  frames  and  imbedded  in  Portland 
cement. 


FIG.  348.  FIG.  349. 

Rubber,  mixed  and  ground  with  sulphur,  subjected  to  heat,  becomes  vulcanized,  and 
is  not  affected  by  moderate  variations  in  temperature.  Soft  rubber,  most  extensively 
used  for  industrial  purposes,  is  subjected  to  a  heat  of  from  265°  to  300°,  aud  for  a  time 
can  withstand  a  temperature  a  little  below  this  without  losing  its  elasticity  ;  after  a  time 
it  will  harden.  Soft  rubber  is  classed  as  pure  rubber,  and  fibrous  rubber,  or  rubber  with 
cloth.  Pure  rubber  contains  about  fifty  per  cent  of  rubber  and  fifty  per  cent  of  com- 
pound, white  lead  and  sulphur.  It  is  used  for  the  buffers  and  springs  of  railway- 
carriages,  and  for  the  faces  of  valves  and  seats  of  water-pumps,  but  it  is  not  well  suited 
for  the  pumping  of  hot  water,  especially  above  212°,  as  it  is  liable  to  lose  its  elasticity ; 
and,  although  some  valves  may  stand  a  considerable  time,  it  is  almost  impossible  to 
secure  uniformity  in  the  rubber.  Fibrous  rubber — rubber  ground  with  cotton  or  other 
fibre,  or  spread  on  cloth,  on  more  or  less  thicknesses — is  used  for  the  packing  of  faced 
joints  of  pipes  and  gaskets  for  water  or  steam.  It  makes  a  stanch  joint,  and,  even  when 
hardened  under  heat,  it  still  preserves  it.  Rubber  cloth  is  also  used  for  belting  and 
hose-pipes.  When  used  for  the  conveyance  of  steam,  the  inner  coat  is  the  first  affected, 
and  it  may  be  some  time  before  the  whole  pipe  suffers.  In  buying  rubber,  explain  the 
purpose  to  which  it  is  to  be  applied,  and  depend  on  the  guarantee  of  the  vender.  Rubber 
is  often  to  be  designated  by  the  draughtsman,  which  it  may  be  by  a  bluish-black  tint,  or 
by  lines  across  it  parallel  to  its  length. 

Paints  are  used  for  a  twofold  purpose  —for  covering  and  preserving  the  material  to 
which  they  are  applied,  and  for  ornamentation.  The  best  and  the  most  general  is  white- 
lead  ground  with  linseed-oil,  either  used  by  itself  or  mixed  with  various  other  pigments, 
as  ochre,  chrome,  lamp-black,  etc.  It  is  often  adulterated  with  barytes.  For  the  cover- 
ing of  iron,  or  for  the  packing  of  close  joints  in  it,  nothing  is  better  than  pure  red-lead, 
but  many  of  the  oxides  of  iron,  red  or  yellow,  form  good  covers  of  iron,  and,  as  cheap 
and  good  paints,  are  used  on  tin  roofs.  All  the  leads  and  pigments  are  ground  in  oil: 
if  the  oil  is  raw,  it  dries  slowly;  driers,  as  litharge,  are  added  to  hurry  the  process,  but, 
with  boiled  oil,  no  drier  is  necessary.  Almost  any  inert  substance,  as  cement,  chalk,  or 
sand,  if  fine  enough,  can  be  ground  with  oil  for  a  paint,  and  make  a  good  cover,  and  for 
these  fish-oil  will  answer.  The  general  specification  for  painting  is  "paint  with— good 
coats  of  white-lead,  of  sucli  colour  as  may  be  directed."  The  priming-coat  of  new  wood- 
work requires  more  oil  than  paint.  For  the  next  coats,  one-half  pound  of  paint  to  the 
square  yard  would  be  considered  a  good  coat.  If  the  paint  is  on  old  work,  or  that 
which  has  been  already  painted,  there  will  be  a  little  less  lead  required.  Wood  should 
be  fairly  dry  before  the  application  of  paint,  so  that  it  may  properly  adhere  and  not  in- 


MATERIALS. 


185 


close  moisture  that  may  rot  the  wood.  The  knots  should  bc.Mlled,  that  is,  covered  with 
shellac  varnish  or  similar  preparation,  to  prevent  the  exuding  of  the  resin.  The  heads 
of  nails  should  be  sunk,  and  the  holes  and  cracks  filled  with  putty,  and  the  surface  of 
the  wood  smoothed. 

Coals  and  other  minerals  are  represented  like  rocks  or  stones,  in  varied  shades  of 
tones  and  colours.  Fig.  350  represents  the  fire-box  of  a  locomotive,  with  coal  in  the 
state  of  ignition  in  its  usual  type.  In  colour,  flame  is  represented  in  streaks  of  red- 
yellow,  with  dark  tints  for  smoke.  Water  occupies  the  lower  half  of  the  boiler;  but,  as 


FIG.  350. 


FIG.  &>L. 


steam  under  pressure  is  invisible  like  gas,  the  space  occupied  by  it  is  shown  as  empty. 
If  the  direction  of  its  movement  is  desired,  it  is  indicated  by  arrows.  Steam  issuing 
into  atmosphere,  or  boiling  in  an  open  kettle,  has  the  appearance  of  a  very  light  smoke 
or  cloud  (Fig.  351). 

There  are  many  substances  used  in  such  masses  in  construction,  or  to  be  shown  in  the 
processes  of  manufacture,  that  must  be  graphically  represented  by  the  draughtsman  by  a 
general  imitation  of  their  natural  appearance,  or  conventionally  with  explanatory  mar- 
ginal blocks  and  legends. 


MECHANICS. 


THE  draughtsman  in  designing  a  structure  should  be  conversant  not  only  with  the 
nature  of  the  material,  but  also  with  the  forces  to  which  it  is  to  be  subjected — their 
magnitude,  direction,  and  points  of  application,  and  their  effects;  that  is,  he  should 
know  the  first  principles  of  mechanics,  the  science  of  rest,  motion,  and  force — to  wit, 
Statics,  Dynamics,  and  Kinematics.  Statics  treats  of  balanced  forces,  or  rest ;  dynamics, 
of  unbalanced  forces,  where  motion  ensues;  and  kinematics,  of  the  comparison  of  mo- 
tions with  each  other.  Considering  statical  forces  simply  in  the  abstract,  the  bodies  to 
which  they  are  applied  are  assumed  to  be  perfectly  rigid,  without  breaking,  binding, 
twisting,  or  in  any  wise  changing  upon  the  application  of  such  forces. 

Force  is  a  cause  tending  to  change  the  condition  of  a  body  as  to  rest  or  motion.    Force 
is  measured  by  weight.     In  England  and  the  United  States  the  unit  of  force  is  the  pound ; 
on  the  Continent,  the  gramme.     All  bodies  fall,  or  tend  to  fall,  to  the  earth.     This  force 
is  called  the  attraction  of  gravitation.     Its  direction  is  that  of  a  string  from  which  a 
weight  is  suspended  (Fig.  352).     It  is  called  a  vertical  line,  and  its  di- 
rection is  toward  the  centre  of  the  earth.     Practically,  all  such  lines 
are  considered  parallels.     Let  a  mass,  P  (Fig.  353),  be  suspended  by  a 
cord.     Each  particle  is  acted  on  by  gravity,  and  the  resultant  of  all 
these  parallel  forces  is  the  force  resisted  by  the  cord,  or  the  entire 
weight  of  the  body.     If  a  mass  (Fig.  354)  be  suspended  from  two  dif- 
ferent points,  P  and  Q,  the  directions  of  the  string  will  meet  at  a  point 
C,  which  is  called  the  centre  of  gravity,   where  all  the  weight  may  be 
considered  to  be  concentrated.     When  a  body  of  uniform  density  has 


rHr- 


Fio.  352. 


FIG.  353. 


Fm.  354. 


FIG.  355. 


a  centre  of  symmetry  (a  point  which  bisects  all  straight  lines  drawn  through  it),  this 
point  coincides  with  the  centre  of  gravity.  The  middle  of  a  straight  line,  the  centre  of 
a  circle,  the  intersection  of  the  diagonals  of  a  parallelogram,  the  intersection  of  lines 
drawn  from  any  two  angles  of  a  triangle  to  the  centres  of  the  opposite  sides,  are  the  cen- 
tres of  symmetry ;  in  solids,  the  centre  of  a  sphere,  the  middle  point  of  the  axis  of  a 
cylinder,  and  the  intersection  of  the  diagonals  of  a  parallelepiped. 

The  centre  of  gravity  of  the  triangular  pyramid  (Fig.  355)  is  in  the  straight  line  A  E, 
connecting  the  apex  A  with  the  centre  of  symmetry  of  the  base  triangle  BCD,  and  dis- 
tant J  of  the  length  of  the  line  A  E  from  E. 

186 


MECHANICS. 


187 


The  centre  of  gravity  of  solids  which  may  be  divided  into  symmetrical  figures  and 
pyramids,  as  for  all  practical  purposes  most  may  be,  can  be  found  by  determining  the 
centre  of  gravity  of  each  of  the  solids  of  which  it  is  composed,  and  then  compounding 
them.  The  centre  of  gravity  of  bodies  inclosed  by  more  or  less  regular  contours,  as  a 
ship,  for  instance,  is  determined  by  dividing  it  into  parallel  and  equidistant  sections, 
finding  the  centre  of  gravity  of  each,  and  compounding  them. 

The  centre  of  gravity  of  a  body  may  be  determined  practically,  as  shown  above,  by 
its  suspension  from  different  points.  It  can  be  done  generally  more  readily  by  balancing 
the  body  in  horizontal  positions  on  different  lines  of  support ;  the  centre  of  gravity  will 
lie  in  the  intersection  of  planes  perpendicular  to  these  lines.  A  body,  unless  the  vertical 
line  from  the  centre  of  gravity  falls  within  the  base  of  support  (Fig.  356),  will  fall  over 
(Fig.  357).  A  person  carrying  a  weight  insensibly  throws  a  portion  of  the  body  forward, 
backward,  or  laterally,  to  balance  the  load.  Thus,  in  Fig.  358,  the  body  is  thrown 


FIG.  356. 


FIG.  357. 


FIG.  358. 


back,  so  that  the  vertical  from  the  centre  of  gravity  g,  compounded  of  the  centre  of 
gravity  G  of  the  woman  and  H  of  the  load,  falls  within  the  base  of  the  feet. 

When  a  figure  rests  in  such  a  position  that  its  centre  of  gravity  is  in  its  lowest  posi- 
tion, it  is  said  to  be  in  stable  equilibrium.  A  ball  may  rest  in  any  position,  as  the  centre 
of  gravity  is  neither  depressed  nor  raised  by  movement ;  but  in  the  toy  (Fig.  359)  any 
movement  tends  to  raise  the  centre  of  gravity,  and,  on  the  cessation  of  the  force,  the 
body  returns  to  its  original  position.  The  ellipsoidal  form  (Fig.  360),  placed  on  its 
pointed  end,  is  balanced,  but  the  slightest  movement  lowers  the  centre  of  gravity,  and, 
without  the  application  of  an  outside  force,  it  can  not  be  raised,  and  therefore  falls. 


FIG.  359. 


FIG.  360. 


FIG.  361. 


This  is  called  unstable  equilibrium,  while  in  the  position  shown  in  Fig.  361  it  is  in  stable 
equilibrium.  In  the  toy  (Fig.  362)  the  body  of  the  figure  is  light,  and  the  weight  of  the 
balls  brings  the  centre  below  the  point  of  support.  This  will  admit  of  great  oscillation, 
and  return  to  its  original  position. 

When  two  parallel  forces,  F  F',  are  applied  at  the  extremities  of  a  straight  line  (Fig. 
363),  they  have  a  resultant,  R,  equal  to  their  sum,  and  acting  at  a  point,  C,  which 
divides  the  line  inversely  in  proportion  to  the  forces.  If  the  forces  are  equal,  the  point 
C  will  be  at  the  centre  of  the  line;  if  the  force  F  is  double  that  of  F;,  C  A  will  be  equal 
to  one  half  C  B.  This  is  called  the  principle  of  the  lever. 


188 


MECHANICS. 


Levers,  in  practice,  are  called  of  the  first  (Fig.  864),  the  second  (Fig.  365),  and  the 
third  class  (Fig.  366),  according  to  the  positions  of  the  three  forces,  the  weight,  W,  the 
power  applied,  P,  and  the  fulcrum,  or  support  or  turning-point,  F,  of  the  lever.  The 
two  extreme  forces  must  always  act  in  the  same  direction ;  the 
middle  one  must  act  in  the  opposite  direction,  and  be  equal  to 
the  sum  of  the  other  two ;  and  the  magnitude  of  the  extreme 
forces  is  inversely  proportional  to  their  distances  from  the  mid- 
dle one.  Let  the  middle  force,  c,  be  measured  by  a  spring-bal- 
ance (Fig.  367),  it  will  mark  the  sum  of  the  weights  a  and  b. 


FIG.  362. 


F 


FIG 


FIG.  364. 


Call  the  distance  from  a  to  c,  x,  and  from  &  to  c,  y,  then  the  weight  a  will  be  to  the 
weight  &  as  y  is  to  x,  or  a  x  =  b  y.  Suppose  the  weight  a  to  be  6  pounds  and  at  J  3 
pounds,  at  c  it  will  be  9  pounds,  and  x  will  be  to  y  as  6  to  3,  or,  if  the  lever  is  48  inches, 
5  c  will  be  16  inches  and  ac  32  inches. 


W    F 


FIG.  367. 


FIG.  366. 


FIG.  368. 


To  find  graphically  the  fulcrum,  or  point,  at  which  a  lever  should  be  supported  to 
sustain  in  equilibrium  weights,  or  equivalent  forces,  acting  at  the  extremities  of  the 
lever.  Let  A  B  (Fig.  368)  be  the  lever.  At  A  and  B  let  fall  and  erect  perpendiculars  to 
the  lever.  Lay  off  from  A,  on  any  convenient  scale,  A  B',  corresponding  to  the  weight 
applied  at  B ;  and  at  B,  on  the  same  scale,  B  A',  the  weight  applied  at  A ;  draw  the  line 
A'  B' ;  its  intersection,  F,  with  the  lever  will  be  the  position  of  the  fulcrum.  This  is  on 
the  hypothesis  that  there  is  no  weight  to  the  lever,  or  that,  after  determining  the  posi- 


MECHANICS. 


189 


F± 


c' 


FIG.  369. 


tion  of  the  fulcrum,  the  lever  itself  is  balanced  on  the  point  by  the  addition  of  weight 
on  the  short  arm  F  A,  or  the  reduction  of  weight  on  the  long  one  F  B.     If  the  lever  is 
of  uniform  weight,  on  perpendiculars  to  C,  the  centre 
of  the  lever  (Fig.  369),  and  to  F,  the  fulcrum,  as  before 
determined,  lay  off  F  C',  the  weight  of  the  lever,  and 
C  F',  the  sum  of  the  weights  applied  at  A  and  B ;  draw 
C'  F'.     Its  intersection,  F",  will  be  the  actual  fulcrum, 
taking  into  consideration  the  weight  of  the  lever  in  ad- 
dition to  the  weights  suspended  at  the  extremities. 

The  Wheel  and  Axle. — If  a  weight,  P,  be  suspended 
from  the  periphery  of  a  wheel  (Fig.  370).  while  another 
weight,  "W,  is  suspended  on  the  opposite  side  of  a  bar- 
rel or  axle  attached  to  the  wheel,  the  principle  of  ac- 
tion is  the  same  as  that  of  the  lever.  P  multiplied  by 
its  length  of  lever,  the  radius  ca  of  the  wheel,  is  equal 
to  W  multiplied  by  its  length  of  lever,  the  radius  of  the  ™" 
axle  c&;  the  axle  c  is  the  fulcrum.  If  a  movement 
downward  be  communicated  to  P,  as  shown  by  the 
dotted  line,  a  rotary  motion  is  given  to  the  wheel  and 
axle ;  the,  cord  of  P  is  unwound  while  that  of  W  is 
wound  up,  while  P  is  still  suspended  from  a  and  W  from  5;  the  leverage,  or  distance 
from  the  fulcrum,  of  each  is  the  same  as  atx  first.  The  wheel  and  axle  is  a  lever  of  con- 
tinuous action.  Since  the  wheel  has  a  larger  circumference  than  the  axle,  by  their  revo- 
lution more  cord  will  be  unwound  from  the  former  than  is  wound  up  on  the  latter;  P 

will  descend  faster  than  W  is  raised  in  the  proportion  of 
the  circumference  of  the  wheel  to  that  of  the  axle,  or  of 
their  radii — that  is,  as  c  a  to  c  b.  When  P  has  reached  the 
position  P',  W  will  have  reached  W.  If  c  a  be  four  times 
c  J,  then  P  will  have  moved  four  times  the  distance  that 
W  has.  The  movement  is  directly  as  the  length  of  the 
levers,  or  the  radii  of  the  points  of  suspension.  Therefore, 

\  to  move  a  large  weight  by  the  means  of  a  smaller  one,  the 

smaller  must  move  through  the  most  space,  and  that  the 
spaces  described  are  as  the  opposite  ends  of  the  lever,  or 
inversely  as  the  weights. 

It  is  the  fundamental  principle  of  the  action  of  all  me- 
chanical powers,  that  whatever  is  gained  in  power  is  lost  in 
space  travelled ;  that,  if  a  weight  is  to  be  raised  a  certain 
number  of  feet,  the  force  exerted  to  do  this  must  always 
be  equal  to  the  product  of  the  weight  by  the  height  to 
which  it  is  to  be  raised;  thus,  if  200  pounds  are  to  be 
raised  50  feet,  the  force  exerted  to  do  this  must  be  equal 
to  a  weight  which,  if  multiplied  by  its  fall,  will  be  equal 
to  the  product  200x50,  or  10,000;  this  force  may  be  a 
weight  of  10,000  pounds  falling  1  foot,  or  of  1  pound  fall- 
ing 10,000  feet. 

It  is  now  common  to  refer  all  forces  exerted  to  a  unit  of 
pounds-feet  (see  p.  72,  Fig.  181),  that  is,  1  pound  falling  1 
foot ;  and  the  effect  to  the  same  unit  of  pounds-feet,  1  pound 
raised  1  foot.  Thus,  in  the  example  above,  the  force  exerted  or  power  is  10,000  pounds- 
feet  falling;  the  effect  10,000  pounds-feet  raised.  In  practice,  the  pounds-feet  of  force 
exerted  must  always  be  more  than  the  pounds-feet  of  effect  produced;  there  must  be  some 
excess  of  the  former  to  produce  movement  and  to  overcome  resistance  and  friction  of  parts. 


FIG.  370. 


190 


MECHANICS. 


The  measure  of  any  force,  as  represented  by  falling  weight,  is  termed  the  absolute  power 
of  that  force ;  the  resulting  force,  or  useful  effect  for  the  purposes  for  which  it  is  applied, 
is  called  the  effective  power. 

The  Pulley.  —The  single  fixed  pulley  (Fig.  371)  consists  of  a  single  grooved  wheel 
movable  on  a  pin  or  axis,  the  strap  through  which  the  pin  passes  being  attached  to  some 
fixed  object.  A  rope  passes  over  the  wheel  in  the  groove ;  on  one  side  the  force  is 
exerted,  and  on  the  other  the  weight  is  attached  and  raised.  It  may  be  considered  a 
wheel  and  axle  of  equal  diameters,  or  as  a  lever  in  which  the  two  sides  are  equal,  the  pin 
being  the  fulcrum.  P,  the  force  exerted,  must  therefore  be  equal  to  the  weight  W,  raised ; 
and,  if  movement  takes  place,  W  will  rise  as  much  as  P  descends. 

The  fixed  pulley  is  used  for  its  convenience  in  the  application  of  the  force ;  it  may  be 
easier  to  pull  down  than  up,  for  instance ;  but  the  pounds-feet  of  force  must  be  equal 
to  the  pounds-feet  of  effect.  The  tension  on  the  rope  is  equal  to  either  the  force  or 
weight. 

Fig.  372  is  a  combination  of  a  fixed  pulley,  A,  and  a  movable  pulley,  B.     The  sim- 
plest way  to  arrive  at  the  principle  of  this  combination  is  to  consider  its  action.     Let  P 
be  pulled  down,  say,  two  feet ;  the  length  of  rope  drawn  to  this  side  of  the  pulley  must 
be  furnished  from  the  opposite  side.     On  that  side  there  is  a  loop,  in  which 
the  movable  pulley,  with  the  weight  W  attached,  is  suspended.     Each  side 
of  this  loop,  2  and  3,  must  go  to  make  up  the  two  feet  for  the  side  or  end 
1.     Cords  2  and  3  will  therefore  furnish  each  one  foot. 
As  these  cords  are  shortened  one  foot,  the  w/eight  W  is 


FIG.  371. 


FIG.  374. 


raised  one  foot,  and,  as  the  movement  of  W  is  but  one  foot  for  the  two  feet  of  P,  W 
must  be  twice  P. 

In  the  combination  of  pulleys  (Fig.  373),  let  P  be  pulled,  say,  three  feet;  then  this 
length  of  rope,  drawn  from  the  opposite  side  of  the  pulley,  is  distributed  over  the  three 
cords,  2,  3,  4,  and  the  weight  W  is  raised  one  foot ;  consequently,  W  is  three  times  P. 
The  cord  1  supports  P,  the  cords  2,  3,  4,  the  weight  W,  or  three  times  P;  consequently, 
the  tension  on  every  cord  is  alike.  The  same  rope  passing  freely  around  pulleys  must 
have  the  same  tension  throughout ;  so  that,  to  determine  the  relation  of  W  to  P,  count 
the  number  of  cords  which  sustain  the  weight.  Thus,  in  Fig.  374,  the  weight  is  sus- 
tained by  four  cords ;  consequently,  it  is  four  times  the  tension  of  the  cord,  or  four  times 
the  force  P.  In  order  not  to  confuse  the  cords,  the  pulleys  are  represented  as  in  the 
figures;  but,  in  construction,  the  pulleys,  or  sheaves,  are  usually  of  the  same  diameter, 
and  when  connected,  as  A  and  B,  and  C  and  D,  they  run  on  the  same  pin. 

The  Inclined  Plane. — To  support  a  weight  by  means  of  a  single  fixed  pulley,  the  force 
must  be  equal  to  the  weight.  Suppose  the  weight,  instead  of  hanging  freely,  to  rest 
upon  an  inclined  plane  &  d  (Fig.  375) ;  if  motion  ensue,  to  raise  the  weight  W  the  height 
a  &,  the  rope  transferred  from  the  weight  side  of  the  pulley  will  be  equal  to  b  d,  and  P 
will  have,  consequently,  fallen  this  amount ;  thus,  if  &  d  be  six  feet,  and  a  ft  one  foot, 


MECHANICS. 


191 


while  "W  is  raised  one  foot,  P  has  descended  six  feet ;  and,  as  pounds-feet  of  power  must 
equal  pounds-feet  of  effect,  P  will  be  one  sixth  of  W ;  thus,  P  is  to  W  as  a  ft  is  to  &  d,  or 
as  the  height  of  the  incline  is  to  its  length.  If  the  end  of  the  plane  d  be  raised,  till  it 
becomes  horizontal,  the  whole  weight  would  rest  on  the  plane,  and  no  force  would  be 
necessary  at  P  to  keep  it  in  position ;  if  the  plane  be  revolved  on  &,  till  it  becomes  per- 


FIG.  375. 


FIG.  376. 


pendicular,  then  the  weight  is  not  supported  by  the  plane  at  all,  but  it  is  wholly  depend- 
ent on  the  force  P,  and  is  equal  to  it.  Between  the  limits,  therefore,  of  a  level  and  a 
perpendicular  plane,  to  support  a  given  weight  W,  the  force  P  varies  from  nothing  to 
an  equality  with  the  weight. 

The  construction  (Fig.  376)  illustrates  the  principle  of  the  wedge,  which  is  but  a 
movable  inclined  plane;  if  the  wedge  be  drawn -forward  by  the  weight  P,  and  the  weight 
W  be  kept  from  sliding  laterally,  the  fall  'of  P  a  distance  equal  to  a  d  will  raise  the 
weight  W  a  height  c  6.  P  will  therefore  be  to  "W  as  c  &  is  to  a  d.  For  example,  if  the 
length  of  the  wedge  a  d  be  ten  feet,  and  the  back  c  I  two  feet,  then  P  will  be  to  W  as 
two  to  ten,  or  one  fifth  of  it. 

Let  the  inclined  plane  a  b  d  (Fig.  376)  be  bent  round,  and  attached  to  the  drum  A 
(Fig.  377),  to  which  motion  of  revolution  on  its  axis  is  given,  by  the  unwinding  of  the 
turns  of  a  cord  from  around  its  periphery,  through  the  action  of  a  weight  P  suspended 
from  a  cord  passing  over  a  pulley.  If  the  weight  W  be  retained  in  its  vertical  position, 

by  the  revolution  of  the  drum  it  will  be  forced  up 
the  incline,  and  when  the  cord  has  unwound  one  half 
turn  from  the  drum,  and  consequently  the  weight  P 
descended  a  distance,  c  e,  equal  to  one  half  the  cir- 
cumference of  the  drum,  the  weight  W  has  been 

raised  to  the  height  a  b 
by  the  half  revolution 
of  the  plane;  P  must 
therefore  be  to  W  as 
a  &  is  to  one  half  the 
circumference.  Extend 
the  inclined  plane  so  as 
to  encircle  the  drum 
(Fig.  378).  The  figure 
illustrates  the  mechan- 
ism of  the  screw,  which 
may  be  considered  as  formed  by  wrapping  a  fillet-band  or  thread  around  a  cylinder  at  a 
uniform  inclination  to  the  axis.  In  practice,  the  screw  or  nut,  as  the  case  may  be,  is 
moved  by  means  of  a  force  applied  at  the  extremity  of  a  lever;  a  complete  revolution 
raises  the  weight  the  distance  from  the  top  of  one  thread  to  the  top  of  the  one  above,  or 
the  pitch.  If  the  force  be  always  exerted  at  right  angles  to  the  lever  (Fig.  379),  the 
lever  may  be  considered  the  radius  of  a  wheel,  at  the  circumference  of  which  the  force 
is  applied.  Thus,  if  the  lever  be  three  feet  long,  the  diameter  of  the  circle  would  be  six 
feet,  and  the  circumference  6  x  3'1416,  or  18^  feet;  if  the  pitch  be  one'inch,  or  one 


FIG.  377. 


FIG.  378. 


192 


MECHANICS. 


twelfth  of  a  foot,  then  the  force  would  be  to  the  weight  as  one  twelfth  is  to  18-85;  and 
if  the  force  be  one  pound,  the  weight  would  be  226 '20  pounds. 

The  resultant  of  two  forces  of  exertion,  as  has  been  shown,  is  their  sum,  and  counter- 
balances the  force  of  re- 
sistance, which  must  be 
applied  at  a  point  inter- 
mediate between,  and 
distant  from  each  of 
them  inversely  as  the 
forces  exerted. 

The  resultant  of  any 
number  of  parallel  forces 
acting  in  one  direction 
is  equal  to  their  sum  act- 
ing in  the  same  direc- 
tion at  some  intermedi- 
ate point;  that  is,  the 
effect  of  all  the  forces 
is  just  the  same  as  if 
there  were  but  one  force,  equal  to  their  sum,  acting  at  this  point,  and  is  balanced  by  an 
equal  force  acting  in  the  opposite  direction.  This  central  point  may  be  determined  by 
finding  the  resultant,  i.  e.,  the  sum,  and  the  point 
of  application  for  any  two  of  the  forces,  as  shown 
graphically  in  Figs.  368,  369,  and  then  of  the  other 
two,  the  resultants  thus  determined  being  again 
added  together  like  simple  forces. 

Inclined  Forces  are  those  whose  directions  are  in- 
clined to  each  other.  When  two  men  of  equal 
strength  pull  directly  opposite  to  each  other,  the  resultant  is  nothing.  Let  a  third  take 
hold  of  the  centre  of  the  rope  (Fig.  380),  and  pull  at  right  angles  to  the  rope ;  he  will 
make  an  angle  in  the  rope,  and  the  other  two  now  pull  in  directions  inclined  to  each 
other.  The  less  the  force  exerted  at  the  centre,  the  less  the  flexure  in  the  rope ;  but 


FIG.  379. 


FIG.  380. 


MECHANICS. 


193 


when  it  becomes  equal  to  the  sum  of  tiie  forces  at  the  ends,  the  two,  to  balance  it, 
must  pull  directly  against  it,  bringing  the  ends  of  the  rope  together,  and  acting  as  paral- 
lel forces.  Between  the  smallest  force  and  the  largest  that  can  be  exerted  at  the  centre 
and  maintain  a  balance  or  equilibrium,  the  ends  of  the  rope  assume  all  varieties  of  angles, 
which  angles  bear  definite  relations  to  the  forces. 

Represent  these  forces  by  weights  (Fig.  381).  Let  P  and  P'  be  the  extreme  forces 
acting  over  the  pulleys  M  and  N,  and  tending  to  draw  the  rope  straight,  which  the 
weight  P"  prevents.  Lay  off 
the  weight  of  P  (90  pounds) 
along  A  B,  and  the  weight  of 
P'  (60  pounds)  along  A  C. 
Draw  B  D  parallel  to  A  C, 
and  C  D  parallel  to  A  B. 
Connect  D  with  A.  If  this 
is  measured  with  the  same 
scale  that  A  B  and  A  C  were 
laid  off  with,  it  will  be  found 
that  it  equals  120  pounds, 
which  will  be  found  to  be  Fl° 


Fio.  384. 

the  same  as  the  weight  P".  A  D,  therefore,  gives  the  amount  and  direction  of  the  re- 
sultant of  the  two  forces  P  and  P',  which  resultant  is  balanced  by  P".  In  the  same 
way  the  resultant  of  any  number  of  inclined  forces  (Fig.  382)  may  be  found  by  com- 
pounding the  resultant  of  any  two  forces  with  a  third,  and  so  on. 

As  two  forces  may  be  compounded  into  a  single  resultant,  so  conversely  one  force 
may  be  resolved  into  two  components;  thus,  let  the  weight  P  (Fig.  383)  be  supported  by 
two  inclined  rafters,  C  A  and  C  B.  Each  resists  a  part  of  the  force  exerted  by  the  weight 
P.  To  find  the  force  exerted  against  the  abutments  A  and  B,  in  the  direction  of  C  A 
and  C  B,  draw  c  A'  (Fig.  384)  parallel  to  C  A,  c  B'  to  C  B,  and  c  d,  a  parallel  to  the  line 
C  P,  the  direction  in  which  the  weight  P  acts ;  lay  off  c  d  from  a  scale  of  equal  parts,  a 
length  which  will  represent  the  number  of  pounds,  or  whatever  unit  of  weight  there  may 
be  in  the  weight  P ;  draw  d  a  parallel  to  c  B',  and  d  &  parallel  to  c  A' ;  c  a,  measured  on  the 
scale  of  equal  parts  adopted,  will  represent  the  pounds  or  units  of  weight  exerted  against 
A  in  the  direction  of  C  A,  and  c  b  the  pounds  or  units  of  weight  exerted  against  B  in  the 
direction  of  C  B. 

This  method  of  finding  the  resultant  of  two  forces,  or  the  components  of  one  force,  is 
called  the  parallelogram  of  forces.  If  two  sides  of  a  parallelogram  represent  two  forces 
in  magnitude  and  direction,  the  resultant  of  these  two  forces  will  be  represented  in  mag- 
nitude and  direction  by  the  diagonal  of  the  parallelogram  and  conversely. 

The  sum  of  a  c  and  c  &  is  greater  than  c  d;  that  is,  the  weight  P  exerts  a  greater  force 

in  the  direction  of  the  lines  C  A  and  C  B,  against  A  and  B,  than  its  own  weight;  but  the 

down  pressure  upon  A  and  B  is  only  equal  to  the  weight  of  P  and  of  the  rafters  which 

support  it,  which  last,  in  the  present  consideration,  is  neglected.     Resolve  c  &,  the  force 

14 


194 


MECHANICS. 


acting  on  B  in  the  direction  of  c B',  into  gb  or  c e  the  downward  pressure,  and  eg  or  eb 
the  horizontal  thrust  on  the  abutment  B,  and  c  a  into  cf  and  fa.    To  decompose  a  force, 

form  a  triangle,  with  the  direction  of  the  other 
forces,  upon  the  line  representing  the  magni- 
tude and  direction  of  the  given  force ;  c  e  repre- 
sents the  weight  on  B,  c/the  weight  on  A;  cd, 
or  ce  +  de,  the  whole  weight  P;  therefore,  the 
weight  upon  the  two  abutments  A  and  B  is 
equal  to  the  whole  weight  of  P. 

The  steelyard  (Fig.  385)  is  a  lever,  from  the 
short  arm  of  which  a  dependent  hook  or  scale 
supports  the  article  to  be  weighed;  while,  on 
Fio.  385.  the  long  arm,   a  fixed  weight,  P,  is  slid  in  cr 

out  from  the  fulcrum  till  it  balances  the  article ; 

the  distance  as  marked  on  a  scale  on  the  long  arm  determines  the  weight.     In  plat- 
form-scales, when  very  heavy  weights  are  balanced  by  small  weights  on  a  graduated  arm, 


Fio.  386. 


combinations  of  levers  are  used,  the  principle  of  which  can  be  understood  from  Fig.  386. 
Thus,  suppose  P  F  to  be  7",  a  F  2",  a  F'  9",  I  F'  2",  b  F"  11",  F"  W  3". 

P  is  to  force  a  as  a  F  to  P  F,  or  as  2  to     7 

Force  a  is  to  5  as  &  F'  to  a  F,  or  as  2  to     9 

I  is  to  W  as  F"  W  to  &  F",  or  as  3  to  11 


P  is  to  W  as 


12  to  693 


The  differential  axle,  or  Chinese  capstan,  consists  of  an  axle  with  two  different  diam- 
eters (Fig.  387),  the  weight  W  being  suspended  in  the  loop  of  a  cord  wound  around 


FIG.  387. 

these  axles  in  opposite  directions  by  a  single  turn  of  the  axle.  The  weight  is  only  raised 
or  lowered  by  the  difference  between  these  two  circumferences;  one  takes  up  while  the 
other  lets  out,  and  the  P,  to  balance  W,  must  be  as  these  differences  of  circumference  of 
axles  is  to  the  circumference  of  the  wheel  from  which  P  is  suspended. 

The  differential  screw  (Fig.  388)  consists  of  an  exterior  screw,  A,  and  an  interior 
screw,  B.     By  the  revolution  of  the  arm,  the  screw  A  is  moved  through  the  plate  D  in 


MECHANICS. 


195 


proportion  to  its  pitch,  but  the  interior  -screw  B  moves  inward  its  pitch,  and  the  move- 
ment of  W  is  only  the  pitch  of  A  less  that  of  B,  and  the  power  applied  is  to  the  weight 
moved  as  the  difference  of  these  pitches  is  to  the  circumference  described  by  the  power. 
As  the  lever  (Fig.  889)  moves  under  the  action  of  power  or  weight,  the  lever  be- 
comes inclined  to  the  direction  of  the  forces,  but  the  forces  are  still  parallel.  The  rela- 
tions of  the  forces  to  each  other  are  not  changed,  but  the  absolute  action  of  each  is  only 
that  due  to  the  length  a  &  and  &  c,  to  which  the  directions  of  the  forces  are  perpendicular. 
In  the  bent  lever  (Fig.  390)  the  action  of  the  forces  is  estimated  on  lengths  of  arms, 


r 


C 


m 

§ 


FIG.  391. 


FIG.  389.  FIG.  390. 

determined  by  the  perpendiculars  a  b  and  &  c  let  fall  from  the  fulcrum  on  the  directions 

of  the  forces. 

The  toggle-joint  (Fig.  391)  is  much  used  for  presses.     The  force  is  exerted  in  the 

direction  of  the  arrow  at  C,  and  the  effective  force  is  to 

separate  the  plates  A  and  B.     The  action  is  as  shown  in 

Fig.  391a.      Equal  movements,  as  C-l,   1-2,   2-3,  corre- 
spond to  unequal  movements  at  A  and  B,  as  A  a',  a'  a?, 

a?  a3.      The  nearer  the  force  C  is  to  the  line  A  B,  the 

less  the  movement  <zaa3;  and,  consequently,  the  force  C 

exerts  greater  effects  in  intensity,  but  the  latter  is  less  in 

movement. 

Fig.  392  exhibits  the  principle  of  the  hydraulic  press. 

The  small  plunger  or  piston  may  be  considered  the  application  of  the  force,  and  the 

large  one  the  weight  to  be  raised  to  balance  each  other;  the  pressure  per  square  inch  of 

surface  must  be  the  same, 
and  the  force  must  be  to 
weight  as  the  surface  of 
its  piston  is  to  that  of 
the  weight  -  piston.  If 
motion  takes  place,  the 
force  will  move  through 
space  corresponding  to 
the  area  of  weight-pis- 
ton, while  the  weight  will 
move  that  of  the  area  of 

the  force-piston.     And  this  is  the  great  principle  of  all  mechanism  in  the  transmission 

of  force :  there  can  be  no  total  gain.     What  is  gained  in  force  is  lost  in  movement,  and 

in  many  complicated  machines  the  theoretical  comparison  of  force  applied  and  resultant 

force  may  be  ascertained  by  the  measures  of  their  movements. 


FIG.  391o. 


196 


MECHANICS. 


1  Ib. 


FIG.  392. 


The  resultant  effects  of  forces,  as  heretofore  treated, 
have  been  without  motion,  or  static.  But  when  motion 
is  produced,  the  forces  are  called  dynamic.  A  weight  sus- 
pended or  supported  exerts  a  force,  which  is  balanced  by 
the  resistance  of  the  suspending  or  supporting  medium; 
but  a  falling  weight  acquires  an  increasing  velocity  with 
every  unit  of  time  or  space  passed.  All  bodies  would  fall 
with  the  same  velocities  were  it  not  for  the  different  re- 
sistances from  the  air  due  to  their  different  bulk  in  pro- 
portion to  their  weight.  Dense  articles,  as  stones  and  met- 
als, acquire  a  velocity  in  this  latitude  of  about  32 '2  feet  in 
each  second,  called  the  intensity  of  gravity,  or  g.  The 
value  of  g  at  the  equator  is  32-088;  at  the  poles,  32 -253. 
A  body 


Starting  with  a  velocity 

Falls  during  the  1st  second 

Acquiring  a  velocity  of 

falls  during  the  2d  second  

Acquiring  a  velocity  of  twice  32,  or 

Falls  during  the  3d  second 

Acquiring  a  velocity  of  3  X  32  = 

Falls  during  the  4th  second 
Arxjuiring  a  velocity  of  4  X  32  = 

Falls  during  the  5th  second 
Acquiring  a  velocity  of  5  X  32  = 


.0  Ft.    Tot.  Fall. 

16\=      , 16        16 

\32  feet  per  second. 


\64  feet  per  second. 


48       64 


16\=     80        144 


96vfeet  per  second. 

16\=      112       256 

128  feet  per  second. 


16\  = 


..   144        400 


160  feet  per  second. 


Calling  s  the  space  passed  over,  V  the  terminal  velocity  in  feet,  t  the  time  in  seconds 
of  falling,  s  =  $gt*,  v  =  gt  or  =  ^/64.4s.  In  determining  the  velocity  of  issuing  water 
under  a  head  A,  corresponding  to  8  in  the  equation,  it  is  generally  near  enough  to  reckon 
v  as  eight  times  the  square  root  of  the  head  (^h). 

The  motion  of  falling  bodies  is  a  uniformly  accelerated  one,  but  there  are  also  uni- 
formly retarded  motions  in  which  the  velocity  is  decreased  by  equal  losses  in  equal  times. 
There  are  also  uniform  motions  when  bodies  are  impelled  by  a  constant  force  and  op- 
posed by  constant  resistances. 

In  Fig.  393,  o  s  represents  the  trace  of  a  body  impelled  horizontally  by  a  uniform, 
but  falling  through  the  action  of  gravity  with  an  accelerated,  force.  This  curve,  a 
parabola,  represents  approximately  the  curve  of  the  thread  of  stream  issuing  from  an 
orifice,  or  flowing. 

It  will  be  seen  that  to  produce  twice  the  velocity  the  body  must  fall  through  four 
times  the  space ;  that  there  is  four  times  the  force  stored  in  the  body.  But  to  maintain 
this  velocity  uniformly,  only  twice  the  force  is  necessary.  The  momentum  of  a  body  is 
its  mass  multiplied  by  its  velocity,  but  its  inertia  is  as  the  square  of  the  velocity.  It  is 
an  established  principle  of  mechanics  that  the  results  must  be  proportional  to  the  causes : 
if  a  body  has  to  be  raised  four  feet  to  obtain  a  double  velocity  in  falling,  the  destructive 
result  of  that  fall  must  also  be  four  times. 

Under  statics,  it  has  been  shown  that  forces  may  be  resolved  and  compounded.  The 
same  may  be  done  dynamically — that  which  has  been  treated  as  weight  must  now  be 
considered  as  momentum. 


MECHANICS. 


197 


In  treating  of  dynamic  forces  the  re"sultants  have  been  considered  as  equal  to  the  exer- 
tion, without  any  losses  by  resistances.  This  never  happens  in  practice ;  the  resistances 
are  a  very  large  element.  Resistances  from  the  medium 
in  which  the  bodies  are  moved  are  from  the  surfaces  on 
which  the  bodies  are  supported ;  resistances  due  to  the 
displacement  of  the  fluid  in  which  the  bodies  move,  and 
frictional  resistances,  or  what  is  termed  skin-resistances, 
of  bodies  moving  through  air  or  water;  and  the  surface- 
resistance  of  bodies  sliding  or  rolling  on  each  other. 
Suppose  a  weight  to  rest  on  a  horizontal  surface — it  will 
take  a  certain  force  to  move  the  insistent  weight  depend- 
ing on  the  amount  of  this  weight  and  the  kind  of  sur- 
faces in  contact,  and  the  force  that  will  just  cause  motion 
overcomes  the  friction,  or  frictional  force,  and  is  equal  to 
it.  The  frictional  force  is  only  a  percentage  of  the  in- 
sistent force  of  the  body,  and  this  percentage  is  called 
tbe  coefficient  of  friction.  If  the  horizontal  surface  of  sup- 
port be  raised  at  one  end,  so  as  to  make  the  surface  in- 
clined, it  will  after  a  time  become  so  steep  that  the  insist- 
ent body  will  slide  down  the  surface.  Thus,  in  Fig.  394, 

if  the  body  Q  is  ready  to  slip  on  the  surface  A  B,  the  angle  BAG,  which  represents  the 
angle  of  the  surface  with  the  horizontal,  is  called  the  angle  of  repose,  or  limiting  angle 
of  frictional  resistance;  or  thus  (Fig.  395),  if  the  force  acting  in  the  direction  P"Mis 


FIG. 


just  sufficient  to  produce  motion  of  the  mass  M  along  the  plane  F  Q,  the  angle  P  M  P" 
is  the  limiting  angle  of  resistance. 

General  Morin  has  made  an  elaborate  course  of  experiments  on  friction,  some  of  the 
results  of  which  are  given  in  the  table  on  the  following  page. 

In  Morin's  experiments  the  surfaces  of  the  woods  were  first  planed  and  those  of  the 
metals  filed  and  polished  with  the  utmost  care.  When  the  friction  without  lubrication 
was  to  be  determined,  any  unctuosity  was  especially  provided  against.  For  unctuous 
surfaces,  the  unguent  was  carefully  wiped  off,  so  that  no  layer  of  it  should  prevent  their 
intimate  contact. 

When  lubricated,  the  resistance  from  the  viscidity  of  the  lubricant  may  be  overlooked, 
compared  with  the  friction.  As  respects  the  nature  of  the  substance  used  in  lubrication, 
it  was  observed,  by  comparison  of  the  coefficient  of  the  friction  of  motion,  that  with 
hog's  lard  and  olive  oil  surfaces  of  wood  on  metal,  wood  on  wood,  metal  on  wood,  and 
metal  on  metal,  had  all  very  nearly  the  same  friction — between  0'07  and  0'08.  With  tal- 
low the  coefficient  was  the  same  except  in  the  case  of  metals  upon  metals. 

Practically  the  sliding  of  wooden  surfaces  on  each  other  or  on  metal  surfaces  is  con- 
fined within  small  limits.  As  far  as  possible,  sliding  surfaces  in  most  machines  or  me- 
chanical appliances  are  of  metals,  and  when  surfaces  are  liable  to  be  affected  by  rust  and 
adhere,  they  are  made  of  brass  or  bronze.  But  in  the  moving  of  houses  or  the  launching 
of  ships  the  ways  are  of  wood,  and  in  this  country  of  Southern  pine,  as  being  without 
knots  and  extremely  stiff. 


198 


MECHANICS. 


Sliding  Friction  of  M.  Morin's  Experiments  on  Plane  Surfaces. 


Sliding 
surface. 

8. 

Surface 
at  rest. 

s'. 

STATE  OF  THE  SURFACES. 

FRICTION  OF 
MOTION. 

FRICTION   OF 
QUIESCENCE. 

II 
il 

t°l 

2  ,2  a 

.W 

il 

ioi 

B-fi 

B<H 

OtM 

Oo 

S  M.5S 

"3  M  01 

M  4  S 

K 

Btl 

<ij  <w 

o^ 

G  iCW 

"1  «  03 

h-1  d  o> 

Oak  

Oak  

Fibres  s  s'  parallel  to 
motion. 
Fibres  s  perpenclic-  j 
ular  to  motion..  .  \ 
Fibres    s  s'    perpen- 
dicular to  motion. 
Fibres  s  s'  parallel  ( 
to  motion. 
Fibres  s  s'  parallel  j 
to  motion.              { 
Fibres  s  perpendicu- 
lar to  motion. 
Fibres  s  s'  parallel  j 
to  motion            .  ( 

Without  lubrication 

Without  lubrication 
Unctuous  

0-478 

0-324 
0-143 
0-336 

0-246 
0-136 
0-432 
0-119 
0-450 

0-360 
0-330 
0-490 
0-107 
0-372 

0-195 
0-125 
0-138 
0-177 
0-194 

25°33' 

17  58 
8  9 
18  35 

13  50 
7  45 
23  22 
6  48 
24  16 

19  48 
18  16 
26  7 
6  7 
20  25 

11  3 
7  8 
7  52 
10  3 
10  59 

0-625 

0-540 
0-314 

0-376 

0-694 
0-420 
0-570 

0-530 

o-ioo 

0-137 

0-194 
0-118 

0-100 
0-162 

0-100 

o-ioo 

0-164 

32°  1' 

28  23 
17  26 

20  37 

34  46 
22  47 
29  41 

27  56 
5  43 

7  49 

10  59 
6  44 

5  43 
9  13 

5  43 
9  19 

Oak      .  .    . 

Oak  

Oak    

Oak  

Without  lubrication 

Without  lubrication 
Unctuous  

Oak      . 

Elm  

Elm  

Beech  
Cast-iron.. 
Oak  

Oak...  J 

Oak  
Oak  .... 

Without  lubrication 
Unctuous  

Without  lubrication 

Without  lubrication 
Unctuous  

Fibres  s  s'  parallel  j 
to  motion         .       | 

Without  lubrication 
Unctuous  

Cast-iron  . 

Elm  

Wrought- 
iron. 

Cast-iron  . 

Wrought- 
iron. 

Cast-iron  . 

Bronze  .  .  . 

Wrought- 
iron. 
Bronze  .  .  . 

Cast-iron  . 
Bronze  .  .  . 
Cast-iron  . 

Fibres   of    the   wood 
perpendicular       to 
motion. 
Fibres  of  the  wood  ( 
parallel  to  motion.  ( 
Fibres  s  s'  parallel  j 
to  motion  | 

Without  lubrication 

Without  lubrication 
Surface  unctuous.  .  . 
Without  lubrication 
Surfaces  unctuous.. 
Without  lubrication 
Surfaces  unctuous.. 
Lubricated         with 
olive  oil  

Cast-iron.. 

Wrought- 
iron. 

Wrought- 
iron. 

Cast-iron.. 

Cast-iron  .  . 

Wrought- 
iron. 
Bronze..  .  . 

Cast-iron.. 
Bronze..  .  . 
Bronze..  .  . 
Steel  

Fibres  s  s'  parallel  J 
to  motion  ] 

Fibres  s  s'  parallel  \ 
to  motion  1 

0-066 
0-143 
0-152 
0-144 
0-314 
0-197 
0-100 
0-070 
0-064 

0-055 
0-172 
0-160 
0-161 
0-166 
0-147 
0-132 
0-217 
0-107 
0-201 
0-134 
0-202 

Surfaces  unctuous.. 
Without  lubrication 
Surfaces  unctuous.. 
'  water  
soap  

8  9 
8  39 
8  12 

5  43 

Fibres  s  s'  parallel  \ 

Lubri-     tallow  
cated  •{  lard  

to  motion  1 

Fibres  s  s'  parallel 
to  motion  \ 

with       olive  oil.   : 
lard       and 
(_    plumbago 
Without  lubrication 
Surfaces  unctuous.  . 
Without  lubrication 
Surfaces  unctuous.. 
Without  lubrication 
Surfaces  unctuous.. 
Without  lubrication 
Surfaces  unctuous.. 
Without  lubrication 
Surfaces  unctuous.. 
Without  lubrication 

9  46 
9  6 
9  9 
9  26 

8  22 
7  22 
12  15 
6  7 
11  22 
7  38 
11  26 

Fibres  s  s'  parallel  j 
to  motion  | 

Fibres  s  s'  parallel  { 
to  motion  | 

Fibres  s  s'  parallel 
to  motion  

Fibres  s  s'  parallel 
to  motion  

Fibres  s  s'  parallel  to 
motion. 

In  the  launching  of  a  vessel,  the  width  of  the  ways  must  be  proportioned  to  its 
weight,  not  to  exceed  three  tons  per  square  foot.  A  slope  of  f "  to  the  foot  permits  the 
control  of  the  vessel  if  necessary.  On  a  slope  of  £"  to  the  foot,  a  vessel  will  move 
steadily  and  gently  down  without  attaining  a  high  speed,  and  is  the  one  adopted  where 
other  circumstances  do  not  affect  the  choice.  A  slope  of  |"  to  the  foot  is  often  used 
for  large  vessels;  the  speed  attained,  however,  is  very  high,  and  in  narrow  water  both 
dangerous  and  inconvenient.  A  slope  of  1  in  12  may  be  used  where  the  distance  to  be 
traversed  is  short,  and  the  ship  launched  broadside  in. 


MECHANICS. 


199 


Before  striking  the  dog-shore,  which  prevents  the  ship  from  sliding  down  the  ways, 
they  are  thoroughly  slushed  with  some  greasy  mixture,  like  tallow  and  soap. 

It  was  formerly  held  that  friction  was  directly  as  the  weight,  without  regard  to  the 
amount  of  surface  or  velocity  of  movement,  and  Morin's  experiments,  referred  mostly  to 
the  friction  of  quiescence  and  slow  movements,  come  within  this  rule ;  the  results  give 
coefficients  that  may  be  considered  maxima,  but  in  practice  it  has  been  found  that  the 
coefficient  of  friction  with  unguents  is  reduced  by  increase  of  velocity  and  of  tempera- 
ture, that  extent  of  surface  may  be  prejudicial,  and  that  careful  selection  of  unguents, 
according  to  the  work  to  be  done,  will  reduce  friction. 

Axle  and  Rolling  Friction. — Axle  friction  has  been  generally  supposed  to  follow  the 
laws  of  sliding  friction,  with  the  exception  that  its  coefficient  is  a  smaller  fraction  of  the 
total  pressure  applied.  There  are  but  few  experimental  data  relating  to  this  branch  of 
the  subject.  The  results  of  some  experiments  by  Morin  are  given  in  the  following  table : 

Ratios  of  Friction  to  Pressure  for  Axles  in  Motion  in  their  Bearings. 

I.— ACCORDING  TO   MORIN'S   EXPERIMENT. 


DESIGNATION  OF  SURFACES 
IN  CONTACT. 

State  of  surfaces  and  nature  of  lubrication. 

Dry  or  slightly 
greasy. 

Greasy,  and  wet 
with  water. 

Lubricated,  and 
wet  with  water. 

Oil,  tallow,  or 
hogs1  lard. 

•  Purified  very 
soft  grease. 

Hogs1  lard  with 
plumbago. 

Greasy,  very 
soft  to  the  touch. 

Supplied 
in  the 
ordinary 
manner. 

The 
grease 
continu- 
ally 
renewed. 

I'.ronze  on  bronze  

0-079 

Bronze  on  cast-iron  

0-049 
0-054 
0-054 
0-054 
0-054 

1  ron  on  bronze  

0-251 

0-189 

0  075 
0-075 
0-075 
0-075 
0-125 

o-ioo 

0-116 

0-090 

0-111 

Iron  on  cast-iron  ... 

Cast-iron  on  cast-iron  

0-137' 
0-161 

0-079 

Cast-iron  on  bronze  

0-194 
0-188 
0-185 

0-065 

0-1-37 
0-166 
0-140 
.0-153 

Iron  on  lignum-vitae..  . 

Cast-iron  on  lignum-vitae  
Lignum-vitjB  on  cast-iron  

0-92 

0-109 

Lignum-vitas  on  lignum-vitae.. 

0-170 

It  is  well  known  that  the  obstruction  which  a  cylinder  meets  in  rolling  along  a  smooth 
plane  is  quite  distinct  in  its  character,  and  far  less  in  amount,  to  that  which  is  produced 
by  the  friction  of  the  same  cylinder  drawn  lengthwise  along  a  plane. 

In  the  composition  of  machines  attrition  should  be  avoided  as  much  as  possible,  and 
rolling  motions  substituted. 

On  this  principle  depend  the  advantages  of  the  application  of  friction-wheels  and  fric- 
tion-rollers. The  extremity  of  an  axle  c,  Fig.  395a,  instead  of 
resting  in  a  cylindrical  socket,  is  made  to  rest  on  the  circum- 
ferences of  two  wheels,  A  and  B,  to  the  axles  of  which,  a  and  &, 
the  friction  is  transferred,  and  consequently  diminished  in  the 
ratio  of  the  radius  of  the  wheel  A  to  the  radius  of  the  axle  a. 

At  speeds  and  pressures  usual  in  machinery,  the  resistance 
from  friction  decreases  as  the  journals  and  bearings  heat  up  to 
limits  which  the  engineer  and  mechanic  would  consider  safe. 

With  very  heavy  pressures  and  slow  speeds,  the  lubricant 
may  be  forced  out  and  journal  and  lubricant  be  brought  into 

close  bearing,  while  with  light  pressure  and  low  speeds  the  journals  float  on  the  film  of 
fluid,  and  the  frictional  resistance  is  independent  of  the  materials  of  which  journal  and 
bearing  are  composed. 

Mr.  C.  J.  H.  Woodbury,  in  his  experiments  on  the  driving  of  cotton  spindles,  found 
the  coefficient  of  friction  to  be  from  7  to  SO^er  cent,  the  load  being  from  1  to  5  pounds 


FIG   395a. 


200  MECHANICS. 

per  square  inch,  while  Prof.  Thurston,  with  heavy  loads  of  1,000  pounds  per  square  inch, 
as  on  the  crank-pins  of  the  North  River  steamboat  engines,  found  the  coefficient  of  fric- 
tion was  one  half  of  one  per  cent,  the  unguent  being  sperm  oil.  Practically,  it  may  be 
said  that  the  coefficient  of  friction  for  light-running  spindles  should  not  exceed  10  per 
cent,  and  for  the  usual  work  in  shops,  of  say  100  to  200  pounds,  should  not  exceed  from 
2  to  3  per  cent. 

For  lubricants  under  heavy  pressure  and  slow  speeds,  use  graphite,  soapstone,  tallow, 
lard,  and  greases.  For  the  journals  of  calender  rolls  in  paper  mills,  it  is  common  to  lay 
on  the  top  of  the  journals  a  large  piece  of  salt  pork,  skin  up. 

Cast  iron  holds  oil  better  than  any  other  metal  or  alloy,  and  is  the  best  metal  to  use 
for  light  bearing,  perhaps  for  heavy. 

It  has  been  proved  by  Mr.  Waite's  experiments  that  a  highly  polished  bearing  is 
more  liable  to  friction  than  any  surface  finely  lined  by  filing.  The  lines  left  by  the  file 
serve  as  reservoirs  for  the  oil,  while  the  high  polish  leaves  no  room  for  the  particles  be- 
tween the  metal  surfaces. 

Mr.  Waite's  experiments  on  very  heavy  bearings  at  Manchester,  N.  H.,  go  far  "to 
prove  that  a  considerable  quantity  of  thin,  fine  oil  keeps  the  bearing  much  cooler,  and 
requires  less  power  than  a  smaller  quantity  of  thick,  viscous  oil.  No  vegetable  oil  is  fit 
to  use  as  a  lubricant,  and  castor  oil  is  the  worst  of  all,  because  the  most  viscous,  and  all 
vegetable  oils  in  connection  with  fine  vegetable  fibre,  like  cotton,  are  liable  to  spontaneous 
combustion. 

"  The  rule  of  best  lubrication  is  to  use  an  oil  that  has  the  greatest  adhesiveness  to  metal 
surfaces,  and  the  least  adherence  as  to  its  own  particles.  Fine  mineral  oils  stand  first  in 
this  respect,  sperm  second,  neat's-foot  third,  lard  fourth." 

Experiments  on  rolling  friction  usually  include  that  of  the  axles.  The  resistance 
of  a  wheel  rolling  on  a  smooth  and  resistant  plane  is  very  different,  and  much  less 
than  that  of  the  same  wheel  fixed  and  sliding  on  the  same  plane;  a  moving  railroad 
train  is  brought  to  a  stop  by  the  brake  reducing  or  stopping  the  rotation  of  the 
wheels. 

Between  the  usual  diameters  of  wheels  the  resistance  has  not  been  found  to  increase 
inversely  as  the  diameter,  but  rather  as  their  square  roots  of  the  diameter,  and  less  on 
hard  and  well-graded  roads. 

Of  the  resistance  dependent  on  the  material  and  character  of  the  roads  there  have 
been  many  experiments.  The  following  formula  and  table  is  from  Prof.  Thurston  on 
"Rolling  Friction." 

W 

R=/_   in  which  R  =  resistance,  W  the  total  weight,  and  r  the  radius  of  the  wheel: 
r 

Kind  of  road.  Value  of  friction. 

Well  paved 0'02 

Hard,  smooth  ground 0'02 

Well  macadamized  and  rolled , O'OIS 

Smooth  wooden  pavement O'Ol 

Ordinary  railroads 0  '003 

Best  possible  railroad O'OOl 

"On  railway  trains  a  minimum  resistance  is  reached  usually  at  a  speed  between  10 
and  15  miles  per  hour,  but  the  increase  is  not  great  at  higher  speeds  where  the  common 
system  of  lubrication  is  practised ;  in  ordinary  work,  the  resistance  varies  as  low  as  from 
4  pounds  per  ton  of  train  up  to  25,  and  sometimes  above  30  pounds. " 

At  a  speed  of  25  miles  per  hour,  Chanute  makes  the  increase  of  resistance  due  to 
curvature  about  0'4  pound  per  degree  per  ton. 

The  amount  of  resistance  is  measured  by  the  weight  resting  on  the  axles,  multiplied 
by  c,  which  is  dependent  on  the  condition  of  the  surface  of  the  rails : 


MECHANICS.  201 

Perfectly  dry . ._. c  =  £ 

Average  condition \  to  ^ 

Damp  in  rain,  fog,  or  tunnel ^ 

Greasy  or  iced ^ 

With  head  winds  the  resistance  is  increased  with  the  square  foot  of  front  exposed  and 
as  the  square  of  the  velocity  in  miles  per  hour. 

Side  winds,  by  forcing  the  flanges  of  the  wheels  against  the  rails,  adds  very  seriously 
to  the  resistance  of  draught. 

On  street  railways  the  resistance  to  the  movement  of  cars  is  greater  than  upon  rail- 
roads, and  may  be  considered  from  3  to  5  times  as  much. 

From  his  experiments  in  1840,  Morin  states  the  resistance  applied  at  the  circumfer- 
ence of  the  wheel  on  pavements  and  macadamized  roads  to  be  inversely  proportional  to 
the  diameter  of  the  wheel  independent  of  the  breadth  of  the  tire  and  increasing  with  the 
velocity. 

By  the  Studebacker  experiments  in  South  Bend,  Ind.,  it  was  found  that  there  was  no 
reduction  in  resistance  on  hard  roads  in  increasing  the  width  of  the  tire,  but  rather  the 
contrary,  nor  in  soft  mud  or  slush ;  but  on  sandy  roads  or  across  fields  the  resistance  is 
very  much  less  with  a  broad  tire. 

In  many  States  there  are  laws  regulating  the  width  of  tire  in  proportion  to  the  load, 
and  even  on  the  harder  roads  it  is  supposed  that  the  broad  tire  deteriorates  the  track 
less  than  the  narrow  one,  and  in  fact  acts  as  a  roller  and  improves  the  roadway,  and  for 
the  same  purpose  the  front  wheels  are  of  less  gauge  than  the  hind  ones,  that  they  may 
not  track  in  the  same  rut. 

It  is  of  importance  that  the  line  of  draught  should  be  horizontal,  as  with  an  oblique 
pull  the  effort  of  the  animal  may  either  be  exerted  in  carrying  the  load  or  by  increasing 
the  resistance  of  it  on  the  roadway. 

MECHANICAL   WORK   OR   EFFECT. 

Mechanical  work  is  the  effect  of  the  simple  action  of  a  force  upon  a  resistance  which 
is  directly  opposed  to  it,  and  which  it  continuously  destroys,  giving  motion  in  that  di- 
rection to  the  point  of  application  of  the  resistance ;  it  is  therefore  the  product  of  two 
indispensable  qualities  or  terms : 

First. — The  effort,  or  pressure  exerted. 

Second. — The  space  passed  through  in  a  given  time,  or  the  velocity. 

The  unit  of  force  in  England  and  here  is  represented  by  the  pound,  and  the  unit  of 
space  by  the  foot. 

The  amount  of  mechanical  work  increases  directly  as  the  increase  of  either  of  these 
terms,  and  in  the  proportion  compounded  of  the  two  when  both  increase.  If,  for 
example,  the  pressure  exerted  be  equal  to  4  pounds,  and  the  velocity  one  foot  per  second, 
the  amount  of  work  will  be  expressed  by  4  x  1  =  4.  If  the  velocity  be  double,  the  work 
becomes  4x2  =  8,  or  double  also ;  and  if,  with  the  velocity  double,  or  2  feet  per  second, 
the  pressure  be  doubled  as  well — that  is,  raised  to  8  pounds — the  work  will  be  8  x  2  =  16 
pounds  feet.  It  is  more  usual  to  write  foot-pounds  ;  but  as  explained  before  the  Conti- 
nental idiom  of  Tcilogrammetre  is  followed,  in  which  the  unit  of  force,  kilogramme,  pre- 
cedes that  of  space,  the  metre,  it  should  be  pounds-feet. 

In  comparison  of  motors  with  each  other,  it  is  usual  to  speak  of  them  as  so  many 
horse-power  equivalent  to  550  pounds-feet  per  second,  or  33,000  pounds-feet  per  minute. 
The  Continental  horse-power  is  equal  to  75-  kilogrammetres  or  542 '48  pounds-feet  per 
second. 

It  is  very  common  to  use  other  units  of  force  and  space,  as  tons-miles;  and  train- 
miles,  in  railway  practice. 

The  time  must  also  be  expressed  or  understood.     It  is  impossible  to  express  or  state 


202  MECHANICS. 

intelligibly  an  amount  of  mechanical  effect  without  indicating  all  the  three  terms — force, 
space,  and  time. 

The  motors  generally  employed  in  manufactures  and  industrial  arts  are  of  two  kinds 
— living,  as  men  and  animals ;  and  inanimate,  as  water  and  steam. 

What  may  be  termed  the  amount  of  a  day's  work,  producible  by  men  and  animals,  is 
the  product  of  the  force  exerted,  multiplied  into  the  distance  or  space  passed  over,  and 
the  time  during  which  the  action  is  sustained.  There  will,  however,  in  all  cases  be  a 
certain  proportion  of  effort,  in  relation  to  the  velocity  and  duration,  which  will  yield  the 
largest  possible  product  or  day's  work  for  any  one  individual,  and  this  product  may  be 
termed  the  maximum  effect.  In  other  words,  a  man  will  produce  a  greater  mechanical 
effect  by  exerting  a  certain  effort  at  a  certain  velocity  than  he  will  by  exerting  a  greater 
effort  at  a  less  velocity,  or  a  less  effort  at  a  greater  velocity,  and  the  proportion  of 
effort  and  velocity  which  will  yield  the  maximum  effect  is  different  in  different  indi- 
viduals. 

In  the  manner  and  means  in  which  the  strength  of  men  and  animals  is  applied  there 
are  three  circumstances  which  demand  attention: 

1.  The  power,  when  the  strength  of  the  animal  is  exerted  against  a  resistance  that  is 
at  rest. 

2.  The  power,  when  the  stationary  resistance  is  overcome,  and  the  animal  is  in  mo- 
tion. 

3.  The  power,  when  the  animal  has  attained  the  highest  amount  of  its  speed. 

In  the  first  case  the  animal  exerts  not  only  its  muscular  force  or  strength,  but  at  the 
same  time  a  very  considerable  portion  of  its  weight  or  gravity.  The  power,  therefore, 
from  these  causes  must  be  the  greatest  possible.  In  the  second  case  some  portion  of  the 
power  of  the  animal  is  withdrawn  to  maintain  its  own  progressive  motion ;  consequently 
the  amount  of  useful  labour  varies  with  the  variations  of  speed.  In  the  third  case  the 
power  of  the  animal  is  wholly  expended  in  maintaining  its  locomotion ;  it  therefore  can 
carry  no  weight. 

Weisbach  calls  the  mean  effort  of  an  animal  one  fifth  its  weight,  which  may  serve  as 
a  general  rule,  but,  in  practice,  will  be  considerably  modified,  when  applied  to  the  indi- 
vidual, depending  upon  the  exertions,  and  the  conditions  and  circumstances  under  which 
it  is  made.  A  man-power  is  usually  estimated  at  one  sixth  of  a  horse-power  (H.  P.); 
yet,  if  the  muscular  force  of  a  man  be  required  for  an  effort  of  short  duration,  it  will  ex- 
ceed one  horse-power.  Thus,  a  horse-power  is  equal  to  33,000  pounds-feet  per  minute, 
or  550  pounds-feet  per  second;  and,  if  a  man  weighing  150  pounds  move  upstairs  at  the 
rate  of  four  feet  per  second,  he  exerts  a  force  of  600  pounds-feet,  which  he  can  readily 
double  for  a  few  seconds. 

The  force  of  a  man  is  utilized  mechanically  through  levers,  as  in  pumping  or  rowing, 
or  at  a  vertical  capstan,  or  at  a  crank,  carrying  or  dragging  loads,  shovelling,  etc.  In 
continuous  work  at  the  lever  he  will  exert  from  25  to  30  pounds ;  at  the  crank,  from  15 
to  20  pounds. 

The  muscular  force  of  horses  is  utilized  in  the  draught  of  carriages,  in  hoisting,  and 
in  horse-powers,  either  moving  in  a  circle  round  a  central  shaft  or  on  a  revolving  plat- 
form, or  on  an  endless  belt.  The  draught  of  a  horse  varies  with  the  speed  of  movement 
and  its  duration.  Trautwine  gives  the  draught  of  a  horse  at  two  and  a  half  miles  per 
hour  for  10  hours  per  day,  100  pounds;  8  hours,  125  pounds;  6  hours,  166f  pounds;  5 
•hours,  200  pounds.  The  omnibus -horses  here  average  nearly  six  miles  per  hour,  and 
make  18  to  24  miles  per  day;  the  average  will  not  exceed  16  miles.  At  the  Manhattan 
Gas  Works  a  span  of  horses  hoist  from  the  lighter  200  tons  gross  in  10  hours  to  the 
height  of  say  25  feet,  with  charges  of  6  to  the  ton,  in  a  bucket  weighing  150  pounds,  the 
rope  passing  over  a  single  block  and  through  a  snatch-block.  On  a  horse-power,  the 
force  exerted  by  a  single  horse  is  from  125  to  175  pounds,  at  an  average  speed  of  about 
three  milos  per  hour,  and  for  eight  hours  per  day.  Beyond  a  speed  of  four  miles  per 


MECHANICS. 


203 


hour  the  pounds-foot  of  work  of  a  horse  will  decrease  in  an  increasing  ratio  up  to  the 
limits  of  his  speed,  when  the  whole  work  done  will  be  used  up  in  locomotion.  In  pro- 
portioning levers,  cranks,  traces,  chains,  through  which  animal  force  is  transmitted  to 
machines,  or  for  mechanical  purposes,  it  is  not  safe  to  estimate  the  stress  as  the  average 
force ;  there  are  impulses  and  stresses  in  action  which  will  exceed  the  weight  of  the 
animal. 

Water-Power. — Water,  used  for  the  purposes  of  power,  moves  machinery  either  by  its 
weight,  by  pressure,  by  impact,  or  by  reaction,  and  is  applied  through  various  forms  of 
wheels. 

Fig.  396  is  what  is  termed  a  tub  wheel  with  a  vertical  shaft,  the  wheel  running  in  a 
bottomless,  wooden  case  or  tub  to  which  the  water  is  conveyed  by  a  wooden  trunk  or  spout 

and  acting  on  the  floats  or  buckets  by  im- 
pact. The  wheel  was  commonly  used  for 
grist  mills,  and  the  power  was  applied  di- 
rectly to  the  stones  through  the  vertical 
shaft.  The  same  wheel  on  a  horizontal 


FIG.  390. 


FIG.  397. 


shaft,  without  the  tub,  was  called  a  flutter  wheel,  and  the  power  was  transferred  by  a 
crank  on  the  shaft  through  a  wooden  connecting  rod  or  pitman  to  the  saw  frame  of  a 
saw  mill.  A  similar  wheel,  but  of 
larger  diameter,  was  suspended  over 
the  surface  of  a  stream,  the  floats  be- 
ing dipped  into  the  water  sufficiently 
to  give  motion  and  power. 

Fig.  397  is  the  section  of  the  up- 
per part  of  a  breast  wheel,  in  which 
the  water  is  admitted  through  the 
gates  g  g  g,  acting  after  its  delivery 
into  the  buckets  through  gravity ;  the 
power  is  transferred  through  the  cir- 
cumferential gear  to  a  jack  shaft,  usu- 
ally placed  below  the  gates ;  a  plank 
case  called  the  breast  is  set  outside 
the  wheel  with  but  little  clearance 
from  the  gates  to  within  a  few  feet 
of  the  bottom  of  the  wheel.  Wheels 
of  this  class,  where  water  is  brought 
over  the  top  of  the  wheel  and  dis- 
charged into  the  buckets  without  a 
breast,  is  called  an  overshot  wheel, 
and  when  the  water  is  discharged  be- 
neath the  wheel,  an  undershot.  The 
overshot  and  breast,  when  properly  FIG.  398. 


204 


MECHANICS. 


proportioned,  give  a  good  percentage  of  effect,  but  occupy  considerable  space,  and  the; 
speed  of  the  gear  is  slow. 

Fig.  398  is  one  of  the  earliest  improvements  of  the  reactor,  the  Scotch  wheel ;  the 
principle  is  that  of  the  sky-rocket.  It  is  very  simple  in  construction;  the  central  curve 
of  the  hollow  arm  or  adjutage  is  constructed  like  a  cam,  in  which  the  horizontal  move- 
ment is  a  percentage  of  the  radial  velocity  due  to  the  head,  and  the  cross  sections  of  the 
arm  a  contracted  vein. 

The  above  wheels  belong  rather  to  history,  but  there  are  positions  and  circumstances 
which  make  them  the  most  available. 

The  wheels  now  in  use  are  mostly  of  cast  iron  or  bronze,  occupying  small  space,  and 
the  shafts  giving  a  velocity  nearly  proportioned  to  the  speed  of  the  machinery  which  it 
is  to  drive. 

.  Fig.  399  is  a  Fourneyron,  called  in  this  country  a  Boyden  wheel,  from  the  improve- 
ments which  he  made  upon  it.  The  water  flowing  downward  through  a  pipe  is  diverted 
by  guides  at  the  bottom,  which  give  it  an  outward  direction  with  a  tangential  whirl  as  it 
strikes  the  buckets  of  the  wheel,  which  are  formed  to  give  a  reactive  impulse. 

In  Fig.  400,  the  Jonval,  there  are  fixed  guides  in  the  tube  that  give  motion  to  the 
water  against  guides  in  the  wheel  beneath  and  a  resulting  reaction. 


FIG.  399. 


FIG.  400. 


FIG.  401. 


Fig.  401  is  the  type  of  wheel  commonly  used ;  the  fixed  guides  are  at  the  outside  of 
the  wheel  and  the  motion  of  the  water  is  inward  and  downward  against  the  buckets. 
The  shaft  of  this  wheel  is  generally  vertical,  and  the  power  transmitted  generally  through 
bevel  gears,  but  it  is  often  preferable  to  set  the  shaft  horizontally  and  transmit  the  power 
through  belting.  These  wheels,  whether  horizontal  or  vertical,  can  be  set  above  the  tail 
race  and  the  entire  fall  utilized  through  draught  tubes  below  the  wheels,  and  admit  of 
the  use  of  belts.  The  greatest  length  of  draught  tube  from  the  centre  of  horizontal 
shaft  to  tail  water  at  Manchester,  N.  H.,  is  26  feet. 

Wheels  can  be  furnished  by  many  makers  from  stock  from  6  to  84  inches  in  diameter, 
the  smaller  ones  for  very  extreme  heads  of  water,  and  the  larger  to  the  limit  of  100  feet. 
The  power  for  the  different  wheels  depends  on  the  head,  the  speed  of  the  shaft  on  the 
size  of  the  wheels.  For  the  best  percentage  of  effect,  the  wheel  must  be  of  good  de- 
sign, material,  and  workmanship,  and  the  makers  will  give  their  opinion  as  to  which  of 
their  wheels  they  consider  best  adapted  for  any  given  position. 

Fig.  402  is  the  elevation  of  a  Pelton  wheel,  in  which  the  action  of  the  water  on  the 
bucket  is  by  impact,  and  Fig.  403  a  section  of  the  bucket  showing  the  action  of  the 
water  upon  it;  they  work  under  heads  as  high  as  1,000  feet  and  to  2,000  H.  P.,  giving  n 
large  percentage  of  efficiency. 

However  used,  the  mechanical  effect  inherent  in  water  is  the  product  of  its  weight 
into  the  height  from  which  it  falls;  but  there  are  many  losses  incurred  in  its  application, 


MECHANICS. 


205 


so  that  only  a  portion  of  the  mechanical  effect  becomes  available ;  and  the  comparative 
efficiency  of  any  water-wheel  or  motor  is  represented  by  this  percentage  of  the  absolute 
effect  of  the  water  applicable  to  power. 

The  watershed  of  the  Merrimac  River  at  Lowell  is  4,085  square  miles;  and  the  per- 
manent water  equal  to  one  cubic  foot  per  second  per  square  mile  of  shed  during  working 


FIG.  402. 

hours ;  gross  fall,  34£  feet ;  loss  in  canal,  say  1£  foot ;  and  in  flumes  and  races,  1  foot ; 

4.  t  11    on  t    4     4,085  x  62-4  pounds  x  32  feet 

net  fall,  32  feet; —  =  14,830  H.  P. 

550  pounds 

Taking  the  effective  power  on  the  wheel  at  80  per  cent,  which  is  obtained  from  the 
wheels  at  full  gate,  14,830  x  '80  =  11,864  effective  H.  P.  A  very  close  rule  to  deter- 
mine the  E.  H.  P.  is,  multiply  the  number  of  cubic  feet  per  second  by  the  fall  in  feet 

and  divide  by  11,  thus:    4> °85  x  32  =  11,884. 

Wind  is  applied  for  the  purposes  of  power ;  but,  as  there  is  no  constancy  in  its  action, 
its  use  is  mostly  confined  to  the  purpose  of  raising  water  by  means  of  pumps  into  cisterns 
or  reservoirs. 


FIG.  403. 


FIG.  404. 


Steam  is  the  elastic  fluid  into  which  water  is  converted  by  a  continuous  application 
of  heat.  It  is  used  to  produce  mechanical  action  almost  invariably  by  means  of  a  piston 
movable  in  a  cylinder.  Thus,  in  Fig.  404,  the  steam  entering  through  the  lower 


206 


MECHANICS. 


channel-way,  or  port,  presses  against  the  under  side  of  the  piston  in  the  direction 
of  the  arrow,  the  piston  is  forced  upward,  the  steam  above  the  piston  escaping 
through  the  exhaust-channel  o.  When  the  piston  reaches  the  top  of  the  cylinder, 
the  valve  is  changed  by  mechanism,  the  steam  enters  above  the  piston,  and  the 
steam  below  it  escapes  through  the  exhaust ;  in  this  way  a  reciprocating  motion  is  es- 
tablished. 

It  is  not  practicable  at  a  single  instant  to  let  the  whole  pressure  of  the  steam  in  the 
boiler  into  the  cylinder,  nor  maintain  it  uniform  during  the  whole  stroke;  there  are 
losses  of  pressure  due  to  friction  through  the  pipes,  valves,  and  channel-ways,  and  back 
pressure  from  the  same  causes  in  the  exhaust,  condensation  from  exposed  surfaces,  and 
consequent  reduction  of  pressure  and  volume  of  steam,  and  there  are  gains  of  effect  by 
cutting  off  the  introduction  of  steam  to  the  cylinder  at  some  point  of  a  partial  stroke, 
which  is  completed  by  the  expansion  of  the  inclosed  steam,  but  with  a  constantly  di- 
minishing pressure. 

Under  expansion,  the  volume  of  a  confined  gas  is  inversely  proportional  to  the  pres- 
sure to  which  it  is  exposed.  This  is  called  the  law  of  Mariotte,  or  the  law  of  expansion, 
under  equal  temperatures  for  all  gases,  and  is  shown  graphically  in  Fig.  405. 


FIG.  405. 


To  determine  the  action  of  the  steam  within  a  steam-engine  cylinder,  an  indicator  is 
used.  It  consists  of  a  small  cylinder  connected  by  a  steam  pipe  with  the  main  cylinder, 
with  its  piston  controlled  by  a  graduated  spring,  and  recording  by  a  pencil  the  varying 
pressures  in  the  main  cylinder  on  a  paper  card  wrapped  around  a  reciprocating  cylin- 
drical tube ;  to  this,  movement  is  given  by  a  cord  attached  to  some  mechanism  connected 
with  the  steam-engine  piston,  but  with  a  reduced  motion. 

Indicator  cards  show  the  efficiency  of  a  steam  engine  by  a  comparison  with  theoreti- 
cal ones,  the  mean  effective  power  exerted  (M.  E.  P.),  the  volume  of  steam  expended, 
losses  of  pressure  by  imperfect  passages  or  channels,  leaks  in  valves  and  around  pistons 
and  by  radiation. 

Fig.  406  is  an  indicator  card  from  a  non-condensing  engine.  The  steam  exhausts 
directly  into  atmosphere,  and  the  back  pressure,  2  to  3  pounds,  is  shown  by  the  line  just 
above  that  of  the  atmosphere  line. 


MECHANICS. 


207 


In  Fig.  407  the  exhaust  is  into  the  condenser,  where  a  vacuum  is  maintained  by  the 
air  pump  of  from  2  to  3  pounds.     The  M.  E.  P.  of  the  condensing  engine  is  greater  than 


ABOVE  AT.        BELOW  AT. 


Atmospheric  Line 
FIG.  406. 


FIG.  407. 


that  of  the  non-condensing,  but  this  is  not  obtained  without  expense  of  power  in  running 
the  air  pump,  and  more  condensation  in  the  cylinder  due  to  the  lower  temperature  at 
which  the  steam  leaves  it.  See  Table  of  Temperatures  of  Steam,  Appendix. 

The  ends  of  both  cards  are  rounded  by  the  early  opening  of  the  steam  valve  in  the 
out  stroke,  and  by  the  earlier  closing  of  the  exhaust  valve  in  the  return  stroke.  This 
last  shuts  up  the  balance  of  steam  in  the  cylinder,  as  shown  by  the  curve  of  compression, 
and  retains  a  volume  of  some  importance  in  the  next  stroke,  especially  in  quick-running 
engines  regulated  by  movable  eccentrics,  and  cushions  the  piston  at  the  end  of  the 
stroke. 

Both  cards  are  divided  into  ten  equal  spaces,  and  subdivided  for  the  average  pres- 
sures, which  are  given  in  figures  on  the  scale  of  pounds  of  the  indicator.  The  sum  of 
the  pressures  are  then  divided  by  10,  which  gives  the  M.  E.  P.,  which,  multiplied  by  the 
area  in  square  inches  of  the  piston  by  the  travel  in  feet  per  minute  and  divided  by  33,000, 
gives  the  H.  P. 

Assume  the  diameter  of  the  cylinder  in  Fig.  406 
to  be  15"  (area,  176-7);  stroke,  3  feet;  revolutions, 
90  per  minute.  90  x  3  x  2  =  540  feet  travel  per 
minute. 


Then, 


64-7  x  176-7  x  540 


=  187  H.  P. 


33,000 

The  indicator  card  may  be  divided  into  twenty 
equal  spaces,  and  the  first,  third,  fifth,  .  .  .  nine- 
teenth taken  as  subdivision  ordinates,  or  it  may  be 
divided  by  a  flexible  grid ;  but  where  ordinates  are 
not  required  the  M.  E.  P.  may  be  taken  by  plani- 
meter. 

The  M.  E.  P.  of  a  steam  cylinder  can  be  esti- 
mated approximately  from  the  initial  pressure  and 
the  cut-off.  The  reduction  of  pressure  by  the  cut- 
off is  shown  in  the  diagram  (Fig.  408)  constructed 
from  the  formula  of  Rankine  for  dry  saturated 
steam.  Multiply  the  initial  pressure  by  the  decimal 
on  the  vertical  line  of  the  diagram  at  its  intersection 
by  the  curve  of  cut-off,  and  the  result  is  the  M.  E.  P. 
of  the  entire  card  to  0;  from  which  to  find  the 
effective  pressure  as  given  by  the  indicator  card 
there  must  be  subtracted  the  loss  of  pressure  be- 
tween the  lower  line  of  card  and  the  0  line.  Assume  the  initial  pressure  in  Fig.  406 
to  be  124  pounds  above  atmosphere,  and  the  vacuum  14 -7,  or,  together,  138 '7  cut-off 


208 


MECHANICS. 


l, 

i.oo 

1.00 


Q.90 


o 

to   0.80 


0.70 


0.60 


<   0.50 


O 
Ul 

Q 

?  0.40 
id 

(£. 


0.30 


ZERO  0, 

LINE     0 

0 


1.11 

0.90 


EXPANSIONS 
1.25  1.43 

0.80  0.70 


1.67 

0.60 


•CUT, 


0.10 
10 


0.20  0.30 

5  3.33 

EXPANSIONS 
Fio.  408. 


2. 

0.50 
1.00 


0.90 


0.70 


0.60 


0.50 


0.40 


0.20 


0.10 


0.40 
2.5 


0.50 
2. 


at  J,  or  -25  of  the  stroke,  4  expansions  by  diagram  -582  x  138-7  =  80-7  pounds,  less 

80-7 

17-7 
3  pounds  above  atmosphere  and  14-7  below, 


63  x  176-7  x  540 
33,000 


63-0 
=  182 '2  H.  P.     A  result  a  little  less  than  that  of  the  card. 


MECHANICS. 


209 


In  the  appendix  will  be  found  a  table  of  both  dry  and  moderately  moist  steam  from 
the  same  authority. 

At  the  commencement  of  each  stroke  there  is  a  space  between  the  piston  and  the 
cylinder  head  which,  together  with  the  space  between  it  and  the  valve,  are  called  clear- 
ances, and,  as  it  causes  an  expenditure  of  steam,  is  reckoned  in  percentages  of  the 
stroke. 

To  enable  one  to  judge  of  the  economy  of  the  steam  engine,  it  is  necessary  to  know 
how  much  weight  of  steam  is  used.  In  the  example  the  pressure  at  cut-off  is  taken  at 
139  pounds,  and  the  weight  of  a  cubic  foot  of  steam  at  this  tension,  by  tables  of  satu- 
rated steam  in  appendix,  is  -3092  pound ;  the  area  of  cylinder  =  1  -227  square  feet. 

Stroke  3  x  '25  cut-off  =  -75 

Clearance,  3  per  cent  of  stroke  =  '09 

•84  foot. 

1-227  x  -84  x  -3092  =  -319.  '319  x  180  strokes  x  60  minutes  =  3,445  pounds  per 
hour.  If  the  evaporation  be  8  pounds  of  water  per  pound  of  coal,  then  the  consump- 
tion of  coal  would  be  431  pounds,  and  --—  =  2'30  pounds  of  coal  per  H.  P.  per  hour. 

187 

Of  late  years,  the  principle  of  expansion  has  been  very  much  extended  by  the  con- 
struction of  compound  engines.  Fig.  409  shows  the  general  arrangement,  without  valves, 
of  a  simple  compound  engine  of  two  cylinders — a 
high-pressure  (h.  p.  c.)  and  a  low-pressure  (1.  p.  c.) 
one.  The  h.  p.  c.  (ABC  D)  draws  its  steam  from 
the  boiler  and  exhausts  into  the  1.  p.  c.  (A',  B', 
C',  D') ;  the  top  of  the  h.  p.  c.  into  the  bottom 
of  the  1.  p.  c.,  and  vice  versa,  so  that  the  pressure 
on  the  pistons  of  the  two  cylinders  is  in  the  same 
direction. 

To  determine  whether  a  steam  engine  is  work- 
ing properly,  it  is  necessary  to  compare  the  abso- 
lute card  with  the  theoretical  one. 

Figs.  410  and  411  represent  indicator  cards, 

taken  from  a  condensing  and  non-condensing  engine.  On  these  are  shown  the  con- 
struction of  the  isothermal  curve.  It  will  be  observed  that  there  is  a  line,  A  B,  to  the 
top  of  the  card.  The  space  between  this  and  the  card  represents  the  clearance,  which, 
estimated  in  percentages  of  the  capacity  of  the  cylinder,  is  plotted  on  the  indicator  card. 
On  the  indicator  card,  as  taken  by  the  instrument,  the  absolute  0  can  not  be  taken,  but 
only  that  of  the  atmosphere,  the  0  will  be  at  a  distance  below  this,  corresponding  to  the 


FIG.  409. 


FIG.  410. 


FIG.  411. 


barometric  pressure,  usually  14-7  pounds.  Draw  the  0  line  parallel  to  the  atmospheric 
line,  the  clearance  line  perpendicular  to  it,  a  line  parallel  to  the  0  line,  at  the  height  of 
the  initial  pressure,  and  a  line  parallel  to  the  clearance  line  at  the  point  of  cut-off  on  the 
initial  pressure  line.  Any  point  on  the  expansion  line,  'as  la,  2a,  3a,  may  be  determined 

15 


210  MECHANICS. 

by  drawing  lines  B  1,  B  2,  B  3,  and  then  horizontal  lines  la  li,  2a  2i,  33  3i  from  their  in- 
tersections li,  2!,  3i.  With  the  cut-off  line,  parallel  to  the  0  line,  and  perpendiculars 
from  1,  2,  3,  the  intersections  of  these  two  lines,  12,  22,  32,  will  be  the  points  in  the 
curve.  Inversely,  the  indicator  card  may  be  tested  by  the  construction  of  parallelo- 
grams on  the  curve,  and  if  their  diagonals  intersect  at  a  point  on  the  0  line  it  may  be 
considered  that  this  represents  the  amount  of  clearance.  The  curves  in  the  outline  of 
the  cards,  at  the  times  of  admission,  cut-off,  and  exhaust,  show  the  action  of  the  valves 
and  time  occupied  in  change  of  condition.  The  stroke  commences  at  A,  cuts  off  at  C, 
commences  to  exhaust  at  E  ;  about  D  the  exhaust  valve  closes. 

To  enable  a  draughtsman  to  comprehend  the  action  of  the  steam  in  multiple  cylinders 
and  calculate  approximately  the  diameter  and  capacity  of  the  different  cylinders,  a  curve 
of  expansion  is  constructed,  Fig.  405.  The  ratio  of  expansion  is  on  the  Mariotte  curve 
and  is  as  the  reciprocal  of  the  pressures.  Taking  as  the  unit  the  abscissa  of  the  pressure 
of  100  pounds,  at  120  it  is  '833,  at  40  pounds  2  '50,  and  on  this  principle  the  curve  is 
drawn,  taking  cross-section  paper,  for  the  ease  with  which  it  may  be  laid  down  and  as 
more  intelligible  in  its  explanation. 

In  Fig.  405  is  illustrated  a  triple  compound  with  an  initial  pressure  (I.  P.)  of  120 
pounds  and  a  final  expansion  of  twenty-one  times.  To  divide  the  expansions  between 
the  three  cylinders,  V^T  =  2'76  expansions  in  the  first  cylinder,  2'76  x  -833  =  2'30 
abscissa  at  end  of  stroke  of  first  cylinder. 

(1)  f^Wa  —    =  43  '48  final  pressure,  ordinate  corresponding  to  an  abscissa  of  2  '30. 
2"7o. 

120 

(2)  2-76'  =  7-617.    7-617  x  -833  =  6-345  —  —  =  15-76  pounds. 

7"u4 

120 

(3)  2-763  =  21.  21  x  -833  =  17'5    —  r   =  5'71  pounds. 

til 

With  a  cut-off  at  -833,  and  an  expansion  of  2-76,  the  stroke  will  be  2  -3,  which  is  the 
uniform  stroke  in  the  three  cylinders.  Calling  the  diameter  of  the  H.  P.  cylinder  15" 
A  176-7  n",  the  area  of  the  I.  P.  cylinder  will  be  176-7  x  2-76  =  487-69  square  inches 
=  25"  diameter,  and  that  of  the  low  pressure  487-69  x  2'76  =  1,346  square  inches  —  41|" 
diameter.  Taking  the  M.  E.  P.  of  the  different  cards  by  averages  or  by  planimeter,  in 
which  the  area  of  the  card  in  square  inches  is  divided  by  the  length  of  card  in  inches 
and  multiplied  by  the  vertical  scale,  we  find  the  M.  E.  P.  for  first  cylinder  42  '2,  second 
cylinder  15  '4,  third  cylinder  5'6.  The  pounds-feet  per  stroke  will  be: 

First  cylinder,  176  -7  x  2  -3  x  42  -2  =  17,150 
Second  "  487-69  x  2-3  x  15  '4  =  17,274 
Third  "  1,346-  x  2'3  x  5-6  =  17,336 


The  M.  E.  P.  of  the  whole  card  was  16'6,  stroke  17-5,  area  176-7  =  -     -  =  17,110  pounds- 

o 

feet,  a  result  very  nearly  that  of  the  single  cylinder,  but  as  the  areas  measured  by  the 
planimeter  includes  only  that  between  the  lines  of  final  pressure,  while  the  absolute  card 
in  the  low-pressure  cylinder  should  be  carried  to  the  line  of  exhaust,  or  say  3  pounds 
above  0,  the  pounds-feet  of  effect  should  be  more  than  in  either  of  the  others,  which  it 
would  be  impossible  to  equalize  with  the  same  stroke  and  the  same  rates  of  expansion. 
All  these  results  are  obtained  from  the  plotted  isothermal  curve,  but  in  expanding  steam 
does  not  maintain  the  same  temperature,  and  occupies  less  space  than  shown  by  the 
above  curve,  and  making  allowance  for  this  a  curve  is  developed  which  is  called  the 
adiabatic  curve. 

To  plot  this  on  the  diagram  take  the  abscissa  at  120  as  equal  to  3  -65  (or  the  volume 
of  steam  at  this  pressure),  construct  a  scale  taking  the  volumes  at  the  different  pressures 
from  the  table  in  the  Appendix  ;  but  if  the  stroke  and  the  areas  of  cylinders  is  considered 
the  same  as  in  the  previous  calculations,  although  the  area  of  the  cards  is  less,  yet  as  the 


MECHANICS.  211 

length  of  card  is  less,  the  M.  E.  P.  remains  nearly  the  same,  and  consequently  the  pounds- 
feet  of  results,  estimating  pounds-feet  of  work  done  in  the  several  cylinders  by  the  mean 
pressures  as  taken  from  Rankine's  tables  in  the  Appendix.  In  these  cases  the  average 
pressure  is  taken  from  the  0,  from  which  has  been  subtracted  the  initial  pressure  in  the 
next  cylinder. 
Thus: 

Average  pressure  in  first  cylinder 88-04 

Initial  pressure  in  second  cylinder 43 -5 

M.  E.  P.  in  first  cylinder 44 -54 

Average  pressure  in  second  cylinder 31-8 

Initial  pressure  in  third  cylinder 15-8 

M.  E.  P.  in  second  cylinder 16  '00 

Average  pressure  in  third  cylinder 11-56 

Pressure  at  end  of  expansion 5'7 

M.  E.  P.  in  third  cylinder .  If86 

For  dry  steam  the  results  are  very  nearly  the  same  as  by  the  Mariotte  curve.  In  none 
of  the  calculations  is  the  difference  as  great  as  will  be  found  in  practice,  where  it  is 
found  desirable  to  jacket  the  steam  cylinders  and  heat  the  steam  in  the  intermediate 
chambers  to  prevent  condensation  from  the  walls  of  the  cylinders  and  passages,  and  to 
restore  the  heat  which  has  been  converted  into  work. 

The  above  card  refers  to  an  engine  in  which  there  is  an  intermediate  chamber  between 
the  cylinders. 


MOTION. 

In  the  designing  of  machines  it  is  often  important  to  show  the  changes  in  the  moving 
parts,  that  they  may  not  conflict  with  each  other  in  the  practical  working,  and  to  obviate 
the  effect  of  dead-points  through  which  motion  may  have  to  be  transferred. 

To  describe  the  path  of  the  crosshead  of  the  piston  of  the  steam  engine,  its  connect- 
ing-rod, and  crank,  Fig.  412,  draw  the  path  of  the  crosshead  which,  controlled  by 
guides,  is  a  straight  line;  divide  into  equal  parts  0  to  6;  on  the  same  line  lay  off  the 
length  of  the  connecting-rod  from  0  to  0',  and  the  length  of  the  crank  to  the  centre  C ; 
from  C  as  a  centre  with  a  radius  equal  to  the  length  of  the  crank  describe  a  circle  which 
will  be  the  path  of  the  crank-pin.  From  the  points  1,  2,  3,  4,  5,  and  a  radius  equal  to 
that  of  the  connecting-rod,  describe  arcs  cutting  the  crank  path  at  1',  2',  3',  4',  5',  0' 
and  6'  on  the  line  of  the  crosshead  path,  the  commencement  and  end  of  the  strokes. 
The  path  of  the  crosshead  is  divided  into  equal  spaces,  but  that  of  the  crank-path  is  not. 
The  point  3'  corresponding  to  the  mid  stroke  3  of  the  crossbead  is  not  that  of  the  half 
circumference  of  the  crank-path.  These  irregularities  are  due  to  the  angularity  of  the 
connecting-rod,  which  is  here  made  less  than  its  usual  proportion  to  that  of  the  crank. 


212 


MECHANICS. 


Moreover,  when  the  crank-pin  and  the  axle-centre  are  in  the  line  with  the  connecting- 
rod,  as  at  0  0'  or  6  6',  the  driving  force  passes  through  the  fixed  axis  and  no  motion  is 


54          '3210 


FIG.  412. 


possible.  Some  other  mechanism  is  necessary  to  pass  over  the  dead-points;  usually  this 
is  by  means  of  the  fly-wheel,  in  which  the  force  stored  in  the  mass  by  rotation  continues 
the  motion,  and  rightly  proportioned  nearly  with  uniformity,  and  the  irregularities  are 
transferred  to  the  stroke,  Fig.  413. 


654  3    A          2  10 


FIG.  413. 


If  the  crank  is  the  driver  there  will  be  no  dead-point ;  the  circular  movement  of  the 
crank-pin  will  be  converted  into  the  rectilinear  and  reciprocating  one  of  the  crosshead. 

In  locomotives  the  cranks  from  the  cylinders  are  put  at  right  angles,  that  there  may 
be  no  dead-point. 

STANHOPE   LEVERS. 

In  the  Stanhope  hand  press  (Pig.  414)  the  extreme  power  is  obtained  by  a  combina- 
tion of  levers  in  which  the  greatest  pressure  is  exerted  when  the  platen  has  reached  the 
type.  A  is  a  fixed  point  on  which  the  bell-crank  lever  B  revolves,  and  to  the  extremity 
of  which  the  power  is  applied,  and  which  describes  the  circle  designated  by  equal  arcs, 
0-10 ;  at  the  angle  &  of  B  there  is  a  connection  C  with  the  lever  D  revolving  on  a  fixed 
centre,  d;  under  this  action  the  point  of  the  lever  D,  at  which  the  pressure  is  exerted, 
passes  through  the  small  arc  0-10,  corresponding  to  the  arcs  of  the  extremity  of  the 


MECHANICS. 


213 


lever  B,  but  always  with  decreasing  lengths,  as  shown  on  the  figure,  and  consequently 
increasing  pressure. 

To  obtain  the  positions  of  the  lever  from  the  path  of  the  lever  B,  from  A  as  a  centre, 
and  with  a  radius  equal  to  A  0,  describe  an  arc  the  path  of  the  extremity  of  B,  and 


FIG.  414. 


divide  into  equal  arcs  0-10 ;  on  A  as  a  centre  describe  another  arc,  A  &,  and  from  any 
point,  say  5,  with  a  radius  equal  to  60,  describe  an  arc  5",  intersecting  the  arc  &;  from 
d  as  a  centre,  with  a  radius  equal  to  d  c,  describe  an  arc,  and  from  5",  with  a  radius  equal 
to  &c,  intersect  the  previous  arc,  and  through  this  point  draw  a  radial  line  from  d;  with 
a  radius  equal  to  d  0,  describe  an  arc  for  the  path  of  the  extremity  of  the  lever  D ;  the 
intersection  of  the  radial  with  this  arc  will  give  the  point  5  on  the  smaller  arc,  corre- 
sponding to  5  of  the  larger.  In  the  same  manner  other  positions  can  be  determined. 

« 

WHITWORTH'S  QUICK  RETURN  MOTION. 

Fig.  415  is  known  as  Whitworth's  Quick  Return  Motion,  and  consists  of  a  driven 
crank,  a ;  moving  at  a  uniform  speed,  to  the  end  of  the  crank  is  a  block,  d,  sliding  in  a 
slotted  link;,  this  link  is  fastened  to  a  fixed  centre,  e,  and  has  a  vibrating  motion.  A 


FIG.  415. 

tangent  drawn  from  each  side  of  the  crank-path  to  the  point  e  will  give  the  extreme 
movements  of  the  link  c,  and  a  line  at  right  angles  to  this  line  and  from  the  centre  of  the 
crank-shaft  on  each  side  will  divide  the  crank-path  in  two  parts.  The  tool-holder,  /,  or 
planer  platen,  travels  over  an  equal  space  while  the  crank  moves  from  d'  to  d  as  from  d  to 
d' ;  it  follows,  therefore,  as  the  crank  is  moving  uniformly,  the  motion  of  the  tool-holder 
while  cutting  is  slow  and  the  return  quick. 


214 


MECHANICS. 


FIG.  416. 


FIG.  417. 


MECHANICS. 


WATT'S  PARALLEL  MOTIQJ*. 

Watt's  parallel  motion  is  shown  in  Fig.  416,  the 
object  of  this  motion  being  to  obtain  a  rectilinear  mo- 
tion of  the  piston-rod  and  air-pump  rod  under  the 
varying  angularity  of  the  beam. 

In  the  figure  the  line  CD  indicates  the  centre  of 
the  beam ;  from  the  point  H,  situated  midway  between 
C  and  D,  and  from  D,  are  suspended  two  links,  H  I 
and  D  E,  of  equal  length.  Connect  E  and  I  by  a  rod 
equal  in  length  to  D  H ;  the  point  I  is  then  attached 
to  the  fixed  centre  at  O,  and  is  equal  in  length  to  E  I, 
with  an  angle  E  I  O  equal  to  the  angular  motion  of  the 
beam.  By  the  movement  of  the  beam  the  point  H  is 
thrown  outward  from  C  and  I  inward  an  equal  amount ; 
the  centre  point,  K,  connected  with  the  air  pump,  takes 
a  nearly  vertical  movement,  and  the  same  may  be  said 
of  the  point  E ;  the  heavy  lines  illustrate  the  position 
of  the  various  levers  when  the  beam  is  in  the  middle 
of  its  travel. 

It  is  the  practice  in  this  country  to  use  crossheads 
and  guides  for  the  piston  rather  than  parallel  motions. 

Fig.  417  represents  another  form  of  parallel  motion 
to  preserve  the  perpendicularity  of  the  piston  -  rod 
against  the  varying  angle  of  the  connecting-rod. 

This  motion  consists  of  two  pairs  of  equal  radial 
bars,  O  I  and  O'  I',  moving  in  planes  parallel  to  that  of 
the  circle  of  revolution  of  the  crank,  and  on  opposite 
sides  of  the  piston-rod  and  connected  by  a  link  1 1', 
while  the  centres  O  and  O'  are  fixed  at  points  at  equal 
distances  from  the  centre  of  motion  and  on  opposite 
sides;  the  communication  with  the  piston-rod  is  at  C, 
which  point  moves  nearly  perpendicularly. 

The  dotted  lines  show  the  positions  of  rods  and 
levers  when  the  crank  is  at  the  extreme  point  of  its 
revolution. 

JANNEY   CAR    COUPLER. 

Fig.  418  is  a  drawing  of  the  Janney  car-coupling 
device,  the  lower  portion  being  in  section  to  explain 
the  internal  mechanism,  and  the  upper  portion  a  top 
view,  showing  the  exterior  appearance. 

The  section  and  top  view  of  the  coupler,  in  dotted 
lines,  represent  the  couplers  approaching  each  other 
for  coupling,  and  the  section  and  portion  in  solid  lines 
show  the  coupling  completed. 

The  knuckle  B  represents  a  pinion  with  two  teeth 
B'  Ba,  and  the  drawhead  A  and  tooth  or  nose,  B3,  of 
the  other  coupler  representing  the  rack.  When  the 
couplers  are  brought  together  the  teeth  engage  each 
other,  the  hub  revolves,  and  the  long  tooth  B'  is  carried 
around  to  a  locking  position,  the  catch  C  being  forced 
back  by  the  circular  end  of  the  tooth  B'  in  passing, 
after  which  the  catch  is  returned  to  its  locking  position 
by  the  catch  spring  F. 


\ 


216 


MECHANICS. 


The  uncoupling  is  effected  by  throwing  over  a  platform  lever,  which  in  turn  forces 
around  the  coupler  lever  D  and  catch  C,  allowing  the  tooth  B'  to  revolve  outward. 

VALVE    MOTION. 

To  establish  the  reciprocating  motions  of  the  piston,  valves  must  be  moved  so  as  to 
alternately  let  the  steam  into  one  end  of  the  cylinder  and  permit  it  to  escape  at  the  other. 
The  mechanism  by  which  the  valves  are  moved  are  usually  by  means  of  an  eccentric  on 
the  crank-shaft,  and  a  strap  and  rod  connecting  it  with  the  valve  rod. 

The  motion  of  the  rod  is  the  same  as  if  the  eccentric  were  a  small  crank. 


FIG.  419 


Fig.  419  shows  six  positions  of  one  of  the  old  slide  valves  and  piston,  together  with 
the  position  of  the  crank  and  eccentric  for  each  movement  of  the  valve. 


MECHANICS. 


217 


In  Fig.  419  the  valve  is  merely  sufficient  to  cover  the  ports,  and  at  the  slightest 
movement  in  either  direction  passages  wfll  be  opened  for  steam  to  the  cylinder,  and  the 
escape  of  the  exhaust  from  it ;  under  these  conditions  there  can  be  no  cut-off,  and  con- 
sequently no  economy  from  expansion  of  steam. 


FIG.  420. 


For  common  engines  the  cut-off  is  effected  by  the  lap  and  lead  of  the  valve  (Fig. 
420).  When  the  valve  is  placed  centrally  over  the  ports,  the  portion  of  the  valve  over- 
lapping the  steam  ports  is  known  as  lap :  when  on  the  steam  side,  it  is  designated  as 
outside  lap,  and  as  inside  lap  when  on  the  exhaust  side.  In  quick-running  engines,  both 
steam  and  exhaust  ports  are  opened  before  the  completion  of  the  stroke;  on  the  steam 
side  there  is  a  cut-off  or  closing  of  the  valve  before  the  completion  of  the  stroke  to  ad- 
mit of  expansion,  and  before  the  completion  of  exhaust  for  compression,  thus  saving  heat 
and  relieving  the  pressure  and,  consequently,  the  friction  of  the  slide  valve. 

The  channels,  usually  three  in  number,  alternately  exposed  and  covered  during  the 
movement  of  the  valves,  are  called  ports.  The  ones  admitting  steam  to  the  ends  of  the 
cylinder  are  the  steam  ports  ;  the  central  one  giving  exit  of  the  steam  from  the  cylinder  is 
the  exhaust  port ;  the  spaces  between  the  ports  are  called  bridges.  The  working  surfaces 
on  valve  and  cylinder  are  valve  and  valve  seat  faces. 

The  width  of  opening  of  the  steam  ports  at  the  beginning  of  the  stroke  for  the  ad- 


218 


MECHANICS. 


mission  or  release  of  steam  is  termed  lead ;  on  the  steam  side  outside  lead ;  on  the  ex- 
haust side  inside  lead.  When  the  valve  is  placed  at  half  stroke  over  the  ports,  the 
amount  which  it  overlaps  each  port,  either  internally  or  externally,  is  the  lap ;  on  the 
steam  side  outside  lap ,•  on  the  exhaust  side  inside  lap.  Laps  and  leads  by  themselves 
refer  to  outside  laps  and  leads.  The  amount  by  which  the  valve  has  travelled  beyond 
its  middle  position  when  the  piston  is  at  the  end  of  the  stroke  is  the  linear  advance. 

The  proper  understanding  of  the  positions  of  valve  under  the  different  positions 
during  the  stroke  are  of  great  importance  to  the  draughtsman.  It  is  very  common  in  a 
shop  to  have  a  model  of  an  eccentric  in  which  the  throw  can  be  readily  changed  and 
applied  with  a  small  rod  for  connection  to  a  simple  section  of  valve  and  ports.  But  the 
valve  motion  may  be  illustrated  by  diagram. 


VALVE   DIAGRAMS. 


The  separate  drawings  of  the  movements  of  a  valve  may  be  shown  in  one  general 
diagram  containing  the  continuous  movement  of  the  valve ;  for  illustration,  the  valve  of 
the  last  engraving  is  taken. 

Draw  a  perpendicular  line  (Fig.  421),  E  D,  called  the  datum  line ;  from  the  centre,  C, 
of  this  line  describe  a  circle  equal  in  radius  to  that  of  the  eccentric ;  for  the  first  position 


FIG.  421. 

of  the  eccentric  draw  a  line  perpendicular  to  D  E  of  one  inch  and  five  sixteenths  (one 
inch  lap  and  five  sixteenths  lead)  till  it  intersects  the  path  of  the  eccentric  at  1.  Draw 
a  line  from  C  to  1 ;  this  is  the  first  position  of  the  eccentric ;  from  this  point  divide  half 
the  circle  into  six  equal  parts,  representing  six  positions  of  the  eccentric ;  from  each  of 
these  points  draw  a  horizontal  line  till  it  intersects  the  datum  line ;  these  lines  give  the 
linear  movement  of  the  eccentric!,  and  therefore  the  travel  of  the  valve.  From  the  centre 
C  draw  a  circle  equal  in  radius  to  that  of  the  crank;  commencing  at  1',  this  being  the 
first  position  of  the  crank,  divide  half  the  circle  into  six  equal  parts,  the  positions  num- 
bered 1'  2'  3'  on  the  crank-path  corresponding  to  1,  2,  3  of  the  eccentric  path ;  on  the  crank 


MECHANICS. 


219 


circle  construct  a  square,  F,  G,  H,  I,  and  through  each  of  the  points  of  the  crank-path 
draw  lines  parallel  to  the  side  of  the  square.  Draw  a  horizontal  dotted  line  A  B  through 
C,  and  from  A  as  the  centre  of  the  exhaust  port  lay  off  the  ports  and  bridges.  Above 
and  below  this  draw  parallel  lines  abed ef  across  the  square,  indicating  the  limits  of 
the  exhaust  opening  and  ports  on  both  sides  of  the  drawing,  also  horizontal  lines  g  and<?' 
to  define  the  position  of  the  valve  when  placed  centrally  over  the  ports,  and  draw  a  sec- 
tion of  the  valve  according  to  the  dimensions  given.  Lay  off  the  distance  from  D  E  to 
the  first  position  of  the  eccentric  below  g'  on  the  line  F  H,  and  draw  an  outline  of  the 
valve  as  moved  into  this  position.  Lay  off  on  each  successive  perpendicular  line  2',  3', 
etc.,  from  <?',  the  corresponding  positions  of  the  eccentric  as  measured  from  DE,  and 
draw  a  curve  through  these  points.  Lay  off  the  position  of  the  edges  of  the  valve  hijk 
on  the  lines  2',  3',  etc.,  above  the  determined  points  22,  32,  etc.,  and  draw  curves  through 
these  points. 

In  this  position  of  the  valve  the  steam  port  has  been  opened  by  a  distance  equal  to 
pic;  through^?  draw  a  horizontal  line  intersecting  the  elliptical  curve  at  a',  draw  shade 
lines  from  a  to  the  curve  below ;  this  shade  represents  the  continuance  of  the  steam  in 
the  cylinder;  the  intersection  a'  is  the  point  of  cut-off  and  commencement  of  expansion. 
On  the  other  side  the  cylinder  is  wide  open  to  the  exhaust,  as  shown  by  M,  and  is  closed 
where  the  elliptical  curve  intersects  the  line  e.  The  waste  steam  becomes  compressed  and 
is  shown  at  N,  and  is  utilized  on  the  return  stroke,  as  shown  at  L.  The  period  of  admis- 
sion against  the  piston  is  shown  where  the  line  of  the  curve  intersects  a  at  o,  and  is 
shown  by  the  small  space  O  at  the  commencement  of  the  back  stroke  and  at  P  for  the 
forward  stroke. 

This  diagram  entirely  disregards  the  angularity  of  the  connecting-rod. 

With  a  single  valve  it  is  difficult  to  secure  economy  in  the  cut-off;  it  is  usual  in 
the  larger  sizes  of  stationary  engines  to  have  steam  and  exhaust  valves  moved  by  separate 
mechanisms,  and  independent  of  each  other,  and  to  regulate  the  engine  by  a  direct  con- 
nection of  the  steam  valve  with  the  governor. 

Among  this  class  of  engines,  the  widest  known  is  the  CORLISS,  of  which  Fig.  422  is 
a  side  elevation  of  one  of  the  simplest  and  earliest  forms. 


FIG.  422. 


The  exhaust  valves  at  the  bottom  of  the  cylinder  are  connected  positively  with  the 
wrist-plate  w,  vibrated  by  a  hooked  connection  with  an  eccentric  on  the  engine  shaft. 
Connected  with  the  wrist  plate  are  two  vibrating  levers,  R  R',  to  the  upper  ends  of  which 


220 


MECHANICS. 


lever  pawls,  pp,  are  attached,  which  rest  on  the  stems,  s,  of  the  steam  valves.  On  the 
stems  are  notches  against  which  the  pawls  strike,  push  back  the  stems,  compress  the  in- 
closed spring,  and  open  the  valves,  and  this  continues  till  the  outer  end  of  the  pawl 
lever,  coming  in  contact  with  the  head  of  the  lever  a,  controlled  by  the  governor,  releases 
the  spring  which  closes  the  valve.  The  cases,  5,  are  cylindrical,  with  air  cushions  at  the 
ends. 

Fig.  813  shows  sections  of  the  valves  of  which  the  ports  are  very  long  and  narrow. 
In  their  construction,  the  valves  may  be  considered  cylindrical  plugs,  of  which  portions 
near  the  ports  are  cut  away  for  the  prompt  admittance  and  exhaust  of  steam ;  the  valves 
are  fitted  on  the  lathe  and  the  seat  by  boring.  The  motion  given  to  the  valves  is  rock- 
ing, but  the  valves  are  not  firmly  connected  to  the  rocking  shaft ;  in  the  figure  the  valves 
are  shown  shade  lined,  and  the  shaft  or  stem  plain ;  the  valves  are  not  affected  by  the 
packing  of  the  valve  stem,  but  always  rest  upon  the  face  of  the  ports. 


FIG.  423. 

Since  the  lapse  of  the  Corliss  patent,  it  may  be  considered  the  most  popular  form  of 
design,  and  its  manufacture  has  been  taken  up  by  many  shops,  which,  while  in  the 
matter  of  valves  and  cut-off  coming  within  the  claims  of  the  old  patent,  have  been  much 
improved  in  the  details  of  mechanism.  The  dash-pot  is  now  set  vertically ;  the  plunger 
acts  without  springs  by  gravity. 

Fig.  423  is  the  side  elevation  of  a  Corliss  engine  of  the  Fishkill  Landing  Machine 
Company,  of  which  the  details  of  the  dash-pot  are  given  in  Fig.  424.  It  consists  of  a 
cylinder,  A,  of  two  different  diameters,  to  which  is  fitted  the  double-diameter  plunger, 
with  grooved  air  packing,  the  one  in  the  cylinder,  the  other  on  the  lower  plunger.  At 
the  commencement  of  the  lift  the  plunger  is  at  the  bottom ;  as  it  is  raised,  a  vacuum  is 
formed  beneath  the  plunger,  partial,  as  air  is  supplied  from  the  annular  space  x  x  through 


MECHANICS. 


221 


the  channelways  e  e'.  but  the  vacuum  increases  with  the  increase  of  the  space  y  at  the 
cut-off. 

The  plunger's  descent  is  rapidly  retarded  by  a  partial  vacuum  in  e  e',  and  at  the  end 
of  its  stroke  by  the  compression  of  the  air  in  y,  and  seats  without  pounding.     By  the 


FIG.  424. 

valve  v  in  the  passage  e  e'  the  flow  of  air  between  the  upper  and  lower  end  of  the  cylinder 
is  controlled  to  produce  this  effect. 

Figs.  425,  426,  and  427  are  details  of  the  releasing  mechanism  of  the  same  engine. 

To  the  valve  stem  A  is  attached  a  single-armed  lever,  to  which  is  suspended  the 
dash-pot  connection  Y,  and  at  the  extremity  the  steel  catch-plate  c.  The  double  crank 


FIG.  425. 


FIG.  426. 


C  C'  rocks  on  the  valve  stem ;  to  its  lower  end  there  is  a  connection  X  with  the  wrist- 
plate,  from  which  it  receives  motion ;  at  its  upper  extremity  C  there  is  a  small  rocking 


222 


MECHANICS. 


lever  and  hook  E  which  is  pressed  inward  by  the  spring  /,  and  the  hook  E,  engaged 
with  the  catch-plate  c,  gives  the  motion  of  the  wrist-plate  to  C  C',  opens  the  valve,  and 


FIG.  427. 


raises  the  piston  of  the  dash-pot.  The  governor-rod  Z  moves  the  triple  crank  H  H'  H3, 
rocking  on  the  valve  stem  A ;  at  the  extremity  of  H'  there  is  a  roller  R  which  is  thrown 
by  the  governor  into  such  a  position  that  it  comes  in  contact  with  the  roller  R'  on  the 
hook  E  in  its  motion  upward,  and  is  thrown  outward,  disengaging  the  hook  E  from  the 
catch  c;  this  arm,  which  is  connected  with  the  dash-pot,  instantly  falls,  the  valve  closes, 


FIG.  428. 


MECHANICS. 


223 


and  steam  is  cut  off  sharply;  the  return  stroke  again 
engages  the  catch  and  hook,  and  the  release  is  again 
effected  by  the  position  of  the  governor. 

On  the  arm  Ha  there  is  an  adjustable  cam  W, 
which  serves  as  an  automatic  safety  stop-motion. 
When  the  engine  is  at  its  lowest  normal  speed,  and 
the  hook  E  is  at  the  point  of  engagement  with  the 
valve  lever  B,  the  roller  R'  comes  nearly  in  contact 
with  the  camW.  Should  the  balls  fall  below  the 
point  corresponding  to  the  lowest  normal  speed,  the 
bell- crank  H  will  move  in  the  direction  of  the  arrow; 
the  cam  W  will  come  in  the  way  of  the  roller  R', 
which  will  ride  on  the  top  of  it,  thus  preventing  the 
hook  E  from  engaging  with  the  end  of  the  valve 
lever  B,  and  the  valve  will  remain  closed.  No  steam 
being  admitted,  the  engine  will  stop. 

Link  motion  (Fig.  428)  is  a  mechanism  by  which 
the  travel  of  the  valve  is  changed  and  the  motion  of 
the  piston  reversed  at  the  option  of  the  engineer. 
It  consists  of  two  eccentrics  at  nearly  opposite  points 
on  the  crank-shaft,  each  of  which  is  connected  by 
rods  to  the  opposite  ends  of  a  shifting  link  A;  with- 
in the  link  is  a  sliding  block  B ;  the  block  B  is  at- 
tached to  a  rocker  R.  The  link  is  suspended  from  a 
bell-crank  C,  controlled  by  the  engineer  through  the 
rod  a.  As  the  link  A  is  raised  or  lowered  it  slides 
on  the  block  B,  of  which  the  movement  becomes 
more  or  less,  or  is  changed  in  direction  according  to 
its  position  in  the  link,  and  this  motion  is  transferred 
to  the  valve  through  the  rod  r. 

This  is  a  common  form  of  link  motion,  but  the 
same  effect  is  obtained  by  a  fixed  link  and  a  movable 
block  without  a  rocker  shaft  connected  by  a  link  to 
the  valve  rod. 

DIAGRAM    OP    LINK    MOVEMENT. 

The  horizontal  and  vertical  movement  of  the  dif- 
ferent positions  of  the  sliding  block  of  the  stationary 
link  in  connection  with  the  eccentrics  is  shown  in 
Fig.  429. 

The  link  is  attached  to  a  radius  rod  attached  to  a 
centre  O,  which  compels  the  centre  of  the  link  to  vi- 
brate in  an  arc  c  c'.  The  crank-path  is  divided  into  a 
number  of  equal  parts,  say  12,  commencing  at  its  first 
position,  and  the  forward  and  backward  eccentric 
paths  are  similarly  divided,  also  commencing  at  the 
first  position.  The  length  of  the  eccentric  rod  is 
then  taken  in  the  compasses  and  an  arc  described 
from  the  point  1  of  the  fore  eccentric,  and  another 
from  1'  of  the  back  eccentric.  The  arcs  for  the  fore 
eccentric  are  struck  above  the  centre  horizontal  line, 
and  for  the  back  eccentric  are  struck  below  this  line. 
An  arc  is  now  struck  from  the  centre  of  the  link, 


224 


MECHANICS. 


MECHANICS. 


225 


16 


226  MECHANICS. 

with  a  radius  equal  to  the  height  at  which  the  sliding  block  is  in  the  link ;  where  this 
arc  intersects  that  struck  from  the  fore  eccentric  will  indicate  the  point  at  which  the 
sliding  block  will  be  when  the  gear  is  full  forward,  and  the  same  arc  described,  cutting 
the  arc  from  the  back  eccentric,  will  give  the  point  of  the  sliding  block  in  the  link 
when  in  full  gear  backward;  and  an  arc  described  through  these  two  points,  with  a 
radius  equal  that  of  the  link,,  will  give  the  centre  line  of  the  link  when  the  eccentrics 
are  in  the  position  indicated. 

The  other  positions  of  the  link  are  obtained  in  a  similar  manner. 

In  describing  the  centre  line  of  the  link,  numerous  trials  are  necessary  to  get  the 
proper  centre  of  the  arc  passing  through  the  two  points,  and  where  many  positions  of 
the  link  are  necessary  it  will  expedite  the  work  by  making  a  templet  of  the  link  in  card- 
board, which  can  be  readily  applied  to  the  several  series  of  points. 

The  upper  line  on  the  link  movement  connecting  the  series  of  points  indicates  full 
forward  gear.  The  arc  cc',  mid-gear.  The  lower  line,  full  gear  backward. 

This  diagram  also  shows  the  position  of  the  valve  in  forward  and  backward  stroke. 

JOY'S    VALVE    GEAR. 

Figs.  430  and  431  are  drawings  of  Joy's  valve  gear  in  different  positions.  This  gear 
differs  from  the  link  motion  in  that  the  valve  motion,  instead  of  being  given  by  means  of 
eccentrics,  is  imparted  directly  from  the  connecting-rod. 

At  a  point  A  of  the  connecting-rod  a  link  B  is  attached,  the  movement  of  this  link 
being  controlled  by  the  radius  rod  C  attached  to  a  stationary  point  I  of  the  engine ;  from 
a  point  D  of  the  link,  movement  is  given  to  the  lever  E;  from  the  upper  end  E'  of  this 
lever,  motion  is  given  to  the  valve  spindle  G.  The  centre  F  has  also  a  vertical  movement 
due  to  the  vibration  of  the  connecting-rod  at  A ;  the  centre  or  fulcrum  F  of  the  lever 
E  is  therefore  carried  in  blocks  sliding  in  slots  of  the  link  K,  which  has  a  radius  equal 
to  the  length  of  the  valve  spindle  G.  In  Fig.  431  the  link  is  shown  at  mid-gear;  this 
link  can  be  partially  rotated  by  a  point  on  the  outside  of  the  link  corresponding  to  the 
point  F  of  the  lever  E,  shown  in  Fig.  430.  When  the  link  is  thus  inclined,  as  shown  at  X 
and  Y,  the  vertical  movement  of  E  causes  the  blocks  of  the  link  and  the  centre  F  to  trav- 
erse a  path  inclined  to  a  vertical  line.  The  centre  F  has  therefore  a  horizontal  move- 
ment, the  amount  of  which  depends  on  the  obliquity  of  the  link.  It  is  by  this  means 
that  the  cut-off  of  steam  and  the  forward  and  backward  movement  of  the  engine  is  con- 
trolled. 

The  dotted  ellipse  A  N  indicates  the  path  of  the  point  A  of  the  connecting-rod,  and 
the  dotted  curve  beneath  shows  the  path  of  the  pin  D,  which  partakes  of  the  motion  of 
the  point  A  of  the  connecting-rod  and  of  the  extremity  of  the  radius  rod  E. 

WALSCHAERT    VALVE    GEAR. 

Figs.  432,  433,  434,  435  are  drawings  of  the  Walschaert  valve  gear.  In  this  gear 
the  valve  derives  its  motion  partly  from  the  piston-rod  crosshead  and  partly  from  a  single 
eccentric  moving  a  vibrating  link. 

To  the  crosshead  A  is  attached  a  fixed  arm  B;  to  this  arm  is  attached  the  link  C, 
which  communicates  its  motion  to  the  combination  arm  D.  To  the  upper  end  of  this 
arm  is  connected  the  valve  stem  d;  just  below  this  connection  the  combination  arm  is 
pivoted  to  a  centre  e  ;  the  valve  derives  the  other  element  of  its  motion  from  the  radius 
rod  E  attached  to  the  centre  e  and  to  the  slider  in  the  vibrating  slotted  link  F,  which  is 
hung  externally  at  its  centre/*;  the  link  receives  its  motion  from  the  eccentric  rod  G 
attached  to  its  lower  end  and  connecting  with  the  eccentric  g. 

The  sliding  of  the  rod  F  in  the  slotted  link  by  means  of  the  levers,  shown  in  dotted 
lines,  is  the  means  adopted  for  giving  an  earlier  or  later  cut-off  and  forward  or  back- 
ward gear. 

Skeleton  diagrams  (Figs.  433  to  435)  illustrate  the  movement  of  this  gear  : 


MECHANICS. 


227 


228 


MECHANICS. 


MACHINE    DESIGN    AND    MECHANICAL 
CONSTRUCTIONS. 

IN  the  designing  of  new  machines  and  mechanical  constructions,  the  draughtsman 
must  draw  from  his  knowledge  of  well-known  forms  and  parts,  and  combine  them ;  but, 
to  proportion  them  properly,  and  adapt  them  to  the  purposes  required,  he  must  under- 
stand the  stresses  to  which  they  are  to  be  subjected,  and  the  action  and  endurance  of  the 
material  to  be  used,  to  withstand  these  stresses. 

In  the  present  technical  application  of  the  term,  stress  is  confined  to  a  force  exerted 
between  two  bodies  or  parts  of  a  body,  such  as  a  pull,  push,  or  twist.  Strain  is  the 
alteration  produced  by  a  stress.  Stress  is  the  cause,  strain  the  effect ;  the  first  is  meas- 
ured by  the  load,  the  latter  by  the  deformation  of  the  body  produced  by  the  first.  A 
stress,  not  greater  than  the  elastic  limit  of  the  material  acted  upon,  produces  a  strain 
which  disappears  as  soon  as  the  load  is  removed :  up  to  this  limit  the  strain  is  propor- 
tional to  the  stress ;  beyond,  the  strain  increases  faster  than  the  stress,  up  to  the  point 
of  rupture.  The  elastic  limit  is  a  percentage  of  the  breaking  strain,  varying  with  the 
kind  of  material  and  application  of  stress.  Stress  is  usually  designated  as  load,  meaning 
thereby  the  sum  of  all  the  external  forces  acting  on  the  member  or  structure,  together 
with  its  weight. 

Dead  load,  or  weight,  is  a  steady,  unchangeable  load.  Live  loads  are  variable,  alter- 
nately imposed  and  removed,  or  varying  in  intensity  or  direction.  It  is  usual,  in  design- 
ing constructions,  to  proportion  the  parts  to  resist  a  much  greater  load  than  will  be 
brought  on  them  in  the  structure ;  the  load  is  multiplied  by  a  factor  termed  factor  of 
safety,  as  a  security  against  imperfections  in  material  and  workmanship,  contingencies  of 
settlement,  and  other  incidental  stresses.  But  it  must  be  observed  that  these  imperfec- 
tions are  such  as  can  not  be  seen  and  met ;  there  can  be  no  factor  of  safety  to  provide 
for  poor  and  unknown  material  and  defective  workmanship. 

The  factor  of  safety  adopted  for  dead  loads  varies  but  little  with  the  same  kind  of 
material ;  but  for  live  loads  the  factor  varies  not  only  with  the  material,  but  with  the 
character  of  the  stresses,  whether  they  are  applied  and  relieved  gradually  or  suddenly ; 
whether  they  only  vary  in  intensity,  or  also  in  direction,  alternately  compressive  or  ten- 
sile. In  this  latter  case  the  load  should  never  be  considered  less  than  the  sum  of  the 
stresses,  with  a  large  factor  of  safety.  Vibrations,  shocks,  and  changes  in  the  direction 
of  stresses  concentrate  the  strains  at  the  weakest  point  of  the  construction,  and  rupture 
takes  place  at  these  points,  which  would  be  adequate  to  the  strain  if  the  form  through- 
out were  uniform  with  that  at  these  points.  Thus,  boiler-plates  show  wear  just  at  the 
"edge  of  the  lap  of  the  sheets,  and  ear-axles  (Fig.  436),  with  sharp  angles  at  the  journals, 
are  known  to  break  after  a  time,  while  under  the  same  stresses  an  axle  of  uniform  size 
with  the  journal  would  not  break;  nor  if  a  slight  cove  J  inch  radius  (Fig.  437)  be  made 
in  the  angle  to  distribute  stress. 

Besides  provisions  for  strength,  the  draughtsman  should  understand  the  necessities 
of  the  construction,  and  the  character  of  the  material  to  be  used.  He  should  know 
what  parts  of  the  design  are  to  be  forged,  cast,  framed,  and  how  it  is  to  be  done.  He 
should  know  what  wear  is  to  be  met,  and  what  waste,  as  rust  or  rot,  to  be  provided  for. 

229 


230 


MACHINE  DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


This  knowledge  can  only  be  arrived  at  by  reference  to  examples  of  practice  and  by  ob- 
servation of  results  under  similar  conditions  of  use  and  time. 


FIG.  436. 

The  stresses  to  which  constructions  and  parts  of  constructions  are  subjected  are  the 
tensile  or  stretching  stress,  tending  to  lengthen  a  body  in  the  direction  of  the  stress ;  the 
compressive  or  crushing  stress,  tending  to  shorten  a  body  in  the  direction  of  the  stress; 
the  shearing  or  cutting  stress,  tending  to  elongate,  compress,  and  deflect ;  the  torsional  or 
twisting  stress,  the  effect  being  an  angular  deflection  of  the  parts  of  the  body ;  and  the 
transverse  or  lateral  stress,  tending  to  bend  the  body  or  break  it  across. 

In  Appendix  is  given  a  table  of  the  strength  of  various  metals  to  resist  compression 
and  tensional  stresses,  and  examples  will  hereafter  be  given  of  varied  constructions,  with 
their  usual  or  required  factors  of  safety ;  but,  for  a  practical  rule  for  the  common  neces- 
sities of  the  above  stresses,  under  dead  loads,  10,000  pounds  per  square  inch  for  wrought- 
iron  and  12,000  for  steel  may  be  considered  perfectly  safe. 

Posts  in  structures  are  subjected  to  compressive  stresses ;  but,  as  the  action  is  modi- 
fied somewhat  by  a  tendency  to  bend,  depending  on  the  proportion  of  the  length  to  the 
diameter,  and  the  material  of  which  they  are  composed,  the  usual  tables  of  crushing 
strength  are  not  generally  applicable,  and  the  formulae  to  be  depended  on  are  those  de- 
duced from  practical  tests.  The  best  tests  of  wooden  posts  are  those  made  by  Professor 
Lanza,  for  the  Boston  Manufacturers'  Mutual  Fire-Insurance  Company,  and  the  following 
are  the  results : 

"That  the  strength  of  a  column  of  hard  pine  or  oak,  with  flat  ends,  the  load  being 
uniformly  distributed  over  the  ends,  is  practically  independent  of  the  length,  such 
columns  giving  way  by  direct  crushing,  the  deflection,  if  any,  being  very  small.  Tests 
were  on  columns  6"  to  10"  diameter  x  12  feet.  The  average  crushing  strength  of  very 
highly  seasoned,  hard  pine  was  7,386  pounds  per  square  inch.  Some  very  slow-growth 
and  highly  seasoned,  9, 339  pounds;  very  wet  and  green,  3,015  pounds;  seasoned  about 
three  months,  3,400  pounds;  not  very  well  seasoned  and  not  very  green,  4,400  to  4,700 
pounds.  The  average  of  two  specimens  of  thoroughly  seasoned  white-oak,  7, 150  pounds ; 
for  green  and  knotty,  average,  3,200  pounds.  Spruce,  nearly  5,000  pounds.  White- 
wood,  3,000  pounds. 

"That  it  is  a  mistake  to  turn  columns,  taper,  or  even  turn  them  at  all,  square  col- 
umns being  much  stronger,  cheaper,  and  better,  and  that  accuracy  of  fitting  is  of  great 
consequence,  that  the  stress  may  be  directly  vertical."  The  professor  recommends  that 
longitudinal  holes  be  bored  through  the  centre  of  columns  to  allow  of  the  circulation  of 
air  (in  the  experiments  the  holes  were  1'7"  diameter),  and  that  iron  caps  be  used  instead 
of  wooden  bolsters,  as  the  wooden  bolster  will  fail  at  a  pressure  far  below  that  which 
the  column  is  capable  of  resisting,  and  the  unevenness  of  pressure  brought  about  by  the 
bolster  is  sometimes  so  great  as  to  crack  the  column.  He  also  recommends  horizontal 
holes  in  the  iron  caps  to  connect  the  longitudinal  ones  in  the  column  with  the  outer  air. 

From  the  whole  of  the  experiments,  we  estimate  the  safe  load,  for  fair-grained,  well- 
seasoned  oak  or  yellow-pine  columns,  to  be  from  1,000  to  1,500  pounds  per  square  inch; 
for  the  more  imperfect  and  green  specimens,  from  300  to  500  pounds ;  for  good  speci- 
mens of  whitewood,  about  300  pounds ;  and  of  spruce,  about  500  pounds. 

Cast-Iron. — For  the  columns  of  buildings  where  the  load  is  dead,  cast-iron  is  very 
generally  used.  They  are,  in  interiors,  mostly  of  circular  section,  but  for  outer  columns 
forms  are  used  suited  to  the  necessities  of  their  position  or  style  of  architecture.  They 
admit  of  considerable  ornamentation  and  finish  direct  from  the  mould;  but,  as  they  are 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


231 


liable  to  defects  not  readily  detected  in  the  process  of  casting,  the  factor  of  safety  is 
usually  taken  as  high  as  5.  To  protect  them  against  the  effects  of  fire  and  water  in  con- 
flagrations, they  should  be  covered  with  a  shell  of  light  refractory  material,  as  porous 
brick  or  tile. 

The  experiments  of  Hodgkinson  are  the  usual  basis  of  all  formula?  on  the  strength  of 
circular  cast-iron  columns,  and  the  ends  of  all  columns  are  now  required  to  be  faced  by 
architects  and  by  the  rules  of  building  departments,  since  Mr.  Hodgkinson  states  this 
rule,  that  ' '  in  all  long  columns,  of  the  same  dimensions,  the  resistance  to  fracture  by 
flexion  is  three  times  greater  when  they  are  flat  and  firmly  bedded  than  when  they  are 
rounded  and  capable  of  moving." 

Table  of  the  safe  load  of  solid  cylindrical  columns,  with  flat  ends  calculated  with  a 
factor  of  safety  of  5. 


TABLE  OF  SAFE  LOADS  FOE  SOLID  CAST-IKON  COLUMNS,  WITH  FLAT  ENDS. 


Diam. 

8' 
1,000 

11.5. 

9' 
1,000 
Ibs. 

10' 
1,000 
Ibs. 

ll' 

1,000 
Ibs. 

12' 

1,000 
Ibi. 

13' 

1,000 
Ibs. 

14' 
1,000 
Ibs. 

15' 
1,000 
Ibs. 

16' 
1,000 
Ibs. 

17' 

1,000 
Ibs. 

18' 
1,000 
Ibs. 

19' 
1,000 
Ibs. 

20' 
1,000 
Ibs. 

21' 
1,000 
Ibs. 

22' 
1,000 
lb«. 

23' 

1,000 
Ibs. 

24' 

1,000 

11*. 

8" 

29- 

23- 

20- 

17- 

14- 

18- 

11- 

10- 

9- 

8- 

7- 

7- 

6- 

6- 

6- 

5- 

4- 

3}" 

40- 

31- 

26- 

22- 

19- 

17- 

lS- 

13- 

12- 

11- 

10- 

9- 

8- 

7- 

7- 

6- 

6- 

3*" 

50- 

41- 

84- 

29- 

25- 

22- 

19- 

17- 

15- 

14- 

12- 

ii- 

10- 

10- 

9- 

8- 

8- 

3J" 

63" 

54- 

48- 

37- 

82' 

23- 

24- 

2^- 

19 

18- 

16- 

is- 

18- 

12- 

11- 

11' 

10- 

4" 

77- 

66- 

54- 

46 

40' 

85- 

81- 

27- 

24- 

22- 

20- 

18- 

17- 

15- 

14- 

18- 

12- 

41" 

92- 

80- 

70- 

57' 

49" 

43- 

88- 

34- 

80- 

27- 

25 

23- 

21 

19- 

18- 

16- 

15- 

44" 

no- 

96- 

84- 

74- 

61' 

53- 

47- 

41- 

87- 

83- 

30- 

28" 

25- 

23- 

22- 

20- 

19- 

H" 

130- 

113- 

99- 

88- 

73- 

64- 

5B- 

50- 

45' 

41- 

87- 

84 

81- 

28- 

26- 

24' 

23- 

5" 

152- 

133- 

117- 

103- 

92' 

77' 

68- 

60- 

54- 

49- 

44- 

4(1- 

87- 

84- 

81- 

29- 

27' 

51" 

176- 

154- 

136- 

121- 

108- 

97" 

81- 

72- 

64- 

S8- 

58- 

48- 

44- 

40- 

87- 

85- 

32- 

54" 

201- 

177- 

157- 

14:f 

125- 

113 

95- 

85- 

76- 

68- 

62' 

57' 

52- 

48- 

44- 

41- 

88- 

5J" 

230- 

203- 

ISO- 

161- 

144' 

180- 

118- 

99- 

89" 

80- 

73- 

66- 

61- 

56- 

52- 

48- 

45- 

6  ' 

260- 

230' 

205- 

18}' 

165- 

149- 

J35- 

115- 

103- 

98- 

84' 

77- 

7r 

65- 

60- 

56- 

52- 

6J" 

292- 

260- 

232- 

203- 

187' 

169- 

154- 

140- 

119- 

108- 

98- 

89- 

82' 

75" 

69- 

64- 

60- 

6i" 

327- 

292- 

2H1- 

234- 

212- 

192- 

174- 

159- 

146- 

124- 

112- 

102- 

94- 

86- 

80- 

74- 

C9- 

6J" 

864- 

326- 

292- 

263: 

238- 

216- 

197- 

180- 

.163-  1  141- 

128- 

117' 

107- 

99- 

91- 

85- 

79- 

7" 

404- 

362- 

325- 

293- 

266" 

242- 

221- 

202- 

186-     IT!' 

146- 

133- 

122- 

112- 

104- 

96- 

90- 

71" 

445- 

40D- 

361- 

326- 

296" 

269- 

24G- 

2-26- 

208- 

192- 

177" 

151- 

138- 

127- 

118- 

109- 

101- 

q« 

489' 

441- 

3  8- 

361- 

328" 

299' 

274- 

251- 

231- 

214- 

198- 

no- 

156- 

148- 

133-    123- 

114- 

7t" 

536- 

434- 

43^- 

898- 

86^' 

331- 

303- 

5!78- 

257- 

237- 

220- 

204- 

175' 

Ibl- 

149- 

138- 

128- 

8" 

581' 

5^9- 

430- 

436- 

393- 

864' 

a34- 

808- 

284- 

263- 

244- 

227- 

196- 

180- 

167- 

155- 

144- 

8»" 

'639- 

626- 

571- 

521- 

477' 

487- 

402- 

871- 

343- 

318- 

296- 

275- 

257- 

241- 

207- 

192- 

178- 

9" 

802- 

733- 

670- 

614- 

564- 

519- 

479 

442- 

410- 

881- 

3S4- 

331- 

809- 

290- 

272- 

235- 

218- 

94" 

926- 

849- 

780- 

717- 

66D- 

603- 

563- 

522- 

484- 

461- 

420- 

393- 

867- 

345- 

324- 

805- 

265- 

Id" 

1058- 

975- 

898- 

829- 

765- 

708- 

656- 

6'I9- 

566- 

528- 

493- 

461- 

432- 

406- 

382- 

360- 

340- 

104" 

1195- 

1108- 

1026- 

957- 

892- 

8-W 

779- 

74H- 

693- 

653- 

610- 

580- 

546- 

511- 

485-    459- 

433- 

ii" 

1359- 

1264- 

1159- 

1033- 

1017- 

950- 

889- 

846- 

793- 

751- 

708' 

660- 

627" 

589- 

561-    542- 

513- 

114- 

1517- 

1413- 

1319- 

122fi- 

1147- 

1080- 

1018- 

956- 

904- 

852- 

810- 

758- 

727- 

691- 

665- 

613- 

587- 

12" 

1674- 

15S8- 

1470- 

1830- 

1289- 

1221  • 

1142- 

1074- 

1018- 

973- 

916- 

871- 

746- 

701- 

667' 

645- 

611- 

Solid  columns  are  very  seldom  used  in  constructions;  they  are  almost  invariably  made 
hollow,  the  shell  being  \"  to  2"  thick.  To  determine  the  safe  load  of  a  hollow  column, 
it  will  be  sufficiently  accurate  to  take  from  the  table  the  safe  load  of  a  column  equal  to 
that  of  the  exterior  diameter,  and  subtract  from  this  the  safe  load  of  a  column  of  a 
diameter  equal  to  the  core. 

Example.— -To  find  the  safe  load  of  a  column  12  feet  long,  8"  exterior  diameter, 
shell  |". 

Safe  load  of  8"  column 398,000  Ibs. 

"        "     "6V     " 212,000" 

"        "    required  column 186,000  " 

For  square  box-columns,  it  will  be  safe  to  estimate  that  a  square  column  will  support 
as  much  as  a  round  one,  the  side  of  the  one  being  equal  to  the  diameter  of  the  other, 
and  the  thickness  of  shell  the  same. 

For  a  star-column  (Fig.  438),  the  load  should  be  about  \  less  than  on  a  cylindrical 
column  of  same  diameter  and  same  area  of  section. 

There  is  a  convenience  in  the  use  of  cast-iron  that  the  brackets  for  the  support  of 


232 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


beams  and  girders  can  be  readily  cast  on,  but  it  must  be  done  with  care  in  the  design 
and  in  the  moulding.  It  will  be  seen  (Fig.  341)  that  weak  places  occur  in  the  cooling 
when  the  junctures  are  at  right  angles,  which  must  be  avoided  by  easements,  or  coves, 
in  the  patterns,  and  by  intelligence  in  the  moulding,  pouring,  and  cooling.  For  many 
years  cast-iron  was  the  only  metal  used  for  posts,  and  with  but  few  accidents  from  im- 
perfect construction  or  from  conflagrations. 

Wrought-Iron  Columns. — With  the  decrease  in  the  cost  of  the  manufacture  of  shapes 
in  wrought-iron,  columns  of  this  material  have  largely  superseded  those  of  cast-iron  in 


FIG.  439. 


FIG.  440. 


constructions  liable  to  varying  loads  and  shocks.     Fig.   439  shows  the  section  of  a 
Phoenix  column,  Fig.  440  of  the  Keystone. 


TABLE   OF  PHCENIX   COLUMNS. 


MAKK  OF  COLUMN. 

• 
Thick  D  ess  in 
inches. 

Area  in  square 
inches. 

Weight  in  pounds 
per  foot. 

Internal  diam- 
eter. 

A  

i 

2'8 

9-3 

4  segments  

A 

5-8 

19'4 

»f 

B  

y> 

<K 

5'0 

16'7 

4  segments  

1" 

]4'8 

51. 

4rt 

B2  

A 

5'8 

19-4 

4  segments.  . 

& 

17- 

58-6 

Btl 

C..    

A 

8'8 

30-3 

4  segments.  . 

1A 

40' 

138. 

f& 

D..!  

i 

14-0 

48'2 

5  segments.  . 

4 

26- 

89'7 

»* 

B..?  

j 

I8- 

55'2 

6  segments  

i,a« 

60- 

207' 

11 

F  

.a 

24'5 

84-5 

7  segments  

i 

36'4 

125-6 

13 

G  

A 

24- 

82'8 

8  segments  

1&. 

80- 

276- 

14f 

BUILT    COLUMNS. 

Open  columns  should  be  used  in  positions  exposed  to  dampness  and  rust  on  account 
of  their  accessibility  to  painting  and  inspection.  Built  columns  present  advantages  in 
the  facility  with  which  connections  can  be  made  to  floor  beams  or  bracing  rods. 

In  determining  upon  the  proper  sections  for  these  columns,  the  material  should  be  so 
disposed  that  the  tendency  to  yield  will  not  be  greater  in  one  direction  than  in  the  other 
to  secure  the  full  strength  of  the  column. 

The  rivets  at  the  ends  should  be  pitched  not  more  than  three  inches  apart,  and  the 
maximum  distance  between  rivets  in  the  line  of  stress  should  not  exceed  sixteen  times 
the  thickness  of  the  plate. 

Figs.  459  and  460  are  plan  and  elevation  of  a  latticed  column. 

Spacing  of  the  Lattice  or  Lacing  Bars. — The  object  of  these  bars  is  to  join  the  two 
channels  composing  the  post  or  chord,  and  thus  cause  them  to  act  together;  they  should 
be  attached  at  intervals  so  close  that  there  shall  be  no  danger  of  failure  of  the  channels 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


233 


between  the  points  of  attachment,  which  never  should  be  more  than  0'6  of  the  interval, 
and  lacing  bars  are  not  allowed  to  make  an  angle  of  more  than  60°  with  each  other,  or 
less  than  60°  with  the  flanges. 


FIG.  441. 


FIG.  442. 


FIG.  443. 


FIG.  444. 


FIG.  445. 


Fio.  446. 


>       C 


--D  -- 


FIG.  447. 


i  D 

!& 

* 

«! 

FIG.  451. 


FIG.  452. 


FIG.  453. 


FIG.  454. 


FIG.  455. 


FIG.  456. 


FIG.  457. 


FIG.  458. 


On  the  Strength  of  Wrought-Iron   Columns.—  In    the 
former  editions  of  this  work  the  strength  of  wrought      y,,,,,. 
columns  was  shown  by  curves  of  the  average  breaking 
loads  (Fig.  461),  as  determined  by  experiments  on  the 
Phosnix,  Keystone,  Piper,   and  open  columns  with   flat 
ends.     Vertical  distances  represent  the  pounds  of  load      rpz 
per  square  inch,   the  horizontal  the  proportion  of  the      *» 

length  of  the  columns  to  the  diameter— ;  D   is  taken  as 

the  least  outside  diameter  as  marked  on  the  varied  sections  above.     The  lower  curves 
represent  the  safe  loads,  under  factors  of  safety  of  3,  4,  and  5.     In  looking  at  these 
curves,  it  will  be  observed  that,  within  the  common  limits  of  prac- 
tice, of  15  to  35  - — » these  lines  may  be  considered  straight ;  that 

diameter 

with  iron  of  a  breaking  strength  of  52,000  pounds  per  square  inch, 
and  within  the  above  limits,  and  a  factor  of  safety  of  3,  the  safe  load 
may  be  taken  at  11,000  per  square  inch;  with  a  factor  of  safety  of  4, 
at  8,000  pounds;  with  a  factor  of  safety  of  5,  at  6,500  pounds;  and 
that  for  common  and  usual  purposes  10,000  pounds  per  square  inch 
is  a  safe  load. 

At  present  there  are  few  wrought-iron  columns 
manufactured;  they  are  almost  invariably  steel,  but 
the  diagram  still  represents  in  their  working  propor- 
tions the  action  of  columns  under  stress.  The  steel 

When,  as  ob- 


FIG.  459. 


FIG.  460. 


column  is  about  20  per  cent  stronger. 


234 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


served  above,  the  common  and  usual  safe  load  on  iron  is  10,000  pounds  per  square  inch, 
that  on  steel  is  12,000  pounds. 

For  struts,  angle  irons,  or  a  combination  of  them  forming  an  angle  or  cross  (Figs.  441 

L 


D 


and  442),  with  or  without  separators,  are  generally  used,  and  in  these  cases  for  D  in 

take  D  equal  to  0-8  of  the  shortest  leg  or  legs. 

It  has  generally  been  considered  that  columns  with  pin  or  cylindrical  ends  had  about 


ZO  30 

FIG.  461. 


three  fourths  of  the  resisting  strength  of  flat  ends,  but  if  the  pin  ends  are  closely  fitted, 
so  that  the  strains  are  uniformly  in  the  direction  of  the  length  of  the  column,  the  differ- 
ence is  but  little  between  the  two  kinds  of  ends. 

Shearing  Stresses. — Parts  of  machines  and  of  constructions  subjected  to  these  stresses 
have  often  the  resistances  modified  by  friction,  combined  with  other  stresses.  The  sizes 
of  parts  necessary  to  resist  such  stresses  practically,  as  in  the  cases  of  bolts,  rivets,  and 
the  like,  will  be  hereafter  illustrated  by  examples  and  determined  by  particular  rules. 
In  general,  the  strength  to  resist  shearing  stress  is,  in  wrought-iron  and  steel,  from  70  to 
80  per  cent  of  its  tensile  strength;  in  cast-iron,  about  40  per  cent  of  its  crushing  strength. 
The  softer  woods,  as  spruce,  white  pine,  hemlock,  resting  on  walls  or  girders,  will  safely 
sustain  a  load  of  200  to  300  pounds  per  square  inch  of  bearing  surface,  and  the  harder 
woods,  as  oak  and  Southern  pine,  300  to  500  pounds.  By  experiment,  oak  treenails,  1" 
to  If"  diameter,  were  found  to  have  an  ultimate  shearing  strength  of  about  two  tons  per 
square  inch  of  section;  but,  according  to  Rankine,  the  planks  thus  connected  together 
should  have  a  thickness  of  at  least  three  times  the  diameter  of  the  treenails.  In  3"  planks, 
If"  treenails  bore  only  1-43  tons  per  square  inch  of  section;  in  6"  plank,  1'73  tons. 

Torsional  Stress.' — Every  shaft  through  which  power  is  transmitted,  whether  through 
gears,  cranks,  or  pulleys,  is  subjected  to  a  torsional  stress,  of  which  the  power  acting 
tangentially  to  the  shaft  in  one  direction  is  resisted  by  the  load  in  an  opposite  direction. 
When  this  stress  exceeds  a  certain  limit  depending  on  the  material,  the  fibres  are  twisted 
asunder,  but  much  below  this  limit  the  elasticity  of  the  shaft  may  be  too  great  to  trans- 
mit power  uniformly. 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


235 


The  length  of  the  axle  subjected  to  torsion  does  not  affect  the  actual  amount  of  pres- 
sure required  to  produce  rupture,  but  only  the  angle  of  torsion  which  precedes  rupture, 
and  therefore  the  space  through  which  the  pressure  must  be  made  to  act. 

A  practical  limit  of  torsional  deflection  is  1°  in  a  length  equal  to  twenty  diameters 


FIG.  462. 


Fio.  463. 


of  the  shaft — or  T^  part  of  a  full  turn.  D.  K.  Clark  gives  the  following  rule :  "To 
find  the  diameter  of  a  shaft  capable  of  transmitting  a  given  torsional  stress  within  gaod 
working  limits.  Divide  the  torsional  stress  in  foot-pounds  by  18 '5  for  cast-iron;  27'7 
for  wrought-iron;  and  57'2  for  steel.  The  cube  root  of  the  quotient  is  the  diameter  of 
the  shaft  in  inches. 

Example. — On  the  teeth  of  a  4^-foot  gear,  the  force  exerted  is  2,800  pounds.  What 
should  be  the  diameter  of  a  wrought-iron  shaft  to  transmit  this  force  safely  ? 

The  torsional  stress  will  be  2,800  pounds  multiplied  by  the  radius  of  leverage,  2Jfeet, 

or  6,300  foot-pounds  =  (2  =  228,     «/228  =  6-1. 


Transverse  Stress. — The  strength  of  a  beam  is  influenced  by  the  manner  in  which  its 
ends  are  supported.  Where  the  ends  are  simply  supported — that  is,  resting  upon  the 
abutments — and  the  beam  loaded  with  a  weight  W  (Fig.  462),  the  beam  is  subjected  to  a 
bending  movement,  or  transverse  stress,  composed  of  a  tensile  stress  on  the  lower  part  of 
the  beam  and  compressive  on  the  upper  part.  In  addition,  the  weight  of  the  beam  and 
its  supported  load  act  on  the  abutments  as  shearing  stresses. 

If  the  ends  of  a  beam  are  fixed  in  the  wall,  however,  the  transverse  stresses  are  con- 
siderably relieved  throughout  the  beam,  which  is  thereby  capable  of  sustaining  a  heavier 
load.  Figs.  464  to  471  are  examples  of  beams  with  both  ends  simply  supported  and 
both  ends  fixed,  or  one  end  supported  and  one  end  fixed,  and  a  comparison  of  their 
strength  for  a  centre  load  and  a  load  uniformly  distributed. 

The  strength  of  a  square  or  rectangular  beam  to  resist  transverse  stress  is  as  the 
breadth  and  the  square  of  the  depth;  and  inversely  as  the  length,  or  the  distance  from  or 
between  the  points  of  support.  Thus  a  beam  twice  the  breadth  of  another,  other  pro- 
portions being  alike,  has  twice  the  strength ;  or  twice  the  depth,  four  times  the  strength ; 
but  twice  the  length,  only  half  the  strength. 

It  is  evident,  therefore,  that,  with  the  same  area  of  section,  the  deeper  a  beam  the 
stronger  it  will  be,  if  the  breadth  is  sufficient  to  prevent  lateral  buckling. 

To  cut  the  best  beam  from  a  log,  Fig.  463,  the  section  of  which  is  a  circle :  draw  a 
diameter,  divide  it  into  three  equal  parts,  erect  perpendiculars  at  the  points  of  division 
1,  2,  and  they  will  intersect  the  circumference  at  the  corners  of  the  beam,  of  which  the 
extremities  of  the  diameter  are  the  other  two. 

For  the  transverse  strength  of  rectangular  beams  the  general  formula  is  W  =  — j — ,  in 

which  W  is  the  breaking  weight;  8,  a  number  determined  by  experiment  on  different 
materials ;  ft,  the  breadth,  and  d,  the  depth  in  inches ;  and  ?,  the  length  in  feet. 

Figs.  464  to  471  represent  the  usual  methods  of  loading  beams,  and  the  loads  as 


236 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


drawn  represent  the  comparative  strength  of  beams  under  these  different  conditions. 
Thus,  in  Fig.  464,  the  beam  supports  but  one  unit  of  load,  while  Fig.  465  supports  twice  as 


FIG.  464. 


FIG.  465. 


much.     The  formulae  given  represent  the  safe  dead  loads  with  a  factor  of  safety  of  6, 
deduced  from  experiments  of  Mr.  C.  J.  H.  "Woodbury  on  Southern  pine.     For  spruce  the 


FIG.  466. 


FIG.  467. 


coefficient  would  be  about  \  less,  and  for  live  loads  the  factor  of  safety  should  be  12. 
Beams  fixed  at  one  end  and  loaded  at  the  other  (Fig.  464). 

fid* 
Safe  load  =  30  -=-. 

Beams  fixed  at  one  end  and  load  distributed  uniformly,  not  as  represented  in  the 
figure,  as  the  two  units  of  weight  would  be  spread  over  the  whole  length  of  the  beam 
(Fig.  465). 

7>  fl* 
Safe  load  =  60  -f-. 

L 

Beams  supported  at  the  extremities  and  loaded  at  the  middle  (Fig.  466). 

ft/72 

Safe  load  =  120  -=-. 
l 

Beams  supported  at  the  extremities  and  the  load  uniformly  distributed  (Fig.  467). 

&  d? 
Safe  load  =  240  - 


FIG.  468. 


FIG.  469. 


Beams,  one  end  firmly  fixed,  the  other  supported,  and  loaded  at  the  middle  (Fig.  468). 

bd? 
Safe  load  =  160  -p 

Beams  with  one  end  fixed,  the  other  supported,  and  load  uniformly  distributed 
(Fig.  469). 

Id* 
Safe  load  =  240-^-. 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 
Beams  with  both  ends  fixed,  and  loaded  at  centre  (Fig.  470). 


237 


Safe  load  =  240 


I  ' 


FIG.  470. 


FIG.  471. 


Beams  with  both  ends  fixed,  and  load  uniformly  distributed  (Fig.  471). 

bd'2 
Safe  load  =  360  -y-. 

If  the  loads  on  a  beam  be  neither  at  the  centre  nor  uniformly  distributed, 
but  at  intermediate  points,  it  is  important  to  determine  the  load  which  placed 
at  the  centre  will  produce  an  equivalent  stress. 

Thus  on  a  beam  of  30  feet  span,  if  a  weight  of  800  pounds  be  placed  at  10 
feet  from  an  end.  Lay  off  on  any  convenient  scale  (Fig.  472)  a  horizontal  line 


FIG.  472. 


of  30  feet,  and  at  a  point  10  feet  from  one  end,  draw  a  vertical  or  ordinate  from 
this  point,  and  at  the  ends  A  and  B. 

From  any  convenient  point  on  the  ordinate  beneath  A  draw  a  line  parallel 
to  A  B  and  set  off  to  0,  a  distance  equal  to  £  of  the  span  for  the  pole  distance 
of  the  force  polygon  about  to  be  constructed,  which  is  established  at  i  of  the 
span,  in  order  to  determine  readily  the  equivalent  central  load.  From  the 
point  a  in  the  ordinate  lay  off  on  any  scale  a  a'  =  800  pounds,  draw  lines  0  a 
and  0  a',  and  the  force  polygon  is  complete. 

From  a  extend  the  line  a  0  till  it  intersects  the  weight  ordinate  from  D  at 
E.  Draw  E  F  parallel  to  0  a'  to  intersect  the  ordinate  B  ;  connect  F  with  a  ; 
F  a  is  called  the  closing  line  of  the  equilibrium  polygon. 

The  weight  800  pounds  is  supported  by  the  abutments  A  and  B.  Draw  a 
line  0  c  in  the  force  polygon  parallel  to  F  a ;  the  distance  above  this  line  in 


238 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


pounds  will  be  the  amount  of  the  load  on  A,  533  pounds,  c  a',  below  the  line, 
267  pounds  will  be  that  on  B. 

If  the  weight  be  placed  centrally  (Fig.  473)  and  its  material  sufficiently 
elastic  to  be  considered  uniformly  distributed  for  its  whole  length  ;  to  determine 
its  effect  under  these  conditions,  draw  the  equilibrium  polygon  a  E  F  as  if  the 


FIG.  475. 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


239 


weight  of  800  pounds  were  suspended  from  a  single  central  point ;  divide  the 
weight  into  any  number  of  equal  parts  (say  8,  of  100  pounds  each),  and  draw 
ordinates  through  the  centre  of  these  parts.  Draw  through  1'  a  line  parallel 
to  0  1  and  consecutively  through  2'  3'  4'  5'  6'  7'  8'  lines  parallel  to  0  2,  0  3,  etc. 
The  central  weight  as  measured  on  the  longest  ordinate  is  690  pounds. 

If  the  weight  1,200  pounds  (Fig.  474)  be  distributed  on  a  beam  of  40  feet — 
40  -4-  say  8  =  5.  Lay  off  at  each  extremity  one  half  part  or  2^  feet,  and  for  the 
intermediate  lengths,  7  parts  of  5  feet  each,  and  draw  ordinates  through  these 
divisions ;  follow  the  diagram  construction  as  in  the  preceding,  each  weight 
being  150  pounds,  the  longest  ordinate  is  600  pounds,  or  one  half  the  total 
weight  of  1,200  pounds,  and  each  abutment  load  is  600  pounds. 

In  Fig.  475  the  weights  are  many  and  unequally  distributed;  construct  dia- 
gram as  before,  always  making  the  pole  distance  equal  to  a  quarter  of  the  span ; 
measure  the  longest  ordinate,  which  is  595  pounds,  the  equivalent  central  load. 
Draw  0  c  parallel  to  the  closing  line  a  F ;  the  total  of  the  weights  1,100  pounds 
will  be  supported  by  abutment  A,  500  pounds,  and  by  abutment  B,  600  pounds. 
In  all  the  figures  the  weight  of  the  beam  itself  is  not  taken  into  account,  but, 
if  considered,  it  is  almost  invariably  of  one  section  and  therefore  distributed, 
and  its  central  load  will  be  one  half  the  total  weight. 

The  following  table  for  the  strength  of  yellow-pine  beams  is  calculated  for 
a  safe  central  load,  as  determined  by  the  graphic  constructions  or  by  taking  one 
half  the  uniformly  distributed  load  if  this  is  given. 

TABLE  OF  THE  SAFE  CENTEAL  LOAD   OF  YELLOW-PINE  BEAMS,   CALCULATED 
FROM   THE   FORMULA   120*^!. 

6 


Span  in 


DEPTH    IN    INCHES    OF    YELLOW-PINE    BEAMS,   ONE    INCH    WIDE. 


feet. 

3  ins. 

4  ins. 

5  ins. 

6  ins. 

Tins. 

8  ins. 

9  ins. 

10  ins. 

11  ins. 

12  ins. 

13  ins. 

14  ins. 

15  ins. 

16  ins. 

4 

270- 

480- 

750" 

1080- 

1470- 

1920' 

2430" 

3000' 

3630- 

4320' 

5070- 

5880' 

6750- 

7680- 

5 

216- 

384- 

600' 

864- 

1176- 

1536- 

1944' 

2400- 

2904- 

3456' 

4056" 

4704- 

5400' 

6144- 

6 

180- 

320- 

500- 

720- 

980- 

1280- 

1620' 

2000- 

2420- 

2880' 

3380' 

3920- 

4500- 

5120- 

7 

154- 

274- 

430- 

616" 

840- 

1097" 

1389" 

1714- 

2074- 

2469' 

2897' 

3360' 

3857' 

4388- 

8 

135- 

240- 

375- 

540- 

735- 

960' 

1215' 

1500- 

1815- 

2160- 

2535' 

2940- 

3375- 

3840- 

9 

120- 

213- 

333- 

480- 

£53- 

853' 

1080- 

1333' 

1613. 

1920- 

2253- 

2613' 

3000- 

3413- 

10 

108' 

192' 

300- 

432- 

588' 

768- 

972- 

1200- 

1452. 

1728- 

2028- 

2352' 

2700- 

3072- 

11 

175- 

273- 

392- 

535- 

700- 

882- 

1092- 

1320- 

1571- 

1844. 

2140" 

2457" 

2793- 

12 

160- 

250- 

360- 

490- 

640- 

810- 

1000- 

vio- 

1440' 

1690' 

I960- 

2250- 

2560- 

13 

230- 

332- 

452' 

592- 

747- 

923- 

lin- 

1328' 

1560- 

1808- 

2070- 

2363- 

14 

215- 

308- 

420- 

548' 

693- 

860" 

1037' 

1234- 

1448' 

1680- 

1928- 

2192- 

15 

288- 

392' 

512- 

648- 

800' 

968- 

1155- 

1352- 

1568- 

1800- 

2048- 

16 

270- 

368- 

480- 

607- 

748- 

907' 

1080' 

1267' 

1470- 

1688- 

1920- 

17 

254- 

346- 

452- 

566- 

704- 

854- 

1016' 

1193- 

1384- 

1588- 

1808-  ' 

18 

327- 

427* 

540" 

668- 

806- 

960- 

1126- 

1307- 

1500- 

1707- 

19 

404- 

512' 

632- 

764- 

909- 

1067' 

1238- 

1422- 

1616- 

20 

384- 

486- 

600- 

726- 

864- 

1014- 

1176- 

1350- 

1536' 

21 

463- 

572- 

691- 

823- 

966- 

1120' 

1287- 

1463- 

22 

442- 

546' 

660- 

785- 

922- 

1070- 

1228-  | 

1395' 

23 

522- 

631' 

752- 

882- 

1023- 

1178- 

1329- 

24 

500- 

605- 

720' 

845- 

980- 

1125- 

1280- 

25 

581- 

691' 

811' 

940- 

1080- 

^so- 

30 

558' 

665- 

780- 

904-  ' 

1035- 

il  82- 

240  MACHINE  DESIGN  AND  MECHANICAL   CONSTRUCTIONS. 

The  table  gives  the  load  which  the  beam  can  sustain,  allowing  a  certain 
factor  of  safety,  but  the  strength  given  is  in  excess  of  stiffness,  and  in  perma- 
nent construction  it  is  necessary  to  proportion  the  beams  to  bear  its  load  with 
a  certain  limited  deflection.  Cross-lines  on  the  tables  represent  those  limits, 
but,  as  usually  the  weight  of  construction  is  much  less  than  that  of  the  change- 
able loads,  and  as  the  change  of  deflection  is  that  to  be  guarded  against,  the 
weight  of  construction  may  be  neglected,  and  it  will  only  be  necessary  to  con- 
sider the  amount  of  movable  loads  above  these  lines. 

The  table  is  deduced  from  Mr.  Woodbury's  experiments  on  yellow  pine, 
of  good  quality  and  practical  sizes.  For  spruce  he  takes  loads  of  about  one 
fifth  less. 

The  table  is  intended  to  be  used  as  a  unit  of  width  by  which  the  strength 
of  timber  of  usual  depths  and  spans  can  be  estimated,  by  multiplying  by  such 
widths  as  are  found  in  practice ;  widths  of  less  than  two  inches  are  not  used. 
Mr.  Woodbury  established  the  limit  of  deflection  in  wooden  beams  at  three 

432  W  I3 
quarters  of  an  inch  for  25-feet  span,  and  his  formula  is  E  =  ,  in  which 

E,  the  modulus  of  elasticity  per  square  inch,  is  for  Southern  pine  2,000,000,  and 
for  spruce  1,200,000  :  W  central  load  in  pounds,  I  the  span  in  feet,  b  the  breadth, 
h  the  depth,  and  d  the  deflection  of  beam,  all  in  inches.  Using  this  formula, 
marks  are  drawn  in  each  column  of  depth,  above  which  the  loads  will  be  sup- 
ported stiffly,  and  below  less  than  recommended  ;  the  formula  is  only  applicable 
to  seasoned  wood.  Mr.  Woodbury's  results  are  confirmed  by  late  experiments 
on  the  long-leaved  pine  by  Prof.  Johnson  for  the  Forestry  Division  of  the 
United  States  Department  of  Agriculture. 

He  gives  the  shearing  strength  measured  by  the  cross-section  of  the  beam  at 
about  600  pounds  to  the  square  inch,  and  the  crushing  strength  across  the  grain 
at  about  1,150  pounds.  In  the  resting  of  the  beam  on  abutments  of  masonry  it 
will  be  difficult  to  exert  a  clean  shearing  stress,  and  the  strength  would  be  in 
excess  of  any  likely  to  occur,  but  the  stress  would  be  a  crushing  one,  and  be  met 
by  the  area  in  square  inches  resting  upon  the  wall. 

In  the  above  tables  there  is  a  factor  of  safety  of  six — that  is,  the  rupture 
should  not  take  place  except  at  a  load  six  times  that  given.  This  is  to  provide 
for  some  unknown  weakness  of  the  timber,  or  some  sudden  excess  of  load,  de- 
preciation by  age,  etc.,  but  this  factor  does  not  make  up  for  want  of  inspection 
or  knowledge  of  the  material.  It  is  well  to  load  some  of  the  timbers,  as  a  test 
to  the  elastic  limit,  which  can  be  done  by  placing  two  timbers  at  convenient  dis- 
tances apart  and  loading  with  pig  iron  or  barrels  of  sand. 

The  early  cast-iron  beams  used  in  framing  have  been  almost  entirely  super- 
seded by  wrought  ones,  as  cheaper  and  more  reliable.  In  the  application  of  the 
former,  the  sections  were  adapted  to  the  stresses,  as  shown  in  Figs.  476-478. 
Practical  examples  of  cast-iron  beams  are  given,  as  there  may  be  conditions 
under  which  it  may  be  necessary  to  make  use  of  them. 

A  beam  subjected  to  a  transverse  stress,  as  shown  in  Fig.  462,  one  side  is 
compressed,  while  the  other  side  is  extended  ;  and  therefore,  where  extension 
terminates  and  compression  begins,  there  is  a  lamina  or  surface,  g  h,  which  is 
neither  extended  nor  compressed,  called  the  neutral  surface.  As  the  strains 
are  proportional  to  the  distance  from  this  surface,  the  material  of  which  the 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


241 


beam  is  composed  should  be  concentrated  as  much  as  possible  at  the  outer  sur- 
faces, as  can  readily  be  done  in  beams  of  cast  and  wrought  iron.     Mr.  Hodgkin- 


FIG.  476. 


FIG.  477. 


FIG.  478. 


son  found  that  the  strength  of  cast-iron  to  resist  compression  is  about  six  times 
that  to  resist  extension  ;  the  top  web  is  therefore  made  only  one  sixth" the  area 
of  the  lower  one.  The  depth  of  the  beam  is  generally  about  one  sixteenth  of 
its  length,  the  deeper  of  course  the  stronger  ;  the  thickness  of  the  stem  or  the 
upright  part  should  be  from  £  an  inch  to  1£  inch,  according  to  the  size  of  the 
beam.  The  rule  for  finding  the  ultimate  strength  of  beams  of  the  above  sec- 
tion is  :  Multiply  the  sectional  area  of  the  bottom  flange  in  square  inches  by 
the  depth  of  the  beam  in  inches,  and  divide  the  product  by  the  distance  be- 
tween the  supports  in  feet,  and  2'42  times  the  quotient  will  be  the  breaking 
weight  in  tons  (2,000  pounds).  The  section  thus  determined  is  that  of  the 
greatest  strain,  and  can  be  reduced  toward  the  points  of  support,  either  by 
reducing  the  width  of  the  flanges  to  a  parabolic  form  (Fig.  479),  or  by  reducing 
the  thickness  of  the  bottom  flange  ;  the  reduction  of  the  girder  in  depth  is  not 
in  general  as  economical  or  convenient. 


FIG.  479. 


For  railway  structures  subject  to  an  impulsive  force,  Mr.  Joseph  Cubitt, 
C.  E.,  recommends  that  the  section  of  the  upper  flange  should  be  one  third 
that  of  the  lower. 


1-7 


FIG.  480. 


242 


MACHINE   DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


Fig.  480  is  side  elevation,  plan,  and  section  of  cast-iron  girder,  adopted  by 
him  for  railway  purposes,  a  pair  of  girders  for  each  track,  the  rails  being  sup- 
ported on  wooden  cross-beams. 

DIMENSIONS  FOR  DIFFEEENT  SPANS. 


Opening. 

Bearing  on 
abutment 

Height  of  girder 
at  center. 

Top  flange. 

Bottom  flange 
at  center. 

At  end. 

Thickness  of 
middle  web. 

12ft. 

l'-6" 

l'-3" 

3"   X  11" 

l'-4"  X  If 

l'-8"     X  11" 

11" 

30ft. 

2''6" 

3'- 

5"  x  2" 

l'-6"  X  2" 

l'-10"  x  2" 

2" 

45ft. 

2'-9" 

3'-9" 

7"  x  21" 

2''       x  2£" 

2''         X  21" 

2" 

Rolled  I-beams  (Fig.  481)  may  be  taken  as  the  type  in  wrought-iron  and 
steel  sections.     The  depths  of  the  beams,  A,  and  the  widths,  B,  of  bottom  and 
top  flanges  do  not  vary  much  with  the  different  makers  for  the 
same  class  of  beams,  but  the  thickness  of  the  stems  varies  more. 
The  tables  of  the  Strength  of  Wrought-iron  and  Steel  Beams 
(pages  243,  244)  have  been  made  up  by   comparison   of   the 
tables  of  different  makers,  the  safeload  is  taken  in  units  of  100 
pounds,  and  00  are  to  be  added  to  the  tabulated  figures  to  give 
the  safe  distributed  load  in  pounds. 

It  is  assumed  in  these  tables  that  proper  provision  is  made 
for  preventing  the  beam  from  deflecting  sideways.  They  should 
be  held  in  position  at  distances  not  exceeding  twenty  times  the 
width  of  the  flange ;  this  is  usually  effected  by  the  brick  arches 
between  the  beams,  or  the  wooden  joists  resting  on  them.  The  beams  will 
support  the  loads  as  given  in  the  tables,  but  the  deflection  may  be  too  much 
for  the  purposes  to  be  served.  A  line  is  drawn  in  each  column  in  the  tables, 
at  which  the  deflection  is  -j^  beyond  that  due  to  the  weight  of  the  beams,  or 
one  inch  for  every  thirty  feet  of  span,  beyond  which  the  deflection  is  apt  to 
crack  the  plastering  of  ceilings. 

To  find  the  sectional  area  of  a  beam,  plate  or  rod  from  its  weight,  multiply 
weight  per  foot  by  3  and  divide  by  10  ;  and,  conversely,  to  determine  the  weight 
multiply  the  sectional  area  by  10  and  divide  the  product  by  3. 

Thus,  if  a  steel  bar  12  feet  long  weigh  480  pounds,  or  40  pounds  per  foot, 


FIG.  481. 


its  sectional  area  will  be 


inches  section  will  weigh 


3  X  40 

10 
9  X  10 


,  or  12  square  inches ;   and  a  bar  of  9  square 
=  30  pounds  per  foot. 


For  naval  constructions,  deck-beams  (Fig.  482)  are  from  3"  to  12"  deep,  with 
varied  widths  of  flanges  and  thicknesses  of  stem ;  lighter  than  the 
grades  of  heavy  and  light  I-beams,  but  heavier  can  be  rolled  to  order ; 
bulb  angles  with  terminal  bulbs  similar  to  those  of  deck-beams,  on 
long  legs  of  from  5"  to  10",  and  short  legs  of  2£"  to  3£"  can  be  had 
of  varied  thicknesses.  Properly  proportioned,  they  are  equal  in 
strength  to  the  I-beams. 

Coupled  I-Beams. — When  the  load  is  beyond  the  strength  of  a 
single  I-beam,  two  or  more  may  be  united,  as  shown  in  Fig.  483. 


Fio.  4852. 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS.  243 


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244  MACHINE   DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


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MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


245 


A  cast-iron  block,  or  separator,  is  inserted  between  the  beams,  and  two  bolts, 
through  them  and  the  block,  add  lateral  strength.  The  bolt-holes,  placed  at 
some  distance  from  the  centre  of  the  span,  do  not  reduce  the  transverse  strength. 
To  strengthen  an  I-beam  or  box-girder  composed  of  I-beams,  rivet 
plates  on  the  top  and  bottom  flanges  (Figs.  484  and  485),  thus 
adding  to  the  section  by  the  area  of  the  plate,  less  the  rivet- 
holes.  Box-girders,  except  of  the  larger  sizes,  are  preferably 
composed  of  channel-beams  (Fig.  486). 


Fio.  483. 


FIG.  484. 


FIG.  485. 


FIG.  486. 


The  rivet  spacing  at  the  ends  of  a  box-girder  not  over  3"  at  the  middle  6". 
Channel-beams  can  be  furnished  of  depths  the  same  as  I-beams,  from  three 
to  fifteen  inches,  of  varied  grades  of  light  and  heavy. 

COMPARATIVE  STRENGTH   AND  STIFB^NESS  OF  STEEL  BOX  GIRDERS. 

FIG.  492. 


Depth  of  Girder. 

Inches 

10" 

12" 

15" 

20" 

Weight  of  [s  per  foot. 

Lbs. 

15 

24 

20 

30 

32 

51 

64 

80 

Size  of  Plates. 

Inches 

12  x* 

14  x* 

16  x  i 

18  xf 

10 

694- 

758- 

1004- 

1096- 

1836- 

2052- 

4030- 

4500- 

11 

631- 

689- 

912- 

997- 

1669- 

1866- 

3664- 

4091- 

12 

578- 

631- 

837- 

913- 

1530- 

1710- 

3359- 

3750- 

13 

534- 

583- 

772- 

843- 

1412- 

1579- 

3100- 

3462- 

14 

496- 

541- 

717- 

783- 

1311- 

1466- 

2879- 

3214- 

15 

463- 

505- 

669- 

731- 

1224- 

1368- 

2687- 

3000- 

16 

434- 

473- 

627- 

685- 

1147- 

1283- 

2519- 

2813- 

17 

408- 

446- 

591- 

645- 

1080- 

1207- 

2371- 

2647- 

CO 

18 

386- 

421- 

558- 

609- 

1020- 

1140- 

2239- 

2500- 

E 

19 

365- 

899- 

528- 

577- 

966- 

1080- 

2121- 

2368- 

rM 

o 

20 

347- 

379- 

502- 

548- 

918- 

1026- 

2015- 

2250- 

ft 

P-I 

21 

330- 

361- 

478- 

522- 

874- 

977- 

1919- 

2143- 

i 

22 

815- 

344- 

456- 

498- 

835- 

933- 

1832- 

2045- 

BO 

23 

302- 

329- 

436- 

477- 

798- 

892- 

1752- 

1957- 

§  £ 

24 

289- 

316- 

418- 

457- 

765- 

855- 

1679- 

1875- 

W  |y 

^   fq 

25 

278- 

303- 

402- 

438- 

734- 

821- 

1612- 

1800- 

26 

267- 

291- 

386- 

422- 

706- 

789- 

1550- 

1731- 

|  5 

27 

257- 

281- 

372- 

406- 

680- 

760- 

1493- 

1667- 

w 

28 

248- 

271- 

359- 

391- 

656- 

733- 

1439- 

1607- 

g 

29 

239- 

261- 

346- 

378- 

633- 

708- 

1390- 

1552- 

£ 
^ 

30 

231- 

253- 

335- 

365- 

612- 

684- 

1343- 

1500- 

H 

£2 

31 

224- 

244- 

324- 

354- 

592- 

662- 

1300- 

1452- 

R 

32 

217- 

237- 

314- 

343- 

574- 

641- 

1259- 

1406- 

33 

210- 

230- 

304- 

332- 

556- 

622- 

1221- 

1364- 

( 

34 

204- 

223- 

295- 

322- 

540- 

604- 

1185- 

1324- 

35 

198- 

216- 

287- 

313- 

525- 

586- 

1152- 

1286- 

36 

193- 

210- 

279- 

304- 

510- 

570- 

1120- 

1250- 

37 

188- 

205- 

271- 

296- 

496- 

555- 

1089- 

1216- 

38 

183- 

199- 

264- 

288- 

483- 

540- 

1061- 

1184- 

39 

178- 

194- 

257- 

281- 

471- 

526- 

1033- 

1154- 

40 

173- 

189- 

251- 

274- 

459- 

513- 

1008- 

1125- 

246 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


TABLE  GIVING  INCREASE  OR  DECREASE  OF  STRENGTH,  IN  PER  CENT, 
ABOVE  OR  BELOW  THAT  GIVEN  BY  PRECEDING  TABLE,  FOR  DIFFER- 
ENT THICKNESSES  OF  PLATES  IN  STEEL  BOX  GIRDERS. 


Thickness  ;of  Plate. 

r 

V 

i" 

i" 

i" 

l" 

12" 

10" 

15* 

-19 

0 

+  20 

+  41 

i 

12" 

42 

10" 

'24* 

-18 

0 

+  18 

+  38 

i 

14" 

I 

12" 

20* 

0 

+  19 

+  40 

f-i 

14" 

1 

A 

12" 

30* 

0 

+  18 

+  36 

*o 

16" 

0 

15" 

"32* 

-15 

0 

+  15 

+  30 

a 

16" 

o 

15" 

51* 

-13 

0 

+  13 

+  27 

g 

18" 

fi 

20" 

"64* 

-10 

0 

+  10 

+  20 

18" 

CO 

20" 

'80* 

-9 

0 

+  9 

+  20 

It  may  be  desirable,  on  account  of  position,  to  finish  a  box-girder  as  in  Fig. 
487 ;  in  this  case  the  dimensions  must  be  such  as  to  admit  of  a  helper  inside  to 
hold  the  rivets.  Fig.  488  shows  a  closed  box-beam  made  of  channel-bars  and 
plates.  The  lower  channel  is  first  riveted,  and  the  u-pper  one  afterward.  This 


FIG.  487. 


FIG.  488. 


FIG.  489. 


FIG.  490. 


FIG.  492. 


form  gives  a  dean  surface  below,  but  the  lower  channel-bar  can  be  reversed  and 
riveted  the  same  as  the  upper. 

Where  the  purpose  can  be  served  by  I-beams,  either  single,  or  coupled,  as  in 
Fig.  483,  or  in  numbers,  they  afford  the  best  and  cheapest  construction.  But, 
where  the  spans  are  large  and  loads  heavy,  it  is  often  economical  to  obtain 
greater  depth  by  means  of  plate-girders,  as  in  Figs.  489,  490,  491,  492,  or  per- 
haps from  requirements  of  position,  as  in  Fig.  493,  subject  as  above  to  the 

necessities  of  large  inside  dimen- 
sions. These  girders  are  made  up 
of  plates  of  uniform  thickness, 
and  angle-irons  riveted  together. 

Angle-irons  are  made  of  varied 
dimensions,   and    are    classed    as 


FIG.  493. 


FIG.  494. 


FIG.  495. 


equal-legs  (Fig.  494),  unequal-legs 
(Fig.  495),  and  square-root  angles 
when  the  thickness  of  the  iron  is  uniform  throughout,  and  consequently  the 
interior  angle  a  complete  right  angle  without  rounding. 

Angle  irons  are  manufactured  of  equal  legs,  of  f ",  £ ",  £",  1",  li",  H",  If, 
If",  2",  2V,  2V,  2|",  3",  3£" ,  4",  5",  6",  of  varied  thicknesses,  according  to  the 
size  and  necessities  of  construction,  from  V  on  the  smaller  sizes  to  f"  on  the 
larger  ones. 

Angles  of  unequal  legs— 7"  X  3|",  6V  X  4",  6"  X  4",  6"  X  3V,  5"  X  4", 
5"  X  3V,  5"  X  3",  4V  X  3",  4"  X  3|",  4"  X  3",  3£"  X  3",3V  X  2|",  3i"X  2", 
3"  X  2£",  3"  X  2",  2V  X  2",  2£"  X  H",  3"  X  If",  If"  X  1",  with  the  same 
variety  of  thickness  as  the  equal  legs,  up  to  1  inch  for  the  largest  size. 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


247 


DIMENSIONS  AND  WEIGHTS  OP  Z  BARS. 


Thickness 
of  metal 
in  inches. 

SIZE  IN  INCHES. 

Weight 
per  foot. 

Thickness 
of  metal 
in  inches. 

SIZE  IN  INCHES. 

Weight 
per  foot. 

Flange. 

Web. 

Flange. 

Flange. 

Web. 

Flange. 

f 

34. 

6 

84 

15-6 

if 

3| 

54 

31 

28-3 

A 

3ft 

6ft 

3l% 

18-3 

i 

8ft 

4 

8ft 

8-2 

| 

8f 

64 

3* 

21-0 

A 

8* 

4ft 

84 

10-3 

A 

84 

6 

4 

22-7 

i 

8ft 

44 

8ft 

12-4 

i 

8ft 

6ft 

8ft 

25-4 

A 

8ft 

4 

3ft 

13-8 

A 

31 

84 

31 

28-0 

i 

34 

4ft 

34 

15-8 

i 

si 

6 

84 

29-3 

A 

8ft 

44 

8ft 

17-9 

ft 

8ft 

6ft- 

8ft 

32-0 

i 

8ft 

4 

8ft 

18-9 

i 

8| 

H 

9% 

34-6 

H 

8* 

4ft 

84 

20-9 

A 

Si 

5 

3i 

11-6 

i 

8ft 

44 

8ft 

22-9 

i 

8ft 

5ft 

8ft 

13-9 

I 

s}| 

3 

m 

6-7 

A 

H 

H 

8f 

16-4 

A 

2f 

8ft 

2f 

8-4 

i 

8 

5 

3i 

17-8 

i 

W 

3 

m 

9-7 

A 

8ft 

8ft 

8ft 

20-2 

ft 

2f 

8ft 

2f 

11-4 

t 

3f 

&i 

3| 

22-6 

i 

2*4 

3 

m 

12-5 

H 

8 

5 

3i 

23-7 

A 

2f 

8ft 

21 

14-2 

t 

3& 

5ft 

3ft 

26-0 

T-irons  (Fig.  496)  may  be  used  for  top  and  bottom  flanges  in  the  manufac- 
ture of  plate-girders  by  riveting  a  web  on  one  side  of  the  T,  or  on  both  sides, 
with  a  separator  between  of  the  thickness  of  the  stem  E ;  but,  as 
the  areas  of  section  of  T-irons  to  be  had  are  small,  the  flanges 
will  be  too  slight  in  proportion  to  the  webs  at  depths  above  that 
of  rolled  beams.     Angle-irons  are  then  to  be  preferred  for  flanges. 
The  T-irons  are  well   adapted  in   many  positions  as  struts  or 
FIG.  496.         braces,  and  can  be  bought  of  varied    dimensions  and  weights, 
from  widths,  B,  of  from  2  to  5  inches,  and  equal  or  less  depths,  A,  and  thick- 
nesses from  -fa"  to  f ". 

Rivets  for  plate-girders  are  usually  from  f  "  to  £"  diameter,  and  pitched  or 
spaced  not  more  than  6"  nor  less  than  3"  between  centres.  The  number  of 
rivets  through  flange  and  stem  are  the  same,  but  alternating.  Usually  angle 
irons  and  plates  can  be  had  of  the  full  length  of  girder,  but,  where  joints  are 
necessary,  they  should  be  butt,  with  a  splicing-piece  to  make  the  strength  as 
nearly  as  possible  uniform.  Stiffeners  are  often  necessary  for  the  webs,  which 
may  be  of  band,  angle,  or  T-iron,  and  one  should  always  be  placed  at  each  end, 
where  the  shearing  stress  is  the  greatest. 

A  common  formula  for  determining  the  strength  of  a  wrought-iron  beam 
g  «' 

or  girder  is  W  —  —  — ,  in  which  W  is  the  load  in  pounds,  equally 

.L 

distributed  on  the  beam,  D  the  effective  depth  between  the  centres  of  gravity 
of  the  flanges,  and  L  the  clear  span,  both  in  the  same  unit,  feet  or  inches ;  a 
the  area  of  the  top  or  bottom  flange  in  square  inches ;  a'  the  area  of  the  stem. 
To  construct  a  diagram  from  the  formula,  in  which  the  relation  of  the  fac- 


248 


MACHINE   DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


tors  may  be  shown.     Let  S  be  10,000  for  riveted  girders  of  wrought  iron 


-g)  80,000.     On  a  sheet  of  cross-sec- 


(12,000 for  steel),  then  W  =  y  X 

tion  paper,  from  a  corner,  0,  lay  off  on  the  line  of  ordinates,  5,  10,  15,  20, 

25,  representing  the  factor  a  -f-  —  .     From  the  same  0,  on  the  line  of  abscissas, 

i»  iV>  iV>   fa  &>  TrV>  * 


>  representing  -.     Suppose  ^  =  ^,  then  W  = 


(a  -(_  ^.)  2,000.     If  a  +  ^  be  =  10,  then  W  =  20,000.     From  the  intersection 

of  ordiuate  on  line  of  ^,  and  abscissa  line  of  10,  draw  a  line  to  the  point  0. 
This  line  will  represent  the  safe  distributed  load  W,  and  its  intersections  of  the 


m 


P.         / 

17  /* 


'10 

FIG.  497. 


ordinates  and  abscissas  will  represent  the  relative  proportions  of  the  two  factors 

-Y-  and  a  -}-  —  under  this  load.     On  the  abscissa  line  15,  and  ordinate  3V,  W  = 
Jj  o 

30,000,  on  line  20,  40,000,  and  so  on,  and  lines  drawn  from  these  intersections 
to  0  will  represent  W. 

In  the  diagram  lines  below  5  and  above  30  on  line  of  ordinates  are  erased, 
as  within  these  limits  may  be  found  most  of  the  proportions  required  in 
practice. 

Application  of  the  Diagram. — "What  will  be  the  area  of  section  «  +  —  of  a 

girder,  40-foot  span,  depth  32",  distributed  load  90,000  pounds  ? 

D  in  the  formula  represents  the  distance  between  the  centres  of  gravity  of 
the  flanges,  which  will  be  somewhat  less  than  the  depth  of  beam.  Approxi- 

D       480" 
mately  assume   it  at  30",    y-  =  -^r  =  -fa,  and  the  intersection  of  the  line 


MACHINE   DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


249 


of  load,  90,000,  with  the  ordinate 


,  will  be  18,  on  the  line  of  a  -)  —  . 


A  fair 


proportion  of  a  to  a'  is  5  to  6,  therefore 


O 


-f-  —  —  18  or  a'  =  18. 

O 


18 


=  0-6"  = 


thickness  of  web,  and  a  =  f  of  18  =  15,  or  weight  per  foot  of  one  flange  = 

15  X  10 

—  s  --  =  50  pounds,  which  is  slightly  in  excess  of  the  weight  of  two  angle- 
o 

irons  6  X  4  X  f  ,  compensated  by  thickness  of  web  outside  centres  of  gravity. 

This  calculation  is  sufficiently  near  for  all  practical  purposes,  but  D  can  be 
found  more  accurately  by  plotting  the  angle-irons,  on  thick  card-  board,  cut- 
ting out,  and  then  balancing  for  the  centre  of  gravity. 

Composite  Seams.  —  Often,  in  constructions  where  the  beams  or  girders  are 
of  wood,  and  on  account  of  extent  of  spans  and  loads,  the  stress  is  beyond  the 
strength  and  stiffness  of  beams  of  this  material,  of  readily  available  dimen- 
sions, it  is  usual  to  supplement  by  some  application  of  iron.  A  simple  form,  in 
which  the  iron  is  not  exposed  to  view,  is  by  bolting  a  plate  or  flitch  of  wrought- 
iron  between  two  beams,  of  the  full  length  and  depth  of  the  beams,  and  of  such 
thickness  as  may  be  necessary.  In  bolting  them  together,  let  the  bolt-holes 
be  so  bored  that  the  weight  of  the  beam  may  primarily  be  on  the  wood  ;  the 
stress  will  then  be  better  adjusted  between  the  two  materials  when  in  service. 
It  is  usual  to  make  the  holes  zigzag,  in  two  lines  about  one  quarter  the  depth 
of  beam  from  each  edge,  the  holes  closer  together  nearer  the  ends.  The  safe- 
distributed  load  for  the  iron  may  be  estimated  from  the  formula  :  W.  = 

15000  bh*.  ..  .     .     , 

—  j  --  ,  o  breadth,  h  depth,  I  length  —  all  in  inches. 

I 

Fig.  498  represents  a  bracing  truss  of  wrought-iron  between  two  beams, 
which  should  be  let  into  the  wood.  As  it  is  held  firmly  laterally,  the  factor  of 


FIG.  498. 


safety  may  be  considered  about  one  third  of  the  crushing  resistance  of  the  ma- 
terial. The  load  on  each  inclined  bar  will  be  one  half  the  load  on  the  centre, 
multiplied  by  the  length  of  the  bar  and  divided  by  the  rise.  Instead  of  wrought- 
iron,  cast-iron  or  wood  is  used. 


Fio.  499. 

In  Fig.  499  the  beams  are  strengthened  by  a  tension-rod,  of  which  the 
strength  may  be  determined  by  that  of  the  material ;  allowing  the  usual  factor 
of  safety,  the  load  is  obtained  as  in  the  example  above.  The  deeper  the  block 
beneath  the  centre  of  the  beam,  the  less  the  stress  on  the  rods  for  the  same 
load.  In  construction,  the  beam  should  not  be  cambered  by  the  screwing  up 


250 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


of  the  rod ;  but,  if  the  beams  are  crowning,  the  convex  side  should  be  placed 
upward,  the  nut  turned  by  hand  just  to  a  bearing,  and  the  tension  put  on  by 
the  settlement  of  the  beams  under  the  load. 


FIG.  500. 


Fig.  500  represents  the  trussing  of  a  beam  by  two  struts  and  a  tension-rod. 
The  stress  on  the  tension-rod  is  the  load  on  c,  multiplied  by  the  length  a  d, 
divided  by  c  d. 

The  theory  of  trusses  will  be  treated  and  illustrated  under  "  Bridges  "  and 
"  Hoofs,"  and  the  proportions  of  rivets  and  forms  of  plate-iron  joints  under 
"  Boiler  Construction." 

Bolts  and  nuts  are  of  such  universal  application  that  their  manufacture 
forms  the  centre  of  large  industries.  Much  thought  has  been  given  to  their 


FIG.  501. 


proportions  and  the  forms  of  thread,  but  without  producing  complete  uni- 
formity in  the  practice  of  different  countries  and  makers.  The  old  form  of 
thread  was  the  triangular  pitch  (Fig.  502),  still  used  by  some,  especially  when 
the  threads  are  cut  in  a  lathe.  In  this  country  the  standard  U.  S.  thread  is 


FIG.  503. 


that  recommended  by  the  Franklin  Institute  in  1864  (Fig.  503).  The  angle  is 
60°,  with  straight  sides  and  flat  surface  at  top  and  bottom,  equal  to  one  eighth 
the  pitch,  or  distance  from  centre  to  centre  of  threads. 

In  England,  the  standard  thread  for  bolts  and  nuts  is  the  Whitworth  (Fig. 
504) ;  the  angle  is  55°,  with  top  and  bottom  rounded. 


2.oo 


The  square  and  rounded  threads  (Figs.  505  and  506)  are  only  made  to  order 
and  used  in  presses  and  the  like  as  parts  of  machines. 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


251 


Figs.  507,  508,  and  509  represent  the  proportions  of  the  various  parts  of 
English  nuts  to  the  diameters  of  bolts,  as  1,  or  unity.  Fig.  508  is  a  flange-nut, 
in  which  a  washer-like  flange  is  forged  with  the  nut. 


FIG.  506. 


Fig.  510  is  a  cap-nut,  in  which  the  thread  does  not  go  through  the  nut,  to 
prevent  leaking  along  the  thread,  and  a  soft  copper  washer  is  introduced  to  pre- 
vent leakage  below  the  nut. 


FIG.  507. 


FIG.  508. 


FIG.  509. 


Figs.  511  and  512  are  circular  nuts,  in  one  of  which  holes  are  drilled  to 
insert  a  rod  for  turning,  and  in  the  other  grooves  for  a  spanner. 

Lock-nuts  (Fig.  513)  are  intended  to  prevent  the  gradual  unscrewing  of 


FIG.  510. 


FIG.  511. 


FIG.  512. 


FIG.  513. 


nuts  subjected  to  vibration,  which  is  to  a  great  extent  prevented  by  the  use  of 
double  nuts,  the  lock-nut  being  one  half  the  thickness  of  the  common  nut. 
The  usual  practice  is  as  shown,  the  lock-nut  being  outside ;  the  better  way  is 
inside. 

The  following  figures  are  from  trade  circulars ;  the  limits  of  sizes  given  are 
such  as  can  usually  be  found  in  stock. 

Figs.  514,  515,  and  516  are  machine-bolts,  from  %"  to  f"  diameter,  and  1" 
to  4"  long,  but  not  flanged,  as  in  Fig.  514,  unless  expressly  ordered  ;  the  dot- 
ted line  shows  the  radius  of  curvature  of  a  finished  head.  The  diagonal  lines 
beneath  the  head  (Figs.  515  and  516)  represent  square  bolts  tapering  into  round 
bolts,  as  shown  by  the  curved  lines. 


252 


MACHINE   DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


Figs.  517  and  518  are  tap-bolts  and  set  screws,  from  £"  to  f"  diameter,  and 
from  1"  to  3"  long. 


FIG.  514. 


Fig.  519  is  a  carriage-bolt,  from  ^"  to  f"  diameter,  and  from  1"  to  16"  long. 
Fig.  520  is  a  plough-bolt,  from  f"  to  £"  diameter,  and  from  1"  to  4"  long. 


FIG.  515. 


FIG.  516. 


Fig.  521  is  a  stove-bolt,  from  £"  diameter  and  from  f "  to  3"  long. 

Figs.  522  and  523  are  machine-screws  without  nuts  ;  the  holes  in  the  metals 


FIG.  518. 


are  tapped  to  receive  them  ;  Fig.  522  is  button-headed  ;  Fig.  523  a  counter- 
sunk head — both  slotted  to  admit  of  driving  by  a  screw-driver.  They  are  made 
of  various-sized  wire  and  lengths,  and  sold  by  the  gross  like  the  common  wood- 


FIG.  519. 


screw  (Fig.  524).     The  wood-screw  is  for  connecting  pieces  of  wood  together, 
or  metal  to  wood.     They  are  of  very  great  variety,  usually  with  a  gimlet-point, 


FIG.  521. 


FIG.  522. 


FIG.  523. 


FIG.  524. 


FIG.  525. 


FIG.  526. 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


253 


so  that  they  can  be  screwed  into  the  wood,  without  any  holes  being  previously 
made.  When  made  of  rods,  with  a  square  or  hexagonal  head  (Figs.  525  and 
526)  to  admit  of  the  use  of  a  wrench,  they  are  called  lag-screws.  It  will  be 
seen  that  wood-screws  differ  in  their  thread  from  bolts  and  machine-screws. 
The  thread  is  a  very  sharp  V,  flatter  on  the  upper  surface,  and  the  flat  space 


FIG.  528. 


FIG.  529. 


between  the  threads  wide  as  the  thread,  making  it  of  easier  introduction  into 
the  wood,  and  retaining  as  much  strength  in  the  iron  as  in  the  wood. 

Fig.  527  is  a  stud-bolt,  which  is  screwed  firmly  into  one  of  the  pieces  of 
connected  metal ;  the  other  is  bored  so  as  to  slip  over  the  bolt,  and  the  nut 
then  brought  down  upon  it.  It  is  in  common  use  for  holding  on  the  bonnets 
of  steam-chests  and  water-chambers,  the  bolt  remaining  permanent. 

Fig.  528  is  a  7*oo&-bolt ;  it  relieves  the  necessity  of  a  bolt  through  the  bot- 
tom-piece, and  may  be  turned  like  a  button,  to  loose  or  hold  the  bottom-plate. 

Fig.  529  is  another  kind  of  button-bolt ;  the  lower  end  can  revolve  on  a  stud 
or  pin  if  the  nut  be  raised  enough  to  clear  the  cap  or  upper  plate.  By  this 
arrangement  there  is  no  necessity  of  taking  off  the  nut  entirely ;  the  bolt  lies 
in  a  slot  in  the  cap,  and  the  nut  bears  on  three  sides. 


FIG.  530. 


FIG.  531. 


FIG.  532. 


Figs.  530,  531,  and  532  show  expedients  to  prevent  the  bolt  from  turning 
when  the  nut  is  being  screwed  on  or  off. 

Fig.  533  is  an  anchor-bolt,  flattened  and  jagged,  introduced  into  a  hole  in 
masonry,  and  firmly  leaded  or  sulphured  in;  but  later  experiments  with  deep 
holes  have  established  that  it  was  not  necessary  to  flatten  and  jag  the  bolts,  and 
with  holes  If  and  If  diameter  and  3'  6"  deep,  and  bolts  1*  diameter  when  leaded 
or  sulphured  in,  did  not  develop  as  uniform  adhesion  as  when  the  spaces  were 
filled  in  with  Portland  cement  and  allowed  a  set  of  two  weeks,  when  the  bolts 
broke  under  the  test.  The  resistance  was  400  to  500  pounds  per  square  inch  of 
surface  of  bolt  exposed. 

It  is  very  common  to  split  the  bolt  at  the  bottom  (Fig.  534)  and  insert  a 


254 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


wedge  in  the  cleft  and  drive  it  against  the  bottom  of  the  bolts,  forcing  open  the 
cleft  and  holding  the  bolt  in  the  hole. 

Fig.  535  is  a  bolt  keyed  into  the  stone,  corresponding  to  a  form  of  lewis  for 
raising  stones  in  which  the  key  (Fig.  536)  is  wedged  in,  and  when  the  stone  is 


FIG.  533. 


FIG.  534. 


FIG.  536. 


set  the  wedge  is  struck  and  the  lewis  withdrawn.     Fig.  537  is  a  double  or  chain 
lewis. 

For  small  holes  in  brick  or  stone  masonry  drill  a  hole  and  insert  a  short 
piece  of  lead  pipe  and  force  in  a  wood-screw  of  a  little  larger  diameter  than  the 
bore  of  the  pipe,  or  drive  a  wooden  pin  into  the  hole,  and  screw  into  the'  wood. 

Take  a  clout-nail  or  picture-nail,  turn  up 
the  point,  cast  a  lead  petticoat  on  it,  and 
drive  it  into  a  loosely  fitting  hole ;  by  driv- 
ing, the  point  and  the  wedge  form  of  the 
nail  expands  the  lead  and  gives  a  firm  hold. 
Similar  forms  of  points  to  anchors  of  copper 
wire  are  convenient  in  holding  stones  to- 
gether or  face  stones  of  a  building  to  the 
backing. 

JZxpansion-kolts  (Fig.  538)  from  %"  to  1" 
diameter  are  on  sale  and  very  convenient  in 
connecting  architectural  iron-work  to  ma- 
sonry, and  have  this  convenience :  that  they 
can  be  removed  when  necessary;  all  that  is  required  is  a  hole  of  uniform  diam- 
eter and  of  suitable  size  and  depth  to  insert  the  bolt  with  nut  and  jaw  ;  then 
by  turning  the  head,  the  iron  or  composition  nut  is  drawn  outward, 
opening  the  wedge-shape  jaws  and  causing  them  to  bind  strongly 
against  the  side.  There  is  a  small  split-steel  band  around  the  jaws  to 
keep  them  together  before  insertion  in  the  hole  and  to  free  the  jaws 
when  they  are  to  be  removed.  The  bolts  may  have  a  head  at  the 
top,  or  a  screw  with  a  nut,  or  the  lower  nut  may  be  formed  as  a  head. 
FIG.  538.  -pig.  539  is  a  bolt  with  a  fang-nut  or  corner  turned  down  and 
driven  into  the  wood  to  prevent  turning ;  the  screwing  to  be  done  at  the 
head. 

It  is  often  convenient  to  use  bolts  with  two  nuts,  as  in  Fig.  540,  or  collar- 
bolts,  which  are  readily  made  to  order,  and  of  any  dimensions. 


FIG.  537. 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


255 


Fig.  541  is  a  hanger-bolt, ;  the  Jag-screw  part  is  screwed  into  the  wooden 
beam,  the  hanger  then  put  over  the  bolt,  and  the  nut  put  on. 


FIG.  541 


FIG.  539. 


FIG.  540. 


FIG.  542. 


Figs.  542  and  543  represent  forms  of  turn-buckles,  and  the  swivel  and  pipe, 
sometimes  designated  as  swivels.  Turn-buckles  are  very  useful  in  straining 
tierods,  where  neither  end  of  the  bolt  can  be  got  at.  By  turning  the  buckle, 
the  rod  can  readily  be  made  longer  or  shorter.  In  the  pipe-swivel,  right  and 
left  threads  are  cut  on  the  bolts,  so  that  each  turn  of  the  pipe  shortens  or 
lengthens  the  tie  by  double  the  pitch  of  the  screw.  The  turn-buckle  is  also 
made  in  the  same  way,  with  two  screws  instead  of  a  head  at  one  end. 


FIG.  543. 


Screws,  unless  otherwise  ordered,  are  made  right-handed  ;  that  is,  turning 
the  nut  to  screw  up,  the  hand  moves  from  left  to  right,  the  apparent  motion  of 
the  sun. 

On  the  Strength  of  Bolts. — The  strength  of  a  bolt  depends  on  its  smallest 
section — that  is,  between  the  bottom  of  the  threads.  It  is  very  common,  there- 


FIG.  544. 


fore,  to  upset  the  screw-end,  so  that  the  screw  may  be  cut  entirely  from  this 
extra  boss,  or  re-enforce.  Bolt-ends  (Fig.  544)  are  sold  either  with  or  with- 
out re-enforce,  to  be  welded  to  bolts.  It  will  be  observed  that  the  ends  of  the 
pipe-swivel  bolts  (Fig.  543)  are  thus  upset. 

In  the  following  table  the  sizes  and  dimensions  of  bolts  and  nuts  are  from 
the  United  States  standard,  and  the  strength,  or  safe-load  of  the  bolts,  is  com- 
puted from  the  report  of  the  committee  on  the  test  of  wrought-iron  and  chain- 
cables  to  the  United  States  Government  in  1879.  Nuts  and  heads  as  furnished 
are  either  hexagonal  or  square.  Columns  4,  5,  and  6  apply  equally  to  either. 

There  is  often  an  uncertainty  in  the  determination  of  the  load.  The  ef- 
fective load  due  to  the  forces  acting  on  the  machine  may  be  estimated  with 
tolerable  accuracy.  But  that  due  to  the  forces  used  in  tightening  the  nut  is 
uncertain.  If  the  bolt  is  screwed  up  so  as  to  develop  a  reaction  between  the 
counected  pieces,  the  additional  load  may  be  greater  than  the  effective  one. 


256 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


Washers  (Fig.  545) — in  common  use  to  provide  seatings  for  nuts  which 
would  otherwise  rest  on  rough  metallic  surfaces,  and  also  to  adapt  bolts  to 


Diameter  of 
screw  in 
inches. 

Diameter  at 
root  of 
thread. 

Thread  per 
inch  of 
length. 

Short  diam- 
eter of  nut 
and  head. 

Thickness  of 
nut. 

Thickness  of 
head. 

Safe-load  of 
upset  bolts. 

Safe-load  of 
plain  bolts. 

1 

TV 

1 

& 

TV 

1  3 

-nrn- 
o  & 

TV 

if 

1 

•185 

20 

1 

1 

19 

A 

•240 

18 

tf 

5 

f 

•294 

16 

frr 

r 

II 

1,700 

TV 

•344 

14 

25 
~5S 

TV 

If 

1,900 

1 

•400 

13 

£ 

1 

TV 

2,200 

TV 

•494 

12 

fi 

TV 

u 

2,500 

f 

•507 

11 

1A 

f 

H 

2,800 

-u 

« 

H 

1? 

3,200 

1 

•620 

10 

H 

1 

f 

6,000 

3,600 

H 

Hi 

if 

if 

7,000 

4,300 

f 

•731 

9 

ITV 

1 

ft 

8,000 

5,100 

i 

•837 

.      8 

If 

i 

if 

10,000 

7,000 

H 

•940 

7 

if! 

il 

li 

12,000 

9,000 

it 

1-065 

7 

2 

11 

1 

15,000 

11,000 

if 

1-160 

6 

2  TV 

if 

HV 

18,000 

13,500 

H 

1-284 

6 

2f 

11 

ITV 

21,000 

16,000 

if 

1-389 

51 

2A 

if 

^A 

24,000 

19,000 

it 

1-490 

5 

21 

if 

if 

28,000 

22,300 

1* 

1-615 

5 

2yf 

H 

115 

32,000 

25,500 

2 

1-712 

41 

81 

2 

ITV 

36,000 

29,300 

2fr 

Mr 

21 

1§4 

40,000 

33,000 

21 

1-962 

41 

31 

21 

If" 

45,000 

37,000 

2f 

Hi 

2f 

1|| 

50,000 

41,500 

21 

2-175 

4 

3i 

21 

55,000 

46,000 

2f 

4rV 

2f 

2^V 

2f 

2-425 

4 

41 

2f 

21 

2* 

47-5- 

2| 

3 

2-629 

31 

4f 

3 

2TV 

31 

2-879 

31 

5 

31 

21 

31 

3-100 

31 

5f 

31 

2H 

3 

3-317 

3 

5| 

3| 

4 

3-567 

3 

61 

4 

3TV 

41 

3-798 

2& 

61 

41 

31 

41 

4-028 

24 

6& 

41 

3TV 

41 

4-255 

2f 

71 

4f 

3f 

5 

4-480 

21 

7f 

5 

311 

51 

4-730 

21 

8 

51 

4 

51 

5-053 

2| 

8f 

51 

4T\ 

5| 

5-203 

2f 

8| 

5f 

H 

6 

5-423 

21 

91 

6 

shorter  spaces  than  their  lengths — are  sold  for  bolts  up  to  2"  diameter.  Cir- 
cular in  form,  their  diameter  is  slightly  in  excess  of  that  of  the  largest  diam- 
eter of  the  nut,  and  the  hole  that  of  the  bolt,  and  thickness  from  -fa"  to  £*, 
according  to  the  diameter  of  the  bolt. 

Lock-nut  Washers. — Nuts  subject  to  jars  are  apt  to  unscrew  of  themselves; 
to  prevent  which  many  expedients  are  adopted,  as  cupping  the  washer  or  turn- 
ing up  one  corner  of  a  square  washer  against  a  face  of  the  nut.  The  simplest  is 
Shaw's  Lock-nut,  in  which  one  side  of  a  circular  washer  is  cut  through,  one 
edge  pressed  up  and  the  other  down,  to  form  a  spring  by  which  a  pressure  is 
brought  on  the  thread  when  the  nut  is  screwed  home.  In  the  Billing's  lock- 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


25T 


nut  by  cupping  a  circular  washer  a  similar  effect  is  obtained  through  the  elas- 
ticity of  the  cup. 

The  square  washer  is  used  under  both  head  and  nut  on  surfaces  of  wood, 


FIG.  545. 


FIG.  546. 


and  of  dimensions  suited  to  the  stress.  That  they  may  neither  sink  into  the 
wood  nor  bend  or  break,  cast-iron  is  frequently  used,  and  often,  as  shown  in 
Fig.  546,  for  roof-frames. 

Shafts  and  Axles. — Short  shafts,  revolving  in  bearings  or  boxes,  or  fastened 
with  pulleys,  drum,  or  wheels  revolving  on  them,  are  called  axles ;  but  long 
or  heavy  revolving  bars  are  usually  termed  shafts.  They  may  be  independent ; 
that  is,  a  single  shaft,  revolving  in  its  bearings,  or  coupled,  forming  what  is 
termed  a  line  of  shafting.  The  small  shafts,  as  in  clock-work  and  spinning- 
machinery,  are  termed  pins  and  spindles. 

Shafts  and  axles  are  made  of  wood  and  metal,  and  of  varied  sections  and 
form. 

Wooden  shafts  are  polygonal,  circular,  or  square  section  (Fig.  547). 


Wrought  metal,  iron,  or  steel  shafts,  are  almost  invariably  circular  in  sec- 
tion, but  sometimes  square. 

Cast-iron  is  used  in  great  variety  of  section  and  form  for  shafts  (Fig.  548)  ; 
without  uniformity  longitudinally,  but  adapted  to  their  position  and  load. 


FIG.  548. 

Formerly,  either  wood  or  cast-iron  was  invariably  used  for  water-wheel 
shafts  ;  but  a  change  of  motors,  from  the  breast,  over-shot  and  under-shot 
wheels  to  reactors  or  turbines,  has  involved  an  entire  change  of  construction, 
and  now  only  wrought-iron  is  used.  Wooden  shafts  are  often  used  in  ma- 
chines subject  to  wet  and  shocks,  or  from  the  greater  convenience  in  obtaining 
the  material,  and  from  this  last  necessity  the  journals  and  boxes  are  sometimes 
of  wood;  but  for  wooden  shafts  it  is  the  usual  practice  to  insert  cast-iron  jour- 
nals with  boxes  or  bearings  of  the  same  material. 
18 


258 


is. 


FIG.  549. 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 

Fig.  549  is  a  side  view  of  a  wooden  shaft  with 
one  end  in  section,  and  Fig.  550  an  end  view  of 
the  shaft.  On  the  journal  B  is  cast  four  wings, 
c  c,  and  a  small  spindle,  I.  The  ends  of  the  shaft 
are  bored  for  the  spindle  and  grooved  to  receive 
the  wings ;  the  casting  is  then  drawn  into  place, 
hooped  with  hot  ferules,  a  a,  and  after  this  hard 
wood  wedges  are  driven  on  each  side  of  the  wings 
and  iron  spikes  are  sometimes  driven  into  the 
end  of  the  wood ;  most  millwrights  omit  the  spin- 
dle a. 

Figs.  551,  552,  and  553  represent  different 
views  of  a  cast-iron  shaft  of  a  water-wheel.  Fig. 
551  is  an  elevation  of  the  shaft,  with  one  half  in 
section  to  show  the  form  of  the  core ;  Fig.  552,  an 
end  elevation ;  Fig.  553,  a  section  on  the  line  c  c 
across  the  centre.  The  body  is  cylindrical  and 
hollow,  and  cast  with  four  feathers,  c  c,  disposed 
at  right  angles  to  each  other,  and  near  the  extrem- 
ities of  these  feathers  four  projections,  for  the  at- 
tachment of  the  bosses  of  the  water-wheel  or  pul- 
ley. These  projections  are  made  with  facets,  so 
as  to  form  the  corners  of  a  circumscribing  square 
(Fig.  552),  and  are  planed  to  receive  the  keys 
by  which  they  are  fixed  to  the  naves  which  are 
grooved  to  receive  them.  The  shaft  is  cast  in 
one  entire  piece,  the  journals  turned,  and  the 
feathers  of  an  external  parabolic  outline  to  stiffen 
the  shaft. 

Shafts  like  the  examples  given  are  for  pur- 
poses where  their  loads  are  nearly  constant  and 
for  moderate  speeds,  and  cast-iron  gives  satisfac- 
tory results. 

The  usual  length  of  such  journals  is  from  one 
to  one  half  times  the  diameters,  and  the  safe  load 
500  pounds  to  the  square  inch,  taking  the  area 
as  d*,  the  square  of  the  diameter,  the  diameter 
and  length  of  journal  being  considered  equal. 

To  determine  the  size  of  a  shaft,  considered  as 
a  beam  merely,  but  with  a  shifting  load — as  by 
the  revolution  of  the  shaft — each  longitudinal  line 
of  surface  has  to  undergo  successively  tension  and 
compression.  The  safe  load  of  wrought-iron  is 
estimated  at  6,000  pounds  per  square  inch,  and 
the  formula  on  which  the  graphic  diagram  (Fig. 
554)  is  constructed  is  d  —  '06  \J~wl,  d  being  di- 
ameter, I  =  length  between  bearings,  both  in 
Flo  550  inches,  w  the  load  in  pounds ;  the  load  is  not  only 


MACHINE  DESIGN   AND  MECHANICAL  CONSTRUCTIONS. 


259 


FIG.  552. 


the  weight  of  shaft  and  pulleys  or  gears,  but  also  the 
stress  in  transmitting  the  power. 

Use  of  Diagram. — Suppose  w  =  50,000  pounds, 
and  I  —  6  feet  =  72",  then  w"l  =  3,600,000,  the  or- 
dinate  of  3*6  cuts  the  curve 
on  the  abscissa  9*2,  which 
is  the  required  diameter  of 
the  shaft  in  inches. 

Fly  -  wheel  and  crank 
shafts  are  of  forged  iron  or 
steel,  often  forged  in  steps 
(Fig.  555)  with  the  largest 
boss  beneath  the  wheel  hub, 
and  sufficiently  raised  above 
the  next  to  admit  of  the 
planing  of  the  key  seats. 

The  transverse  stress  upon  the  shaft,  due  to  the 
transmission  of  power,  is  equal  to  the  H.  P.  divided 
by  the  velocity  of  surface, 
whether  of  belt  or  of  gear, 
by  which  it  is  transmitted, 
and  the  same  acts  by  torsion 
through  the  leverage  of  the 
radius  of  the  pulley  or  gear. 
This  stress  is  seldom  calcu- 
lated, as  it  is  sufficiently  met 
by  the  tables  and  diagrams 
for  the  determination  of 
the  diameters  of  shafts. 

Keys  are  pieces  of  met- 
al, usually  steel,  employed  to  secure  the  hubs  of  pul- 
leys, gears,  and  couplings  to  shafts.  They  may  be 
sunk  keys  (Fig.  556),  flat  keys  (Fig.  557),  and 
hollow  keys  (Fig.  558).  The  shaded  circle  repre- 
sents the  shaft.  The  breadth  of  the  key  (Fig.  559) 
is  uniform,  but  the  thickness  is  tapered  about 
one  eighth  of  an  inch  per  foot.  The  shoulder  h 
is  for  the  purpose  of  drawing  out  the  key.  Sunk 
keys  are  not  necessarily  taper.  Some  prefer  them 
of  uniform  section,  and  to  force  the  hub  on  over 
the  key. 

It  is  good  practise  in  fitting  keys  that  they  shall 
always  bind  tight  sideways,  but  not  necessarily 
touch  either  at  the  bottom  of  the  key-seat  or  the 
top  of  the  slot  cut  in  the  hub.  Such  keys  depend 
upon  a  forcing  fit  of  the  wheel  upon  the  shaft  so 
tight  as  to  require  screw-pressure  to  put  the  wheel 
in  place  upon  the  shaft. 


FIG.  553. 


FIG.  551. 


260 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


PROPORTIONS  OF  SUNK  KEYS. 


DIAMETER  OF  SHAFT, 
IN  INCHES. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

ll 

12 

Breadth  of  key  

| 

| 

£ 

u 

1* 

1| 

U 

2-t 

*ft 

OB 

'   2Jr 

31 

Thickness  of  key  
Depth  sunk  in  shaft.  . 
Depth  sunk  in  wheel  . 

•25 
•10 

•15 

•34 
•125 
•215 

•43 
•15 

•28 

•52 
•175 
•345 

•61 
•20 

•41 

•71 
•225 
•485 

•80 
•25 
•55 

•89 
•275 
•615 

•98 
•30 
•68 

1-07 
•325 
•745 

1-16 
•35 

•81 

1-25 
•375 

•875 

14" 


12 


11 


s  9 


456789 
Product  of  Load  and  Span  in  Millions. 

FIG.  554. 


10 


11 


12,000,000 


Car-Axles. — Fig.  560  is  the  form  and  dimensions  of  axle  adopted  as  stand- 
ard by  the  American  Master  Car-Builders'  Association  for  wrought-iron  and 

steel. 


FIG.  555. 


Shafting. — Thus  far,  independent  shafts  or  axles  have  been  treated  of,  and 
the  dimensions  have  been  established  mostly  by  the  load  acting  transversely; 


Flu.  550. 


FIG.  557. 


FIG.  558. 


FIG.  559. 


but,  in  transferring  power  to  machines,  lines  of  shafting  are  necessary,  almost 
invariably  of  wrought-iron  or  steel  bars,  which  are  subject  not  only  to  trans- 


MACHINE   DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


261 


verse  but  also  torsional  stress.  When  there  are  no  pulleys  or  gears  on  the 
shafts  between  the  bearings,  and  the  couplings  are  close  to  the  bearings,  there 
is  still  an  amount  of  deflection  due  to  the  weight  of  the  shaft.  James  B. 
Francis,  C.  E.,  puts  the  maximum  distances  between  bearings  for  shafts  of 
wrought-iron  or  steel,  under  these  conditions,  as  follows : 


Diameter 
of  shaft. 

Distance  between 
bearings. 

Diameter     Distance  between 
of  shaft.            bearings. 

Diameter 
of  shaft. 

Distance  between 
bearings. 

1" 

12ft. 

5" 

21  ft. 

9" 

26  ft. 

2 

15 

6 

22 

10 

27 

3 

18 

7 

24 

11 

28 

4 

20 

8 

25 

12 

28 

The  diagram  (Fig.  561)  is  one  established  by  J.  T.  Hen- 
thorn,  M.  E.,  to  determine  the  size  of  wrought-iron  shaft- 
ing, to  transmit  a  fixed  amount  of  horse-power. 

Use  of  Table. — To  find  the  size  of  a  shaft  making  150 
revolutions,  and  transmitting  350  horse-power. 

The  intersection  of  the  ordinate  of  350  with  the  abscissa 
of  150  is  between  the  diagonals  5  and  5^,  and  the  diameter 
of  the  shaft  may  be  taken  safely  at  5£". 

Mr.  Francis  has  constructed  a  table  from  his  own  experi- 
ments, of  which  the  following  is  a  synopsis : 

"  The  following  table  gives  the  power  which  can  be 
safely  carried  by  shafts  making  100  revolutions  per  minute. 
The  power  which  can  be  carried  by  the  same  shafts  at 
any  other  velocity  may  be  found  by  the  following  simple 
rule  : 

"  Multiply  the  power  given  in  the  table  by  the  number 
of  revolutions  made  by  the  shaft  per  minute;  divide  the 
product  by  100 ;  the  quotient  will  be  the  power  which  can 
be  safely  carried." 

The  diagram  and  table  given  are  applicable  to  shafts 
which  are  called  second  movers,  subject  to  no  sudden 
shock.  For  first  movers,  Mr.  Francis  takes  but  one  half 
the  horse-power  given  in  the  table  for  any  diameter  of 
shafts.  Of  late,  cold-rolled  shafts  can  be  procured  in  the 
market,  which  are  much  stiffer  than  turned  shafts,  but  not 
equal  to  that  given  for  steel  in  the  table. 

It  is  usual  to  make  the  shafts  of  second  and  third  movers 
throughout  manufactories  and  shops  of  uniform  diameter, 
without  reduction  at  the  journals,  the  end-slip  being  pre- 
vented by  collars  keyed  or  fastened  by  set-screws.  The 
usual  length  between  bearings  is  from  7  to  10  feet;  but 
that  they  may  run  smooth,  and  not  spring  intermediately, 
it  is  desirable  that  they  should  never  be  less  than  2  inches 
diameter,  and  that  the  pulleys  or  gears  through  which  the 
power  is  transmitted  to  the  next  mover  or  to  the  machine 
should  be  as  near  as  possible  to  the  bearing. 


FIG. 


262 


MACHINE   DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


Horse-power  which  can  be  safely  transmitted  by  shafts  making  100  revolutions  per  minute,  in  which  the 
transverse  strain,  if  any,  need  not  be  considered  ;  if  of 


Diameter 
in  inches. 

Wrought- 
iron. 

Steel. 

Diameter 
in  inches. 

Wrought- 
iron. 

Steel. 

Diameter 
in  inches. 

Wr  ought- 
iron. 

Steel. 

1- 

2-0 

32 

4-5 

182- 

291- 

7-5 

843- 

1350- 

1-5 

6-7 

10-7 

5- 

250- 

400- 

8- 

1024- 

1638- 

2- 

16-0 

25-6 

5-5 

332- 

532- 

8-5 

1228- 

1965- 

2-5 

31-2 

50- 

6- 

432- 

691- 

9- 

1458- 

2332- 

3- 

54-0 

86-4 

6-5 

549- 

878- 

9-5 

1714- 

2743- 

3-5 

85-7 

137- 

7- 

686- 

1097- 

10- 

2000- 

3200- 

4- 

128- 

204- 

Fig.  562  represents  a  line  of  shafting.  A  is  an  upright  shaft ;  a  a,  bevel- 
gears  ;  b  1),  bearings  for  the  shafts ;  c,  coupling  or  connection  of  the  several 
pieces  of  shafting.  These  shafts  are  of  wrought-iron  or  steel,  of  uniform  sec- 
tion. As  the  power  is  distributed  from  this  line  of  shafting,  the  torsional 
strain  diminishes  with  the  distance  from  the  bevel-gears  or  first  movers,  and 
the  diameter  of  each  piece  of  shafting  may  be  reduced  consecutively,  if  neces- 
sary ;  but  uniformity  will  generally  be  found  to  be  of  more  importance  than  a 
small  saving  of  material.  The  drawing  given  is  of  a  scale  large  enough  to 
order  shafting  by,  but  the  dimensions  should  be  written  in. 

In  laying  out  lines  of  shafting,  the  position  of  the  bearings  is  usually  fixed, 
and  the  lengths  of  shafts  must  be  determined  thereby,  with  as  few  couplings  as 
possible.  When  there  is  no  necking  or  reduction  of  the  shafts,  which  is  usually 
the  case,  the  orders  given  for  shafting  will  be  so  many  lengths  and  of  such 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


263 


diameters,  and  so  many  couplings  and  hangers.  When  there  is  to  be  a  neck- 
ing, the  sketch  for  the  order  may  be  very  simple,  showing  length  and  diameter 
of  shaft,  and  position,  length,  and  diameter  of  bearing. 

The  couplings  and  pulleys  are  to  be  placed  as  near  the  bearings  as  possible. 
It  frequently  happens,  therefore,  that  the  coupling  and  pulley  are  needed  at 


FIG.  562. 


the  same  point ;  to  remedy  this,  as  the  position  of  the  pulley  depends  on  the 
machine  which  it  is  required  to  drive,  it  frequently  can  not  be  moved  without 
considerable  inconvenience  or  loss  of  room ;  the  shaft  will  have,  therefore,  to 
be  lengthened  or  shortened,  to  change  position  of  coupling ;  or,  if  the  coup- 
lings are  plate  couplings,  they  may  be  made  with  faces  for  belts. 


FIG.  564. 


When  a  horizontal  shaft  is  supported  from  beneath,  its  bearing  is  usually 
called  a  pillow-  or  plumber-block,  or  standard ;  if  suspended,  the  supports  are 
called  hangers. 

Figs.  563  and  564  are  the  elevation  and  plan  of  a  pillow-block.  It  consists 
of  a  base  plate,  A,  the  body  of  the  block  B,  and  the  box  C.  The  plate  is  bolted 


264 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


FIG.  566. 


securely  to  its  base,  the  surface  on  which  the  block  B  rests  being  horizontal. 
A  and  B  are  connected  by  bolts  passing  through  oblong  holes  to  adjust  the 
position  in  either  direction  laterally.  The  box  or  bush  C  is  of  composition,  in 
two  parts  or  halves,  extending  through  the  block,  and  forming  a  collar  by 
which  it  is  retained  in  its  place.  The  cap  of  the  block  is  retained  by  the  screws 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


265 


FIG.  568. 


ooo ;  in  the  figure  there  are  two  screws  on  one  side  and  one  on  the  other ; 
often  four  are  used,  two  on  each  side,  but  most  frequently  but  one  on  each 
side. 

The  standard  is  for  the  support  of  horizontal  shafts  at  a  considerable  dis- 
tance above  the  foundation-plate.  Fig.  565  is  a  front  elevation ;  Fig.  566,  a 
plan  ;  and  Fig.  567,  an  end  elevation  of  a  standard.  Like  the  pillow-block,  the 
plate  A  is  fastened  to  the  foundation  itself,  and  the  upper  surface  is  placed  per- 
fectly level  in  both  directions.  On  these  bearing  surfaces,  a  a  a,  the  body  of  the 
standard  rests,  and  can  be  adjusted  in  position  horizontally,  and  then  clamped 
by  screws  to  the  foundation-plate,  or  keyed  at  the  ends. 

Elevations  and  plan  are  usually  drawn  in  such  positions  to  each  other  that 
lines  of  construction  can  be  continued  from  one  to  the  other,  which  not  only 
simplifies  the  drawings,  but  makes  them  more  readily  intelligible.  Letters  and 
dotted  lines  in  these  figures  illustrate  this  sufficiently. 

The  sides  of  the  elevations  are  represented  as  broken ;  this  is  often  done 
in  drawing,  when  the  sides  are  uniform,  and  economy  of  space  on  the  paper  is 
required. 

Hangers. — Figs.  568,  569,  and  570  are  the  plan  side  and  front  elevation  of 
a  side  hanger  especially  adapted  to  a  position  in  which  the  strain  is  in  one  di- 
rection and  against  the  upright 
part. 

Figs.  571,  572,  and  573  are  side 
elevation,  plan,  and  section  on 
line  A  B  of  a  centre  hanger  of  an 
old  pattern,  but  simple,  adapted  to 
any  strain,  and  if  adjusted  to  a 
position  where  the  shaft  is  not 
likely  to  be  moved,  the  form  is 
strong  and  economical. 

Fig.  574  is  of  a  later  pattern, 
in  which  the  shaft  can  be  readily 
adjusted  or  removed. 

Hangers  are  bolted  to  the  floor- 
timbers,  or  to  strips  placed  to 
sustain  them,  the  centres  of  the 
boxes  being  placed  accurately  in 
line,  both  horizontally  and  later- 
ally. 

Figs.  575-578  represent  differ- 
ent views  of  what  may  be  called  a 
yoke-hanger.  A  is  the  plate  which 
is  fastened  to  the  beam,  E  is  the 
yoke,  and  B  the  stem  of  the  yoke,  cut  with  a  thread  so  as  to  admit  of  a  vertical 
adjustment ;  the  box  D  of  the  shaft  C  is  supported  by  two  pointed  set-screws 
passing  through  the  jaws  of  the  yoke  ;  this  affords  a  very  flexible  bearing,  and 
a  chance  for  lateral  adjustment. 

The  last  hangers  are  of  the  design  of  William  Sellers  &  Co.,  who  have  made 
improvements  in  the  designs  for  bearings,  pillow-blocks,  hangers,  shafting,  and 


FIG.  569. 


FIG.  570. 


266 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


couplings,  which  are  in  use  in  their  own  shops  and  have  been  extensively  copied 
by  others.     Some  of  the  distinctive  forms  are  further  illustrated. 


FIG.  571. 


o 


J 


\ 


o 


FIG.  572. 


Figs.  579  and  580  are  the  front  and  side  elevations  of  a  pillow-block,  one 
half  of  each  being  in  section.     The  length  of  the  box  is  about  four  diameters 


FIG.  574. 


of  the  shaft.    The  centre  bearings  are  spherical  and  fit  in  corresponding  recesses 
in  the  block  and  cap,  permitting  the  bearing  to  adjust  itself  to  the  journal  of 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


26? 


the  shaft.     Lubrication  is  ordinarily  through  the  centre  of  the  cap ;  but  the 
upper  box  has  two  cups  containing  a  mixture  of  oil  and  tallow  which  is  usually 


FIG.  577. 


FIG.  578. 


solid  but  melts  when  the  bearing  heats.  The  maximum  pressure  allowed  is 
50  pounds  per  square  inch,  the  diameter  multiplied  by  the  length  of  bearing 
or4D. 


FIG.  580. 


Another  feature  of  the  Sellers  bearings  is  the  spherical-shaped  drip-pan  to 
catch  the  waste  oil.     By  the  distribution  of  the  oil  the  metal  of  the  shaft  will 


268 


MACHINE  DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


not  touch  that  of  the  box.    Any  metal  can  be  used  for  the  box ;  cast-iron  is  the 
cheapest  and  best  if  the  surface  is  kept  oiled,  but  the  poorest  if  allowed  to  run 

dry.     The  oil  cup  at  the  centre  of  the  cap  for  a 
shaft  %%"  in  diameter  making  120  revolutions  per 


FIG.  582. 


minute  has  a  capacity  of  2'2  fluid  ounces,  which  is  sufficient  for  six  months' 
run.  The  above  revolutions  per  minute  are  Messrs.  Sellers  &  Co.'s  -practice 
for  machine  shops,  for  wood-working  machinery  250,  for  that  of  cotton  and 
woollen  mills  300  to  400  per  minute. 


FIG.  583. 


Fig.  581  is  a  ball-and-socket  hanger  the  construction  of  which  is  similar  to 
the  pillow-block.     The  centre  spherical  bearings  are  adjusted  vertically  by  the 


MACHINE  DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


269 


screws  d  and  e,  the  interior  of  which  are  made  in  hexagonal  form  and  into 
which  a  key  is  fitted  for  the  operation  of  the  screw. 

Fig.  582  is  a  view  of  a  side  hanger  adapted  to  a  counter-shaft ;  the  square 
slot  a  is  for  the  shipping  bar. 

Fig.  583  represents  the  elevation  of  a  bracket,  or  the  support  of  a  shaft 
bolted  to  an  upright ;  the  box  is  movable,  and  is  adjusted  laterally  by  the  set- 
screws.  Fig.  584  is  a  front  elevation  of  the  back-plate  cast  on  the  post ;  it  will 
be  seen  that  the  holes  are  oblong,  to  admit  of  the  vertical  adjustment  of  the 
bracket.  The  Sellers  pillow-block  (Figs.  579  and  580)  may  be  used  for  the  same 
purpose. 

For  Upright  Shafts.— Footstep,  or  Step,  for  an  Upright  Shaft.— Fig.  585 
represents  a  half  elevation  and  section  of  the  step.  It  consists  of  a  foundation 
or  bed-plate,  A,  a  box,  B,  and  a  cup  or  socket,  C.  The  plate  A  is  firmly  fast- 


FIG.  585. 

ened  to  the  base  on  which  it  rests  ;  in  the  case  of  heavy  shafts,  often  to  a  base 
of  granite.  The  box  B  is  placed  on  A,  the  bearing  surface  being  accurately 
levelled,  and  fitted  either  by  planing  or  chipping  and  filing ;  the  bearing  sur- 
faces b  are  commonly  called  chipping-pieces,  which  are  the  bearing  surfaces  of 
the  bottom  of  B.  A  and  B  are  held  together  by  two  screws  ;  the  holes  for  these 
are  cut  oblong  in  the  one  plate  at  right  angles  to  those  of  the  other  ;  this  ad- 
mits of  the  movement  of  the  box  in  two  direc- 
tions to  adjust  nicely  the  lateral  position  of  the 
shaft,  after  which,  by  means  of  the  screws,  the 
two  plates  are  clamped  firmly  to  each  other.  C, 
the  cup  or  bushing,  which  should  be  made  of 
brass,  slips  into  a  socket  in  B.  Frequently  circu- 
lar plates  of  steel  (Figs.  586  and  587)  are  dropped 
into  the  bottom  of  this  cup  for  the  step  of  the 
shaft.  The  cup  C,  in  case  of  its  sticking  to  the 
shaft,  will  revolve  with  the  shaft  in  the  box  B  ;  if 
plates  are  used,  these  also  admit  of  movement  in 
the  cup. 

Fig.  588  represents  the  elevation  of  a  bearing  for  an  upright  shaft,  in  which 
the  shaft  is  held  laterally  by  a  box  and  bracket  above  the  step.  The  step  B  is 
made  larger  than  the  shaft,  so  as  to  reduce  the  amount  of  wear  incident  to  a 
heavy  shaft.  The  end  of  the  shaft  and  the  cup  containing  oil  are  shown  in 


FIG.  586. 


FIG.  587. 


270 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


dotted  line.     The  bed-plate  A  rests  on  pillars,  between  which  is  placed  a  pil- 
low-block or  bearing  for  horizontal  shaft. 


Figs.  589  and  590  represent  the  elevation  and  vertical  section  of  the  suspen- 
sion bearing  used  by  Mr.  Boyden  for  the  support  of  the  shaft  of  his  turbine- 
wheels.  It  having  been  found  difficult  to  supply  oil  to  the  step  of  such  wheels, 
it  was  thought  preferable  by  him  to  suspend  the  entire  weight  of  wheel  and 
shaft,  where  it  could  be  easily  attended  to.  The  shaft  (see  section)  is  cut  into 
necks,  which  rest  on  corresponding  projections  cast  in  the  box  b ;  the  spaces  in 
the  box  are  made  somewhat  larger  than  the  necks  of  the  shaft,  to  admit  of  Bab- 
bitting, as  it  is  termed,  the  box  ;  that  is,  the  shaft  being  placed  in  its  position 


Fio.  589. 

in  the  box,  Babbitt,  or  some  other  soft  metal  melted,  is  poured  in  round  the 
shaft,  and  in  this  way  accurate  bearing  surfaces  are  obtained ;  projections  or 
holes  are  made  in  the  box  to  hold  the  metal  in  its  position.  The  box  is  sus- 
pended by  lugs  b,  on  gimbals  c,  similar  to  those  used  for  mariners'  compasses, 
which  give  a  flexible  bearing,  so  that  the  necks  may  not  be  strained  by  a  slight 
sway  of  the  shaft.  The  screws  ee  support  the  gimbals,  consequently  the  shaft 
and  wheel ;  by  these  screws  the  wheel  can  be  raised  or  lowered,  so  as  to  adjust 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


271 


its  position  accurately  ;  beneath  the  box  will  be  seen  a  movable  collar,  to  adjust 
the  lateral  position  of  shafts. 

No  weight  rests  on  the  foot  of  the  shaft,  but  a  cast-iron  plate  is  firmly  bolted 
to  the  floor  of  the  wheel  pit,  with  side  flanges,  and  set  screws  by  which  iron  or 
wooden  cushions  can  be  adjusted  to  preserve  the  shaft  in  its  central  position. 

The  great  care  in  design  and  mechanical  construction  of  his  wheels  and  their 
details  enabled  Mr.  Boyden  to  obtain  large  percentages  of  effect,  and  led  to  the 
general  introduction  of  turbines.  In  form  and  construction  they  have  been 
much  simplified,  and  with  economy.  Some  makers  still  retain  a  form  of  upper 
hangers  and  bottom  guides,  but  wooden  steps  (Fig.  591)  are  now  almost  uni- 
versally adopted.  They  are  made  either  conical  or  a  portion  of  a  sphere,  of 
various  woods,  usually  lignum-vitas,  but  oak  and  poplar  are  preferred  by  some. 


FIG.  591. 


FIG.  594. 


The  load  is  from  50  to  75  pounds  per  square  inch.  The  fibres  of  the  wood  are 
placed  vertically,  and  afford  an  excellent  bearing  surface.  Water  is  sometimes 
introduced  into  the  centre  of  the  wood,  or  into  a  box  around  it,  from  the  upper 
level  of  water.  When  cast-iron  or  steel  is  used  for  the  step,  it  is  usual  to  incase 
the  box  and  supply  oil  by  leading  a  pipe,  sufficiently  high  above  the  surface  of 
the  water,  to  force  the  oil  down. 

For  long,  upright  shafts,  it  is  very  usual  to  suspend  the  upper  portion  by  a 
suspension-box,  and  to  run  the  lower  on  a  step,  connecting  the  two  portions 
by  a  loose  sleeve  or  expansion  coupling,  to  prevent  the  unequal  meshing  of  the 
bevel-wheels,  incident  to  an  alteration  of  the  length  of  shaft  by  variations  of 
temperature.  The  suspension  is  frequently  made  by  a  single  collar  at  the  top 
of  the  shaft. 


272 


MACHINE   DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


Fig.  592  is  a  one  half  outside  end  view,  and  one  half  transverse.  Fig.  593 
is  a  section  on  the  centre  line  of  axle,  and  Fig.  594  sectional  plan  of  box  on 
centre  line  of  axle  with  a  plan  of  journal  and  journal  bearing  of  the  standard 
journal  box  adopted  by  the  Master  Car-Builders'  Association,  1874. 

Thrust  Bearings  for  Screw  Propeller  Shafts.  —  The  thrust  along  the  shaft 
of  a  steamship  propelled  by  a  screw  is  taken  up  by  collar  bearings,  and  through 

them  transmitted  to  the 
ship.  Small  shafts  up  to 
8"  in  diameter  have  gen- 
erally one  thrust  collar, 
but  sometimes  compara- 
tively small  shafts  have 
several  thrust  collars.  In 
the  latter  case  the  bearing 
may  have  a  brass  bush  in 
halves  containing  grooves 
to  receive  the  collars  on 
the  shaft.  The  general 


595. 


FIG.  596. 


practice  is  to  fit  between 
the  collars  cast-iron  or 

cast-steel  horseshoe  -  shaped  pieces,  clamped  between  two  nuts,  which  are 
threaded  on  a  screwed  steel  bar,  supported  at  its  ends  by  solid  bearings  cast 
on  the  block,  as  shown  in  Figs.  595  and  596.  In  this  design  each  horseshoe 
piece  may  be  adjusted  separately  by  the  nuts  on  each  side,  or  they  may  be  all 
moved  together  by  means  of  the  nuts  at  the  ends  of  the  bars. 

A  useful  diagram  (Fig.  597),  with  accompanying  explanation,  by  George  K. 
Bate,  Assoc.  M.  Inst.  C.  E.,  is  presented  in  the  Practical  Engineer  for  Nov.  2, 
1894.  "  In  its  construction  the  effective  horse  power,  or  the  power  actually 
employed  in  propelling  the  ship,  has  been  assumed  to  be  equal  to  two  thirds 
the  indicated  H.  P.  of  the  engines,  so  that 

"  I.  H.  P.  =  the  indicated  H.  P.  of  the  engines. 

"  E.  H.  P.  =  effective  H.  P.  =  I.  H.  P.  x  |. 

"  K  =  speed  of  the  vessel  in  knots. 

"  T  —  total  thrust,  or  load  on  thrust  block  in  pounds. 

"  P  =  pressure  on  thrust  collars,  pounds  per  square  inch. 

"  S  =  surface  of  thrust  collar,  square  inches  per  I.  H.  P. ;  then 

— gTr =  K  X  101  -3  =  speed  in  feet  per  minute  and  work  done  per 

minute  in  foot-pounds. 

"  =  T  x  K  X  101-3,so  that  T  X  K  X  101-3  =  E.  H.  P.  X  33,000  ;  therefore 
E.  H.  P.  X  33,000 


K  X  101-3 

"  Again,  if  E.  H.  P.  =  f  I.  H.  P.,  we  may  write 
_  21  H.  P.  X  33,000  _  I.  H.  P.  x  22,000 


I.  H.  P.  x  217 


3  K  X  101-3  K  X  101-3  K 

therefore  S,  the  surface  of  thrust  collars  in  square  inches  per  I.  H.  P.  = 

217 
K  x  P- 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


273 


"  The  diagram  gives  the  value  of  .S  with  P,  varying  from  30  to  80  pounds 
per  square  inch.  In  ordinary  practice  this  pressure  is  50  to  60  pounds  per 
square  inch  in  naval,  and  40  to  50  pounds  per  square  inch  in  mercantile 
steamers,  although,  in  cases  where  white  metal  is  fitted,  it  is  found  that  these 
loads  may  be  safely  increased  by  25  per  cent. 

"  As  an  example,  suppose  the  case  of  a  thrust  block  for  a  vessel  having  en- 
gines of  3,000  I.  H.  P.,  driving  her  at  a  speed  of  18  knots,  to  determine  the 
necessary  surface  of  thrust  collars  that  the  pressure  on  them  may  not  exceed 
60  pounds  per  square  inch.  At  the  point  marked  18  knots  on  the  scale  for 
speed  of  vessel  follow  the  ordinate  up  till  it  cuts  the  line  marked  60  on  the 
scale  of  pressures  on  the  thrust  collars  to  the  left  of  the  diagram,  at  which 
point  of  intersection  follow  to  the  right,  and  read  off  the  corresponding  surface 
of  collars  per  I.  H.  P. — i.  e.,  0-201  square  inches ;  then  0-201  x  3,000  =  603 
square  inches,  the  total  thrust  surface  required  for  E.  H.  P.  =  3,000  x  f  = 

2,000,  and  -        —      '  —  =  T,  the  load  on  the  block  equal  to  36,180  pounds ; 

-lo   X    -LU.L"  o 

then,  if  pressure  per  square  inch  between  surfaces  is  not  to  exceed  60  pounds, 
we  have  total  surface  of  block  =  — ^—  =  603,  as  per  diagram." 


60 


30 


[40 


50 


0° 
080 


.553 


1  O 


10          11          12  14          16       18      20  25 

SPEED  OF  VESSEL,  KNOTS. 

FIG.  597. 


30 


Couplings  are  the  connections  of  shafts,  and  are  varied  in  their  construction 
and  proportions,  often  distinctive  of  the  mechanic  making  them. 

The  Face  Coupling  (Fig.  598),  the  one  in  general  use  for  the  connecting  of 

wrought-iron  shafts,  consists  of  two  plates  or  disks  with  long,  strong  hubs, 

through  the  centre  of  which  holes  are  accurately  bored  to  fit  the  shaft ;  one 

half  is  drawn  on  to  the  shaft  and  tightly  keyed ;  the  plates  are  faced  square 

19 


274 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


with  the  shaft,  and  the  two  faces  are  brought  together  by  bolts.  The  number 
and  size  of  the  bolts  depend  upon  the  size  of  the  shaft ;  never  less  than  4  for 
shafts  less  than  3  inches  diameter,  and  more  as  the  diameter  increases ;  the 
size  of  the  bolts  varies  from  f  to  1£  inch  in  diameter.  The  figure  shows  a 
usual  proportion  of  parts  for  shafts  of  from  2  to  5  inches  diameter ;  for  larger 
than  these,  the  proportion  of  the  diameter  of  the  disk  to  that  of  the  shaft  is 
too  large. 

Fig.  599  is  a  rigid  sleeve  coupling  for  a  cast-iron  shaft ;  it  consists  of  a 
solid  hub  or  ring  of  cast-iron  hooped  with  wrought-iron ;  the  shafts  are  made 

with  bosses,  the  coupling  is  slipped 
on  to  one  of  the  shafts,  the  ends 
of  the  two  are  then  brought  to- 


FIG.  598. 


FIG.  599. 


gether ;  and  the  coupling  slipped  back  over  the  joint,  and  firmly  keyed.     This 

is  an  extremely  rigid  connection.     Some  makers  use  keys  without  taper,  and 

force  the  couplings  on  the  shafts. 

Fig.  600  is  a  screw  coupling  for  the  connecting  of  the  lighter  kinds  of 

shafts.     It  will  be  observed  that  this  coupling  admits  of  rotation  but  in  one 

direction — the  one  tending  to  bring 
the  ends  of  the  shafts  toward  each 

other ;   the  reverse  motion  tends  to 

.-,  ,1  -, 

unscrew,  throw  them  apart,  and  un- 
couple them. 

Figs.  601  and  602  is  a  double-cone 
vice  coupling  ;  B  is  the  outer  shell  or 
sleeve,  C  C  the  two  cones,  and  D  the  bolts.  The  sleeve  is  cylindrical  outside, 
but  bored  with  a  double  taper  inside,  smallest  at  the  centre.  The  cones  are 
bored  to  fit  the  shaft,  and  turned  outside  to  fit  the  interior  cones  of  the  sleeve. 


FIG.  600. 


FIG.  601. 


FIG.  602. 


There  are  three  bolt  grooves  in  the  cones  and  sleeves,  and  one  is  cut  through  to 
give  elasticity  to  the  cones.  The  sleeves  and  cones  are  adjusted  over  the  joint 
of  the  shafts,  leaving  it  an  easy  fit,  some  f  inch  between  the  ends  of  the  cones. 


MACHINE   DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


2T5 


If  the  bolts  be  introduced  and  screwed  up,  the  cones  are  brought  nearer  to  each 
other  and  the  shafts  are  securely  clamped  together. 

Fig.  603  is  a  clamp  coupling  for  a  square  shaft. 

In  many  cases  it  occurs  that  rigid  couplings,  such  as  have  been  given,  are  ob- 
jectionable; they  necessarily  imply  that,  to  run  with  the  least  strain  possible, 


FIG. 


FIG 


the  bearings  should  be  in  accurate  line ;  any  displacement  involves  the  spring- 
ing of  the  shaft,  heating  of  the  journals,  and  loss  by  friction.  Wherever,  from 
any  cause,  the 'alignment  can  not  be  very  nearly  accurate,  some  coupling  that 
admits  of  lateral  movement 
should  be  adopted.  The 
simplest  of  these  is  the  box 
or  sleeve  coupling  (Fig. 
604),  sliding  over  the  end 
of  two  square  shafts,  keyed 
to  neither,  sometimes  held 

i  ,  •  •  FIG.  605. 

in  place  by  a  pin  passing 

through  the  coupling  into  one  of  the  shafts.  For  round  shafts,  the  loose 
sleeve  Coupling  is  a. pipe  or  hub,  generally  4  to  6  times  the  diameter  of  the 
shaft  in  length,  sliding  on  keys  fixed  on  either  shaft. 


FIG.  606. 


Fig.  605  is  a  horned  coupling.     The  two  parts  of  the  coupling  are  counter- 
parts, each  firmly  keyed  to  its  respective  shaft,  but  not  fastened  to  each  other ; 


276 


MACHINE   DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


FIG.  607. 


the  horns  of  the  one  slip  into  the  spaces  of  the  other,  and,  if  accurately  fitted, 
it  affords  an  excellent  coupling,  and  is  not  perfectly  rigid. 

It  often  happens  that  some  portion  of  a  shaft  or  machine  is  required  to  be 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


277 


stopped  while  the  rest  of  the  machinery  continues  in  motion.  It  is  evident 
that,  if  one  half  of  a  horned  coupling  be  permitted  to  slide  lengthwise  on  the 
key — the  key  being  fixed  in  the  shaft,  forming  in  this  case  what  is  more 
usually  called  a  feather — when  the  horns  of  one  half  are  out  of  the  spaces  of 
the  other,  communication  of  motion  will  cease  between  the  shafts. 

Fig.  606  represents  a  coupling  of  this  sort  for  a  large  shaft,  from  the  Cor- 
liss Steam-Engine  Company.  The  horns  are  8  in  number  on  each  part,  and 
are  thrown  readily  in  or  out  of  action  by  the  handle  h  turning  nut  in  the  loose 
part  of  the  clutch  on  the  screw  cut  on  the  shafts. 

Fig.  607  is  another  form  of  disengaging  a  large  pulley  from  a  main  shaft, 
from  the  Corliss  Steam-Engine  Company.     The  pulley  is  fastened  to  a  cast- 
iron  pipe  or  sleeve  p  through  which  the  main  shaft  s  passes.     The  two  are 
attached  by  means  of  the  coupling  c,  one  half 
of  which  is  attached  to  the  shaft  and  the  other 
to  the  sleeve.     When  bolted  together,  the  pul- 
ley and  main  shaft  move  together ;  but  if  the 
bolts  be  removed,  then  the  pulley  becomes  sta- 
tionary even  if  the  shaft  is  running.     Shaft 
and   sleeve   have    independent    bearings.      A 
section  of  the  coupling  c  on  a   larger   scale 
shows  the  strong  taper  of  the  bolts  without 
head. 

It  is  difficult  to  maintain  shafts  in  exact 
line,  and  slight  disarrangements  are  met  by 
the  elasticity  of  the  shafts  but,  as  a  further 
precaution,  flexible  couplings  are  used,  of  which 
Fig.  608,  called  Oldham's  Coupling,  makes  a 
strong  connection  and  admits  of  considerable 
variation  in  the  lines  of  the  coupled  shafts. 
It  consists  of  two  heads  fastened  to  their  several  shafts,  across  the  face  of  these 
heads  two  grooves  are  cut,  and  between  these  faces  an  intermediate  plate  is  in- 
serted with  two  tongues  at  right  angles  to  each  other,  slide-fitted  to  the  grooves 
in  the  heads,  thus  coupling  the  two  shafts. 

In  Fig.  609  the  coupling  admits  of  more  motion.  The  grooves  are  in  the  in- 
termediate plate,  and  one  of  the  tongues  is  fitted  in  its  head  with  a  T  or  dove- 
tail groove  held  in  position  by  a  set  screw  or  pin,  by  the  removal  of  which  the 
tongue  can  be  withdrawn  and  the  shaft  uncoupled. 


FIG.  608. 


FIG.  609. 


FIG.  610. 


Hooke's  Joint  or  Universal  Coupling  is  used  to  connect  two  shafts  whose 
axes  intersect,  and  it  has  the  advantage  that  the  angle  between  the  shafts  may 


278 


MACHINE  DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


FIG.  611. 


be  varied  while  they  are  in  motion.  Fig.  610  shows  the  entire  coupling  partly 
in  section ;  the  shafts  to  be  coupled  are  forked  at  their  ends ;  these  forked  ends 
carry  between  them  a  cross  the  arms  of  which  are  at  right  angles  to  each  other. 

The  arms  of  the  cross  are  jointed  to 
the  forks  so  that  they  may  turn  freely 
about  their  axes.  The  angular  veloci- 
ties of  the  shafts  will  be  unequal  ex- 
cept at  every  quarter  revolution,  but 
by  using  a  double  Hooke's  joint,  as 

shown  in  Fig.  611,  the  two  shafts  will  have  the  same  angular  velocities,  if 
they  make  equal  angles  with  the  intermediate  shaft  and  are  in  the  same  plane 
with  it. 

It  is  often  necessary  to  engage  shafts,  when  one  is  in  motion,  or  disengage 
when  both  are  in  motion.  One  of  the  oldest  forms  of  clutch  for  this  purpose 
is  the  slide  or  clutch  couplings,  when  the  motion  is  required  but  in  one  direc- 
tion (Fig.  612).  A  represents  the  half  of  the  coupling  that  is  keyed  to  the 
shaft,  B  the  sliding  half,  c  the  handle  or  lever  which  communicates  the  sliding 
movement ;  the  upper  end  of  the  lever  terminates  in  a  fork,  inclosing  the  hub 
of  the  coupling,  and  fastened  by  two  bolts  or  pins  to  a  collar  round  the  neck 
of  the  hub ;  to  support  B  the  end  of  its  shaft  extends  a  slight  distance  into  the 
coupling  A.  Shafts  can  not  be  engaged  with  this  form  of  coupling  while  the 

driving    shaft    is   in   rapid 
,._  .,_  ,_  .          motion  without  shock. 

r-  •  — I 


To 


obviate  this,  other  forms  of 
coupling  are  requisite ;  one 
of  these  is  represented  (Fig. 
613).  On  the  shaft  B  is 
fixed  a  drum  or  pulley, 


FIG.  612. 

which  is  embraced  by  a  friction 
this  band  consists  of  two  straps 
ends  projecting  on  either  side ; 
is  the  common  form  of  bayonet 
affords  a  guide  to  the  prongs  or 
ping  these  prongs  forward,  they 
friction  band ;  the  shaft  A  being 


FIG.  613. 

band  as  tightly  as  may  be  found  necessary ; 
of  iron,  clamped  together  by  bolts,  leaving 
the  portion  of  the  coupling  on  the  shaft  A 
clutch ;  the  part  cc  is  fixed  to  the  shaft,  and 
bayonets  b  b,  as  they  slide  in  and  out.  Slip- 
are  thrown  into  gear  with  the  ears  of  the 
in  motion,  the  band  slips  round  on  its  pulley 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


2T9 


till  the  friction  becomes  equal  to  the  resistance,  and  the  pulley  gradually  attains 
the  motion  of  the  clutch. 

But  of  all  slide  couplings,  to  engage  and  disengage  with  the  least  shock  and 
at  any  speed,  the  friction-cone  coupling  (Fig.  614)  is  by  far  the  best.  It  con- 
sists of  an  exierior  and  interior  cone,  a,  b ;  a  is 
fastened  to  the  shaft-  A,  while  Z»  slides  in  the  usual 
way  on  the  feather  of  the  shaft  B  ;  pressing  b 
forward,  its  exterior  surface  is  brought  in  contact 


FIG.  614. 


FIG.  615. 


with  the  interior  conical  surface  of  a;  this  should  be  done  gradually;  the 
surfaces  of  the  two  cones  slip  on  each  other  till  the  friction  overcomes  the 
resistance,  and  motion  is  transmitted  comparatively  gradually  and  without 
danger  to  the  machinery.  The  longer  the  taper  of  the  cones,  the  more  difficult 
the  disengagement ;  but  the  more  blunt  the  cones,  the  more  difficult  to  keep 
the  surfaces  in  contact.  An  angle  of  8°  with  the  line  of  shaft  is  a  very  good 
one  for  surfaces  of  cones  of  cast-iron  on  cast-iron.  When  thrown  into  gear, 
the  handle  of  the  lever  or  shipper  (Fig.  615)  is  slipped  into  a  notch,  that  it 
may  not  be  thrown  out  by  accident. 

The  objection  to  this  coupling  is 
that  it  will  work  out  of  gear  unless  the 
shipper  -  handle  is  held  firmly  in  its 
position,  and  producing  considerable 
friction  against  the  collar.  To  ob- 
viate this  the  shipper  is  made  to  act 
on  a  toggle-joint  fastened  to  the  shaft, 
and,  once  thrown,  the  pressure  is  self- 
continued  and  preserved  without  any 

action  of  the  shipper,  and  without  fric-  FIG.  eie. 

tion. 

Fig.  616  represents  a  double-friction  clutch,  of  the  Weston-Capen  patent. 
The  clutch  G  is  slid  over  the  toggle,  and  the  friction  cone  is  forced  into  the 
pulley  and  engaged  therewith.  In  the  figure,  D'  is  thus  engaged  with  A',  while 
D  and  A  are  not  in  contact. 


280 


MACHINE   DESIGN   AND   MECHANICAL  CONSTRUCTIONS. 


When  from  any  cause,  as  in  rolling  mills,  the  gearing  is  subject  to  sudden 
shocks,  which  might  be  injurious  unless  some  means  were  adopted  to  modify 
the  blow,  friction  couplings  may  be  introduced  of  which  Fig.  617  is  an  illus- 


Fio.  617. 

tration,  in  which  the  frictional  resistance  is  sufficient  to  transmit  the  required 
power,  but  under  sudden  shocks  yields  and  slips.  It  consists  of  two  hubs,  both 
keyed  to  their  shafts ;  one  of  the  hubs  has  a  wood-lined  groove  into  which  the 
plate  of  the  other  is  inserted  and  friction  is  produced  between  the  two,  by  the 
bolts,  which  bring  together  the  parts  of  the  groove ;  loosening  the  bolts  removes, 
the  frictional  contact  and  disengages  the  clutch. 

Fig.  618  is  a  longitudinal  section  and  Fig.  619  a  transverse  section  of  the 
Weston  clutch.  The  five  iron  disks  A  engage  with  solid  keys  on  the  long  boss 
of  the  spur  wheel  E,  within  which  the  driving  shaft  C  turns  freely  when  no 
coupling  pressure  is  applied  to  the  disks.  The  drum  D  containing  the  six  in- 
termediate wood  disks  B  slides  on  feathers  on  the  shaft  C,  and  the  groove  Gr  on 
the  outer  end  of  the  drum  receives  the  forked  end  of  a  lever  by  which  the  coup- 
ling pressure  is  applied,  compressing  the  disks  against  the  fixed  collar  F  on  the 
shaft,  and  thereby  coupling  the  spur  wheel  E  to  the  shaft  C. 


FIG.  618. 


FIG.  619. 


In  Fig.  620  is  shown  the  cylinder-friction  clutch  of  Koechlin.  In  this  case 
the  clutch  movement  takes  place  readily.  The  part  A  is  a  hollow  cylinder  in 
which  three  internal  clamp  pieces  are  fitted,  each  being  provided  with  a  bronze 
shoe.  These  are  thrown  in  and  out  of  action  by  means  of  a  sliding  collar  B' 
which  operates  right-  and  left  hand-screws  by  means  of  the  lever  b.  The  clamps 
slide  in  radial  grooves.  The  nuts  for  the  right-  and  left-hand  screws  can  be 
closely  adjusted  and  clamped  by  set  screws,  so  that  a  radial  movement  of  less 
than  -"  is  sufficient  to  throw  the  clutch  in  or  out  of  action. 


MACHINE   DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


281 


Figs.  621  and  622  are  sections  and  elevation  of  a  friction  clutch  in  which 
the  piece  A  is  in  the  form  of  a  ring  of  unequal  thickness  and  divided  at  its  thin- 


FIG.  620. 


nest  part.  From  the  thickest  part  of  the  ring  A  a  strong  arm  proceeds  to  a 
central  boss  which  is  keyed  to  the  shaft.  This  ring,  arm,  and  boss  are  all  cast 
in  one  piece.  An  outer  ring  or  shell  B  is  bored  or  turned  to  fit  easily  over  the 


FIG.  621. 


Fm.  622. 


ring  A.  On  the  back  of  the  piece  B  is  a  boss  which  serves  to  carry  a  wheel  or 
pulley.  To  use  the  arrangement  as  a  shaft  coupling,  the  boss  on  the  back  of 
B  is  keyed  to  one  shaft,  the  boss  of  A  being  keyed  to  the  other. 

To  take  the  place  of  fast  and  loose  pulleys,  as  shown  in  the  figures,  the  piece 
B  rides  loose  on  the  shaft,  except  when  it  is  bound  to  the  ring  A.  The  pieces 
A  and  B  are  bound  together  by  the  expansion  of  the  former  caused  by  the  rota- 
tion of  right-  and  left-handed  screws  working  in  two  nuts  which  fit  into  sockets 
in  the  ring  A,  one  on  each  side  of  the  line  of  division.  By  pushing  the  sliding 
boss  C  along  the  shaft,  movement  of  rotation  is  communicated  to  the  screw 
through  the  link  D  and  lever  E.  The  lever  E  is  secured  to  the  middle  portion 


282 


MACHINE  DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


of  the  screw  by  a  grooved  key,  which  is  held  by  a  set  screw.  At  the  back  of 
this  key  there  is  a  clearance  space  sufficient  to  allow  of  the  key  being  with- 
drawn clear  of  the  grooves,  so  that  the  lever  may  be  turned  on  the  screw  into 
another  position  and  take  up  the  wear  of  the  screw  threads. 

Bovet's  magnetic  coupling  (Fig.  623)  consists  of  a  block  or  head  keyed  to 
the  power  shaft,  on  the  face  of  which  is  a  groove  containing  the  iron-wire  core, 
connected  with  the  brushes  which  bear  on  the  rings. 


FIG.  623. 


FIG.  624. 


The  shaft  to  be  clutched  is  provided  with  a  block  F,  capable  of  sliding  along 
and  approaching  C  D  until  it  is  in  contact.  It  follows,  therefore,  that  when  the 
wire  B  is  traversed  by  a  current,  F  is  attracted  against  C  D  and  participates  in 
the  motion  of  A.  Adhesion  is  obtained  without  any  external  reaction. 

Fig.  624  is  a  spring  hub  used  on  a  large  rope-driving  wheel  to  take  up  the 
shock  of  starting.  The  wheel  W  runs  loose  on  the  driving  shaft  S  and  is  pro- 
vided with  lugs  a,  a,  a,  which  project  into  the  spring  hub  H  keyed  to  the  driv- 
ing shaft  S.  Three  heavy  springs  interposed  between  the  lugs  and  the  hub  al- 
low a  circumferential  movement  of  four  feet  on  a  six-foot-diameter  wheel. 

Pulleys  are  used  for  the  transmission  of  motion  from  one  shaft  to  another 
by  the  means  of  belts  ;  by  them  every  change  of  velocity  may  be  effected.  The 
speeds  of  two  shafts  will  be  to  each  other  in  the  inverse  ratio  of  the  diameter 
of  their  pulleys.  Thus,  if  the  driving  shaft  make  100  revolutions  per  minute, 
and  the  driving  pulley  be  18  inches  in  diameter,  while  the  driven  pulley  is  12 
inches,  then, 

12  :  18  ::  100  :  150; 

that  is,  the  driven  shaft  will  make  150  revolutions  per  minute  without  allow- 
ance for  slip.  Where  there  is  a  succession  of  shafts  and  pulleys,  to  find  the 
velocity  of  the  last  driven  shaft :  Multiply  together  all  the  diameters  of  the 
driving  pulleys  by  the  speed  of  the  first  shaft,  and  divide  the  product  by  the 
product  of  the  diameters  of  all  the  driven  pulleys. 


MACHINE   DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


283 


Pulleys  are  made  of  cast-iron  and  of  every  diameter,  from  2  inches  up  to 
20  feet.  The  number  of  arms  v,ary  according  to  the  diameter ;  for  less  than 
8  inches  diameter  the  plate  pulley  is  preferable  (Fig.  625)  ;  that  is,  the  rim  is 
attached  to  the  hub  by  a  plate  ;  for  pulleys  of  larger  diameters,  those  with  arms 
are  used,  never  less  than  four  in  number.  The  arms  are  made  usually  straight 
(Fig.  626),  sometimes  curved  (Fig.  627). 


FIG.  625. 


FIG.  626. 


FIG.  627. 


Fig.  628  represents  a  portion  of  the  elevation  of  a  pulley  sufficient  to  show 
the  proportion  of  the  several  parts,  and  Fig.  629  a  section  of  the  same.  The 
parts  may  be  compared  proportionately  with  the  diameter  of  shaft ;  thus  the 


FIG.  629. 

thickness  of  the  hub  is  about  £  the  diameter  of  the  shaft ;  this  proportion  is 
also  used  for  the  hubs  of  couplings  ;  the  width  of  the  arms  from  f  to  full  diam- 
eter ;  the  thickness  half  the  width  ;  the  thickness  of  the  rim  from  -J-  to  £  the 
diameter ;  the  length  of  hub  the  same  as  the  width  of  face. 

Fig.  630  is  a  large  pulley  of  the  Southwark  Foundry  pattern.  The  hub  is 
cast  with  four  divisions,  to  admit  of  contraction  in  cooling,  and  the  rim  is  in 
halves,  to  admit  of  the  pulley  being  put  on  the  shaft  without  removing  it  from 
its  bearings,  a  very  common  practice  with  large  pulleys.  Wrought-iron  rim- 
pulleys  consist  of  a  spider— that  is,  the  hub  and  arms— of  cast-iron,  and  a 
wrought-iron  plate-rim  is  bolted  to  flanges  on  the  extremities  of  the  arms. 

Fig.  631  represents  a  faced  coupling  pulley,  an  expedient  sometimes  adopted 
when  a  joint  occurs  where  a  pulley  is  also  required ;  the  two  are  then  combined ; 


284 


MACHINE   DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


the  pulley  is  cast  in  halves — two  plate  pulleys,  with  plates  at  the  side  instead  of 
central,  faced  and  bolted  together. 


Wooden  pulleys  called  drums  are  used  for  pulleys  of  very  wide  face.     Fig. 
632  represents  one  form  of  construction  in  elevation  and  longitudinal  section. 

It  consists  of  two  cast-iron  pulleys  A  A,  with  nar- 
row rims  ;  they  are  keyed  on  to  the  shaft  at  the 
required  distance  from  each  other,  and  plank  or 
lagging  is  bolted  on  the  rims  to  form  the  face  of 
the  drum ;  the  heads  of  the  bolts  are  sunk  beneath 
the  surface  of  the  lagging,  and  the  face  is  turned. 


.Jt? 


FIG.  631. 


MACHINE   DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


285 


Fig.  633  represents  a  wooden  plate  pulley,  consisting  of  sectors  of  inch 
boards  firmly  glued  and  nailed  together,  the  joints  of  the  boards  being  always 
broken.  The  face  is  formed  in  a  similar  way  by  nailing  and  gluing  arcs  of 
board  one  to  another  to  the  required  width  of  face ;  these  last  should  be  of 


FIG.  632. 


clear  stuff.  The  whole  is  retained  on  the  shaft  by  an  iron  hub,  cast  with  a 
plate  on  one  side,  and  another  separate  plate  sliding  on  to  the  hub  ;  the  hub  is 
placed  in  the  centre  of  the  pulley,  the  two  plates  are  brought  in  contact  with 
the  sides  of  the  pulley,  and  bolted  through  ;  and  the  pulley  turned.  A  similar 
arrangement  of  hub  is  used  for  the  hanging  of  grindstones. 

Fig.  634  is  an  elevation  of  Chase's  pulley  similar  in  its  rim  to  that  of  Fig. 
633,  but  an  iron  spider  supplies  the  place  of  the  wooden  plate.     They  are  built 


FIG.  633. 


FIG.  634. 


up  with  solid  rims  or  split,  as  in  the  figure.  They  are  made  of  the  usual  pulley 
dimensions  up  to  15  feet  in  diameter,  and  any  desirable  width  of  face,  and  able 
to  transmit  any  amount  of  H.  P.  at  any  speed  safe  for  a  belt, 

Fig.  635  is  a  perspective  of  a  pulley  with  a  wrought-iron  rim.     It  is  shown 


286 


MACHINE  DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


with  two  spiders,  but  it  can  be  made  with  a  single  one  or  with  any  number,  ac- 
cording to  the  width  of  belt  required.  They  are  also  made  in  halves,  adapted 
to  any  position,  and  safe  under  all  practical  requirements. 

A  ctmnter-shaft  is  one  distinct  from  the  main  shaft,  but  connected  with  it 
by  a  belt  for  the  purpose  of  driving  a  machine.  On  the  counter-shaft  there  is 

an  arrangement  of  fixed  and  loose 
pulleys  by  which  motion  can  be 
communicated  to  it  or  cut  off. 

In  Fig.  636,  B  is  the  belt  from 
the  main  shaft  which  is  being 
shifted  on  or  off  the  fast  pulley  F 
on  the  counter  by  the  fingers  f  f 
on  the  shipper  bar.  The  belt  is 
shifted  to  a  full  position  on  either 
the  pulleys  F  or  L.  When  the  belt 
is  on  the  fixed  pulley  F,  the  motion 
of  the  main  shaft  is  communicated 
to  the  counter ;  when  on  the  loose 
pulley  L,  the  counter-shaft  remains 
still  and  the  pulley  revolves  upon 
it.  It  sometimes  happens  that  the 

FIG.  ess.  friction    of   the  loose  pulley   upon 

the  counter  induces  its  revolution  ; 

to  prevent  which  an  arrangement  is  made,  as  shown  in  section  (Fig.  637),  by 
which  the  loose  pulley  moves  on  a  fixed  sleeve. 

The  shipper  handle,  not  shown,  is  held  positively  by  notches,  or  by  some 
arrangement  attached  to  the  shipper  bar.  The  faces  of  the  pulleys  should  be 
flat  or  but  slightly  rounded.  The  fixed  sleeve  should  be  kept  oiled. 


FIG.  636. 


FIG.  637. 


At  the  other  end  of  the  shaft  cone  pulleys  are  shown  which  correspond  to 
similar  cones  on  the  machine  but  reversed  so  that  the  speed  of  the  machine 
can  be  changed  by  shifting  the  belt  from  one  set  of  cones  to  the  other  when 
the  machine  is  stopped. 

Cone  pulleys  may  be  made  continuous  (Fig.  638),  thus  becoming  conoids 
upon  which  the  belt  can  be  shifted  to  any  line  by  an  adjusting  guide. 

It  is  often  necessary  to  reverse  the  motion  of  a  machine.     This  is  readily 


MACHINE  DESIGN   AND   MECHANICAL   CONSTRUCTIONS. 


28T 


done  by  a  system  of  fast  and  loose  pulleys,  as  shown  in  the  plan  and  elevation 
(Figs.  639  and  640),  in  which  A  is  a"  drum  or  wide-faced  pulley  on  the  driving- 
shaft,  B  a  fast  pulley  on  the  driven  shaft,  and  C 
and  D  loose  pulleys  on  the  same.  The  move- 
ment is  indicated  by  the  direction  of  the  arrows. 
The  driving-shaft  revolves  always  in  the  same 
direction,  but  on  the  driven  shaft  the  loose  pul- 
ley of  the  straight  belt  is  drawn  from  the  bottom, 
and  partakes  of  the  same  motion  as  the  driving- 
pulley  ;  while  by  the  cross-belt  the  draft  is  at  the 
top  of  its  pulley,  and  the  motion  reversed.  If 
the  straight  or  open  belt  be  shipped  on  to  the 
fast  pulley  B,  the  motion  given  to  the  shaft  is 
like  that  of  the  driving-shaft ;  if  the  cross-belt  be 
shipped  on  to  the  fast  pulley,  the  motion  of  the 
shaft  is  reversed.  In  the  elevation,  the  lower  side 
of  the  open  belt  is  straight,  while  there  is  a  sag 
in  the  upper;  the  first  is  the  tight  or  leading 
belt,  through  which  the  power  is  transmitted, 
while  the  upper  side  is  the  loose  or  slack  belt. 

When  the  belt  is  shifted,  while  in  motion,  to  a  new  position  on  a  drum  or 
pulley,  or  from  fast  to  loose  pulley,  or  vice  versa,  the  lateral  pressure  must  be 
applied  on  the  advancing  side  of  the  belt,  on  the  side  on  which  the  belt  is  ap- 


FIQ.  638. 


FIG.  640. 

preaching  the  pulley,  and  not  on  the  side  on  which  it  is  running  off.  It  is  only 
necessary  that  a  belt,  to  maintain  its  position,  should  have  its  advancing  side 
in  the  plane  of  rotation  of  that  section  of  the  pulley  on  which  it  is  required  to 
remain,  without  regard  to  the  retiring  side.  On  this  account,  the  shipper  yoke 
or  pins  must  be  on  opposite  sides  of  the  shipper  bar. 

When  the  main  shaft  is  connected  directly  with  a  machine,  and  it  has  to  be 
thrown  out,  the  belt  is  often  slipped  from  the  pulley  (Fig.  641),  and  hangs 
loosely  from  the  shaft,  by  which  the  belt  is  worn  and  often  becomes  entangled 


288 


MACHINE  DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


with  the  shaft  or  with  couplings.  It  is  better  to  have  a  hook  suspended  from 
the  ceiling  to  catch  the  belt  when  thrown  off ;  or,  still  better,  iron  suspended 
bows  (Fig.  641),  from  which  it  is  easier  to  slip  the  belt  on  the  pulley  again. 


•FiG.  641. 


Motion  may  be  transmitted  by  belts  to  shafts  at  right  angles  to  each  other. 

Figs.  642  and  643  is  a  plan  and  elevation  in  which  A  is  the  driving-shaft 
and  pulley  and  B  the  driven  one,  at  ;right  angles  to  each  other.  The  arrows 
show  the  advancing  sides  of  the  belts  and  their  position  with  regard  to  the  face 
of  the  pulleys. 


FIG.  643. 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


289 


In  the  case  of  inclined  axis  (Fig.-  644)  the  leading  line  falls  in  the  middle 
plane  of  each  pulley,  but  the  following  side  of  the  helt  does  not,  hence  such 
systems  can  only  be  run  in  one  direction.  The  leaving  points  in  the  figures 


FIG.  644. 


FIG.  645. 


are  at  a  and  b.  The  arrangement  gives  an  open  belt  when  the  angles  between 
the  planes  of  the  pulleys  =  0°,  and  at  cross  belt  =  180°.  In  the  intermediate 
positions  a  partial  crossing  at  the  belt  is  pro- 
duced, the  angle  =  90° ;  the  belt  is  quarter 
twist  (Fig.  645) ;  if  =  45°,  it  is  quarter  crossed. 
The  maximum  leading-off  angle  is  25°,  which 
occurs  when  the  distance  between  the  axis  is 
equal  to  twice  the  diameter  of  the  largest  pul- 
ley. 

Guide  pulleys  are  very  useful  in  belt  trans- 
mission for  shafts  at  varied  angles,  and  the 
proper  direction  is  obtained  when  each  guide 
pulley  is  placed  at  the  point  of  departure  of 
its  plane  with  that  of  the  next  following  pul- 
ley. 

Fig.  646  is  an  arrangement  adopted  in 
portable  grist-mills  for  driving  the  vertical 
shafts,  #,  #,  of  mill-stones,  from  pulleys  on  a 
horizontal  shaft.  Here  it  is  thought  necessary 
to  use  guide-pulleys. 

Figs.  647  and  648  are  the   elevation  and 
20 


290 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


plan  of  another  arrangement  of  pulleys  and  guide-pulleys ;  a  b  is  the  intersec- 
tion of  the  middle  plane  of  the  principal  pulleys.  Select  any  two  points  a  and 
b  on  this  line,  and  draw  tangents  a  c,  b  d,  to  the  principal  pulleys.  Then  c  a  c 


— F 


FIG.  017. 


FIG.  648. 


and  e  b  d  are  suitable  directions  for  the  belt.  The  guide-pulleys  must  be  placed 
with  their  middle  planes  coinciding  with  the  planes  cacandebd.  The  belt 
will  run  in  either  direction. 

In  Figs.  649  and  650  are  parallel  axes  with  two  guide-pulleys.  In  the  first 
the  guide-pulleys  are  placed  in  planes  tangent  to  both  operating  pulleys,  and 
hence  driving  may  occur  in  either  direction.  Usually,  however,  it  is  required 
to  provide  for  motion  in  .but  one  direction,  in  which  case  the  second  form  is 
used  as  being  simpler.  The  pulley  B  may  be  used  as  one  of  the  guide-pulleys, 
in  which  case  it  may  be  placed  loose  upon  the  same  shaft  as  A,  and  <D  or  D  be 
made  drivers  or  driven. 

It  is  necessary  to  stretch  the  belt  over  the  pulleys  to  prevent  its  slip  while 
conveying  power.  But  if  the  belt  is  very  heavy,  and  runs  nearly  horizontally, 


FIG.  649. 


FIG.  650. 


its  weight  will  supply  a  portion  of  the  adhesion  which  diminishes  with  the  in- 
clination of  the  belt  till  it  becomes  vertical,  when  the  friction  of  the  stretch  is 
the  only  factor  of  the  adhesion  of  the  belt  to  the  lower  pulley ;  and,  as  the  belt 
lengthens  by  use,  the  value  of  this  friction  becomes  nothing.  This  position  of 
pulleys  should  not  obtain  if  it  can  be  avoided ;  but  if  not,  the  friction-stress 
should  be  by  means  of  an  idler  or  binder  (Fig.  651)  on  the  loose  belt;  distinc- 
tively the  idler  rests  in  a  loose  frame  against  the  belt,  acting  by  gravity,  while 
the  binder  is  forced  against  the  belt  by  mechanical  appliances.  By  the  relief 
of  the  binder  the  belt  becomes  slack,  the  friction  of  the  belt  on  the  pulleys  be- 


MACHINE   DESIGN   AND    MECHANICAL   CONSTRUCTIONS. 


291 


comes  nothing,  and  motion  stops  on  "the  driven  pulley  ;  but  that  of  the  belt  may 
continue  by  its  friction  on  the  driver,  from  which  it  can  be  raised  by  a  rope 
attachment  or  by  a  more  positive  contrivance.  This  is  not  found  necessary 
when  the  arrangement  is  used  for  the  engaging  or  disengaging  of  machines, 
but  the  driver  pulley  is  provided  with  flanges  so  that  the 
belt  can  not  slip  off.  Idlers  or  binders  are  of  necessity 
when  the  two  pulleys  are  near  to  each  other,  as  in  steam 
hoist  engines,  either  to  increase  the  bearing  surface  on  the 
pulleys  or  make  up  for  the  slight  weight  of  a  short  belt. 

Belts  run  the  best  when  their  length  and  position  are 
such  as  to  give  the  frictional  stress  without  much  stretching 
on  the  pulleys,  and  without  binders,  and  for  this  purpose 
the  tight  side  of  the  belt — that  is,  the  one  approaching 
the  driver  pulley — should  be  at  its  under  side. 

In  determining  the  necessary  length  of  a  belt  for  any 
position,  the  simplest  way  is  to  measure  it,  if  the  construc- 
tion is  complete ;  if  not,  to  make  a  drawing  of  the  pulleys 
in  position  to  a  scale,  and  measure  on  the  drawing. 

The  width  of  the  belt  should  always  be  a  little  less 
than  the  face  of  the  pulley ;  both  are  to  be  determined  by 
the  power  to  be  transmitted  and  the  velocity  of  movement. 

Allowance  should  be  made  in  calculation  of  speed  of  a 
driven  pulley  for  the  slip  of  the  belt,  which  is  always  some- 
thing, but  should  not  fall  behind  more  than  one  per  cent 
that  of  the  driver ;  the  friction,  with  too  tight  a  belt  is  too 
much,  and  the  slip,  with  a  too  slack  one.  Too  small  dimen- 
sion of  pulley  or  too  little  of  arc  of  contact  increases  slip.  It  does  no  particu- 
lar harm  to  have  a  belt  unnecessarily  wide,  but  it  does  to  have  it  too  narrow. 
If  the  diameter  of  the  pulleys  be  increased,  the  speed  of  the  belt  is  also  in- 
creased, and  for  transmitting  the  same  power,  its  width  decreased. 

By  experiments  of  H.  B.  Gale  at  the  Washington  University,  St.  Louis,  the 
practical  limits  of  speed  of  belt  may  be  taken  at  from  3,000  to  7,000  feet  per 
minute.  The  flesh  side  of  leather  possesses  much  greater  tension  than  the 
grain  or  hair  side,  and  on  this  account,  and  in  the  practice  of  most  mill- 
wrights, the  grain  side  is  put  in  contact  with  the  pulley,  and  in  double  belts 
the  flesh  side  is  placed  centrally. 


FIG.  651. 


John  T.  Henthorn's  formula  for  double  belts  is 


D  x  TT  x  R 


=  H- R  or 


450  450 

per  inch  in  width,  in  which  D  is  the  diameter  of  pulley  in  feet,  R  the  revolu- 
tions per  minute.  This  is  expressed  graphically  in  Fig.  652. 

Use  of  Diagram. — To  find  the  horse  power  that  can  be  transmitted  by  a 
24"  belt  on  a  20-foot  pulley  making  100  revolutions  per  minute :  The  abscissa 
line  100  intersects  the  diagonal  20  on  the  ordinate  line  14 ;  14  x  24  =  336  = 
horse  power  transmissible. 

To  find  the  belt  necessary  to  transmit  100  horse  power  through  a  10-foot 
pulley  and  120  revolutions  per  minute  of  shaft:  The  abscissa  120  cuts  the 

diagonal  10  on  the  ordinate  line  8J;  -.(-  =  12"  width  of  belt.     If  the  pulley 

°i 


292 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


were  12-foot  instead  of  10,  it  will  be  seen  by  the  diagram  that  the  intersection 
of  diagonal  would  be  at  10,  and  the  width  of  belt  -—  =  10". 

This  rule  referred  to  single  belts  capable  of  transmitting  one  half  the  power 
of  the  double  belt,  would  require  a  velocity  of  900  feet  per  minute  for  a  belt  of 


Diameter  of  Pulleys,  shown  by  Diagonals. 


567          8          9         10         u         12         Is 
Horse-Power  per  Inch  of  Width. 
FIG.  652. 

1"  in  width  to  transmit  1  horse  power,  and  if  the  belt  were  triple,  and  running 
with  the  same  velocity,  it  would  transmit  3  horse  power,  which  is  a  rule  in 
common  use. 

The  above  rules  are  applicable  to  India  rubber  and  canvas  belts,  which  are 
largely  used.  They  are  made  of  plies  of  closely  woven  duck,  stitched  and  cross- 
stitched  together,  with  or  without  rubber  between  the  plies  and  on  the  outer 
surfaces;  the  rubber  belts  are  the  only  ones  that  can  be  run  in  wet  places. 
The  plain  duck  belts  depend  largely  on  the  close  stitching  of  the  plies,  and  can 
be  used  as  cross  belts,  or  in  any  place  where  leather  belts  can  be  used. 

There  is  a  great  difference  among  mechanics  as  to  the  amount  of  power 
that  may  be  transmitted  by  a  belt  with  economy,  but  the  rules  as  given  by 
Henthorne  above  are  within  limits  of  practice.  The  Amoskeag  Manufacturing 
Co.,  Manchester,  N.  H.,  run  two  double  belts  each  40"  wide,  and  one  24"  wide, 
on  a  30'  fly-wheel  pulley,  of  110"  face,  making  61  revolutions  per  minute  with 
1,950  indicated  H.  P.  on  the  steam  engine  and  transmitted  through  the  belts, 
say  1,800  H.  P.,  gives  17-3  H.  P.  for  each  inch  in  width  of  belt,  and  Henthorne 
12-8.  The  belts  were  considered  heavily  loaded  but  not  overtaxed. 

Samuel  Webber,  in  the  "  American  Machinist,"  February,  1894,  reports  the 
case  of  a  belt  30"  wide,  f "  thick,  running  for  six  years  at  a  velocity  of  3,900  feet 
per  minute  on  a  pulley  of  5  feet  diameter  and  transmitting  556  H.  P.,  which 
gives  a  velocity  of  210  feet  per  minute  per  inch  width  per  H.  P.  By  Mr.  Fred. 


MACHINE   DESIGN  AND  MECHANICAL  CONSTRUCTIONS.  2(J3 

W.  Taylor's  rule  it  would  be  used  to" -transmit  only  123  H.  P.,  who  as  Mem.  A.  S. 
C.  E.,  in  Vol.  XV.  of  its  "Transactions,"  has  given  conclusions  from  his  prac- 
tical use  of  belts  in  the  running  of  a  machine  shop  day  and  night  for  nine 
years,  a  very  long  life  if  estimated  in  day's  work  of  ten  hours  each,  with  ample 
opportunity  for  repairs,  and  for  narrow  belts  transmitting  power  to  machinery. 
He  finds  by  testing  the  tension  of  belts  by  a  spring  balance  between  two  clamps 
attached  to  the  ends  of  the  belt  whi.e  stretching,  the  most  economical  average 
total  load  for  double  belting  to  be  200  to  225  pounds  per  square  inch  of  sec- 
tion, that  a  total  load  of  111  pounds  per  inch  width  corresponds  to  a  pulling 
power  of  65  pounds,  of  54  pounds  to  26  pounds,  and  that  the  maximum  speed 
for  economy  should  be  from  4,000  to  4,500  feet  per  minute. 

"  Belts  are  more  durable  and  work  more  satisfactorily  when  made  narrow 
and  thick  than  wide  and  thin.  Minimum  diameter  of  pulley  for  a  double  belt 
12",  for  a  triple  20",  for  a  quadruple  30".  The  ends  of  a  belt  should  be  fastened 
together  by  splicing  and  cementing  instead  of  lacing,  wiring,  or  using  hooks  or 
clamps  of  any  kind." 

Leather  belts  may  be  purchased  from  stock  from  1"  to  48"  in  width,  round 
belts  from  £''  to  •§•"  in  diameter. 

Rubber  3-ply  is  equal  to  single  leather.  The  following  are  stock  sizes  :  2-ply 
from  1"  to  28"  width  ;  6-ply  up  to  60"  ;  7-  and  8-ply  to  order. 

Full  rolls  contain  400  to  450  feet,  and  endless  belts  are  made  to  order.  Solid 
cotton  belts,  2-ply  I"  to  6"  wide  ;  4-ply  1"  to  22". 

The  use  of  endless  ropes  instead  of  belts  is  of  very  old  application,  by  single 
lines  of  rope  with  outdoor  exposure,  and  large  pulleys  at  considerable  distances 
apart.  In  Fig.  653  an  arrangement  is  shown  for  the  transfer  of  a  reciprocat- 


FIG.  653. 

ing  power ;  one  end  of  the  rope  is  attached  to  and  wound  on  one  barrel  while 
the  other  end  is  wound  in  an  opposite  direction  on  another  barrel,  so  that  as 
the  ropes  are  unwound  from  one  barrel  they  are  taken  up  by  the  other,  the 
length  of  the  reciprocating  movement  being  the  length  of  transfer  from  one 
barrel  to  the  other. 

This  arrangement  is  sometimes  applied  to  hoists,  and  with  chains  instead  of 
ropes  to  the  old  type  of  planers. 

Of  late  the  use  of  ropes  for  the  t7'ansmission  of  power  has  increased  very 
rapidly  both  in  this  country  and  in  England,  on  account  of  their  economy  in 
first  cost  and  maintenance,  in  transmitting  large  amounts  of  power  to  consider- 
able distances  with  simplicity  in  changes  of  direction  and  distribution  of  power, 
smooth  running,  and  absence  of  slip. 

There  are  two  forms  of  arrangement,  in  one  of  which  a  single  spliced  endless 
rope  by  its  tension  gives  the  necessary  adhesion  (Fig.  654),  and  as  the  rope  grows 
slack  by  use,  taking  it  up  by  a  fresh  splice  ;  in  the  other  the  slack  is  taken  up 
by  a  tension  carriage.  In  both  forms  increase  of  power  is  met  by  multiple 
grooves  or  pulleys  and  in  the  number  of  loops  of  rope. 


294 


MACHINE  DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


Fig.  655  shows  the  tension  carriage  as  applied  to  the  driving  cable  on  the 
Brooklyn  Bridge.     A  is  the  pulley  connected  with  the  steam  engine,  on  which 


FIG.  654. 


there  are  four  grooves  and  lines  of  rope  for  adhesion ;  one  line  passes  over  the 
large  standing  10-foot  sheave  B,  thence  round  the  tension  pulley  C  on  a  weighted 
car  moving  in  inclined  rails,  thence  over  the  sheave  D  to  the  line  of  bridge,  over 


Fio.  655. 


MACHINE   DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


295 


the  bridge  beyond  track,  and  returning  the  other  to  the  pulley  A.  The  cable 
in  diameter  and  general  arrangement  is  similar  to  that  for  cable  roads,  and  is 
only  given  as  an  illustration  of  an  extreme  size  of  tension  car.  For  transmis- 
sion of  power  to  machinery  the  diameter  of  rope  does  not  exceed  2  inches,  and 
the  tension  car  is  usually  a  light  grooved  pulley,  sliding  on  vertical  or  horizon- 


FIG.  656. 

tal  tracks,  with  weights  attached  and  moving  vertically  to  give  the  requisite 
adhesion. 

With  most  makers  the  pulleys  are  single  multiple  grooves,  but  the  Link  Belt 
Engineering  Co.  make  light  pulleys,   with  a  single  groove  to 
each,  which  can  be  bolted  together  to  make  a  multiple  grooved 
sheave  of  the  requisite  number  of  ring  sections. 

"  The  diameter  of  the  pulleys  has  an  important  effect  on  the 
wear  of  the  rope.  The  larger  the  sheaves,  the  less  the  fibres  of 
the  rope  slide  on  each  other,  and  consequently  there  is  less  in- 
ternal wear  of  the  rope.  The  pulleys  should  not  be  less  than 
forty  times  the  diameter  of  the  rope  for  economical  wear,  and 
as  much  larger  as  it  is  possible  to  make  them.  This  rule  applies 
also  to  the  idle  and  tension  pulleys  as  well  as  to  the  main  driv- 
ing-pulley." 

Fig.  G56  is  a  view  of  a  horizontal  tension  carriage  ;  Fig.  657, 
a  half  turn  with  vertical  tension  ;  Fig.  G58,  a  portion  of  the  line 
of  shaft  of  the  factory  of  the  same  company. 

The  usual  material  for  rope  gearing  of  mills  is  either  hemp, 
manilla,  or  cotton.  The  ropes  are  untarred  hawser  laid — that 
is,  formed  with  three  strands  twisted  together  right-handed  ;  a 
strand  is  made  by  twisting  yarns  together  left-handed. 

The  "  Stevedore  "  rope  of  the  Link  Belt  Engineering  Co.  is  a 
4-strand  rope,  manufactured  from  long-fibre  manilla  laid  in  tallow  mixed  with 
plumbago  (to  reduce  the  friction  in  the  bending  of  the  strands  passing  around 


FIG.  G57. 


296 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


the  sheaves),  which  renders  it  nearly  waterproof,  therefore  suitable  for  out-of- 
door  work. 

Fig.  659  represents  a  section  of  the  grooves  of  a  pullc-y  as  designed  by  E. 
D.  Leavitt,  M.  E. 


FIG.  658. 


For  the  strength  of  a  rope,  the  assumption  of  Mr.  C.  W.  Hunt  is  that  "  a 
rope  one  inch  in  diameter  should  have  a  working  strain  of  200  pounds  at  all 
speeds.  This  is  about  one  twentieth  of  the  strength  of  the  splice.  This  large 


\ 


FIG.  659. 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


297 


ROPE  DRIVING. 

Horse  power  of  manilla 
rope  at  various  speeds. 


2i  I 


30          40          50  60          70  80          90          100         110 

VELOCITY  OF  DRIVING  ROPE  IN  FEET  PER  SECOND. 

FIG.  660. 


130        140 


ROPE'  DRIVING. 

The  curves  show  the  sag  of  the 
ropes  when  transmitting  the  normal 
amount  of  power.  It  is  the  same  at 
all  speeds  for  the  driving  part,  but 
variable  for  the  slack  part.  The  sag 
for  the  slack  part  is  computed  for 
speeds  of  40,  60  and  80ft.  per  sec. 


margin  is  to  enable  the  rope  to  perform  a  great  amount  of  useful  work  before 

it  is  so  weakened  by  wear  that  it  is  necessary  to  be  renewed.     There  are  many 

strains  which  can  not  be  computed 

owing   to   the   irregularities  of   the 

power  and  the  work.     The  diagram 

(Fig.  660)  takes  into  consideration 

the  effects  of  the  centrifugal  force 

so  that  the  strain  on  the  rope  is  con- 

stant on  the  driving  side  in  trans- 

mitting the  tabular  horse  power,  no 

matter  what  the  speed  may  be.     It 

shows  also  the  power  a  rope  trans- 

mits  at   various  speeds,  illustrating 

the  rapidity  with  which  the   horse 

power  decreases  when  the  speed  gets 

beyond    about   eighty   feet  per  sec- 

ond." 

It  is  desirable  in  all  cases  of  rope 
transmission  to  so  arrange  the  drive 
that  the  slack  side  of  the  rope  shall 
be  on  the  upper  part  of  the  pulley, 
thus  increasing  the  arc  of  contact,  as 
the  two  sides  will  then  approach 
each  other  when  in  motion. 

In  order  that  the  desired  tensions 
shall  be  attained  in  the  two  parts 
of  a  rope,  the  deflection  or  sag  must 
be  of  predetermined  values.  ' 

Fig.  601  is  another  diagram  of 


„  ™E8 
no.  eei. 


298 


MACHINE   DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


Mr.  Hunt's  showing  the  sag  of  the  rope.  The  rope  is  supposed  to  have  the 
strain  constant  at  all  speeds  on  the  driving  side  and  in  direct  proportion  to  the 
area  of  cross  section,  hence  the  catenary  of  the  driving  side  is  not  affected  by 
the  speed  or  by  the  diameter  of  the  rope. 

The  deflection  between  the  pulleys  on  the  slack  side  varies  with  each  change 
of  load  or  change  of  speed. 

Having  determined  the  sag  of  the  rope  from  the  diagram,  lay  off  the  pulleys 
as  in  Fig.  662,  draw  a  horizontal  line  A  B,  and  from  the  centre  of  this  line  and 
normal  to  it  the  line  E  C  equal  to  the  sag  of  the  rope,  and  construct  a  parabola 


by  dividing  the  line  C  D  into,  say,  five  equal  parts  and  the  line  A  D  into  the  same 
number  of  equal  parts;  the  intersections  of  the  lines  Cl,  C2,  C3,  etc.,  by  the  per- 
pendiculars at  1',  2',  3',  etc.,  give  the  points  of  the  curve. 

The  determination  of  the  sag  of  ropes  whose  points  of  contact  with  their 
pulleys  are  not  level  may  be  determined  by  calculation  ;  but  as  it  can  only  be 
for  one  condition  of  speed  and  load,  it  will  be  sufficient  to  determine  it  practi- 
cally by  taking  a  cord  equal  to  the  whole  distance  between  the  points  of  con- 
tact, and  that  of  the  sag  as  given  by  the  Hunt  diagram,  when  the  sag  is  central. 
Fix  one  end  of  the  cord  and  raise  the  other  to  the  level  of  the  position  it  is  to 
occupy  in  running,  and  the  amount  of  sag  and  its  position  will  be  defined  by 
the  cord.  If  it  is  necessary  to  represent  it  by  drawing,  construct  two  parabolas. 

Wire-rope  power  transmission  is  applicable  for  distances  of  from  50  to  400 
feet,  and  withstands  weather  exposure.  It  is  of  much  less  diameter  than  hemp 
rope  to  transmit  the  same  power  and  has  more  endurance.  For  endurance  the 
diameters  of  wheel  and  rope  and  sag  must  be  proportioned  to  each  other.  The 
table  below  is  from  the  circular  of  the  Trenton  Iron  Works  Co.,  gives  the  pro- 
portionate diameters  of  wheels  and  ropes,  and  the  H.  P.  transmission  at  100 
revolutions : 


Diameter 

Diameter 

Diameter 

Diameter 

Diameter 

Diameter 

of  wheel, 
in  feet. 

of  rope, 
in  inches. 

H.  P. 

of  wheel, 
in  feet. 

of  rope, 
in  inches. 

H.  P. 

of  wheel, 
in  feet. 

of  rope, 
in  inches. 

H.  1 

3 

1 

7 

7 

ft 

36 

9 

4 

82 

4 

* 

9 

6 

f 

38 

10 

f 

91 

5 

1 

11 

7 

£ 

44 

8 

I 

ft 

5 

ft 

16 

8 

£ 

51 

9 

I 

112 

5 

i 

20 

7 

ft 

54 

10 

I 

124 

6 

\ 

24 

8 

1  1 
'i  fi 

01 

8 

l 

13C 

5 

A 

26 

9 

1! 

69 

9 

1 

14( 

G 

ft 

31 

8 

4 

73 

10 

1 

102 

In  applying  this  table  for  a  given  amount  of  horse  power,  preference  should 
be  given  to  the  larger  wheels  as  most  serviceable. 


MACHINE   DESIGN   AND   MECHANICAL  CONSTRUCTIONS. 


299 


If  more  H.  P.  is  to  be  transmitted  Jt  may  be  obtained  by  increasing  the  revo- 
lution in  a  direct  proportion  np  to  the  limit  of  80  feet  per  second,  but  not  by 
the  increase  of  tension  of  rope  as  shown  by  sag,  which  may  be  taken  for  a  span 
of  100  feet  at  •?  feet,  and  for  other  spans  directly  as  their  squares — that  is,  for 
200  feet  it  would  be  •?  X  4  =  2'8  feet.  The  sag  as  given  is  that  measured  from 
a  horizontal  line  through  the  point  at  which  the  rope  leaves  the  wheel.  If  the 
two  wheels  are  not  on  the  same  level  the  sag  must  be  measured  from  the  level 
of  the  point  of  contact  with  the  lower  wheel,  and  the  span  to  be  used  in  deter- 


FIG.  663. 


FIG.  664. 


mining  the  sag  below  this  level  is  the  distance  along  the  horizontal  line  from 
the  wheel  to  the  point  at  which  it  again  intersects  the  rope.  This  point  may 
be  ascertained  by  hanging  a  wire  in  place  on  the  wheels  before  splicing  the  rope. 

If  the  difference  of  level  is  very  great,  run  the  rope  over  intermediate  carry- 
ing sheaves  so  placed  as  to  give  a  level  stretch  of  rope  of  which  the  sag  can  be 
taken  from  the  rule  of  sag. 

Intermediate  supporting  pulleys  should  be  avoided  as  far  as  practicable,  as 
each  one  increases  the  wear  on  the  rope.  When  they  can  not  be  dispensed  with 
they  should  not  be  less  than  one  half  to  two  thirds  the  diameter  of  the  main 
wheels. 

The  sag  of  the  rope  when  doing  full  work  will  be  one  half  that  when  at  rest. 
The  driving-sheaves  should  always  be  lined  with  some  elastic  material,  as  rubber, 
leather,  or  wood.  Figs.  663  and  664  give  the  section  of  grooves  as  made  at  dif- 
ferent works. 


Power-transmission  by  Chains. — Fig.  665  is  a  sectional  perspective  of  a  pul- 
ley in  which  there  is  a  groove  for  the  vertical  links  of  the  chains  and  a  face  for 


300 


MACHINE   DESIGN   AND   MECHANICAL  CONSTRUCTIONS. 


the  horizontal  ones,  which  serve  merely  as  guides  for  hoisting  in  cranes  or  saw- 
mills and  the  like.  By  the  introduction  of  ribs  on  the  face  (Fig.  666)  adapted 
to  the  length  of  the  link  or  pitch 
of  the  chain  the  motion  is  deter- 
minate and  is  used  to  transmit 
power. 

Fig.  667  is  a  sprocket  wheel  for 


FIG.  665. 


FIG.  663. 


FIG.  687. 


punched  links  with  teeth  between  each  link,  especially  adapted  to  position 
where  the  stress  is  great  and  the  movement  slow,  for  which  they  can  readily  be 
proportioned.  '  .- 

The  same  class  of  wheel  and  chains  are  made  light  and  used  as  in  bicycles, 
and  driven  at  considerable  speeds  with  little  friction. 


FIG.  668. 


FIG.  669. 


FIG.  670. 


The  link  belting  is  made  with  malleable  iron  links  and  detachable,  so  that 
the  belt  can  be  readily  lengthened  or  shortened.  The  sprocket  wheels  are 
machine  finished  to  pitch. 

Figs.  668,  669,  and  670  are  drawings  of  links  of  different  forms.     They  are 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


301 


made  of  all  dimensions  to  suit  the  purposes  and  stresses  required.     At  the 

usual  speeds  of  leather  belts,  link  belting  is  noisy  and  wears  rapidly,  but  at 

moderate  speeds — for  conveyors  of 

grain,  clay,  and  the  like — they  are 

admirably  adapted,  and  in  such 

positions  and  conditions  of  speed 

can  be  used  to  transmit  power. 

Leather  link  belting  consists 
of  links  made  of  leather  con- 
nected by  iron  or  steel  pins.  A 
belt  of  this  design  can  be  made  of 
any  width,  works  freely  on  a  pul- 
ley of  small  diameter,  and  can  be 
driven  at  very  high  speed,  which, 
combined  with  its  great  strength, 
make  this  form  of  belt  very  suita-  / 


FIG.  671. 


ble  for  driving  dynamos.  When 
the  link  belt  runs  between  guides, 
or  on  flanged  pulleys,  the  rivet 
heads  are  faced  on  the  outside 
links  with  leather  after  the  belt  is 
riveted  up. 

When  a  link  belt  of  considerable  width  works  on  a  curved  pulley,  either 
there  is  contact  at  the  centre  only,  or  the  pins  are  bent  where  the  band  is  in 
contact  with  the  pulley.  The  belt  in  this  case  is  in  two  or  more  longitudinal 
strips,  hinged  together,  as  shown  in  Fig.  671. 

GEARING. 

The  term  gearing,  in  a  general  sense,  is  applied  to  all  arrangements  for  the 
transmission  of  power;  but,  in  a  particular  sense,  to  toothed  gearing,  which 
may  in  general  be  divided  into  three  classes — spur,  bevel,  and  screw.  In  the 
former  the  axis  of  the  driving  and  driven  wheels  are  parallel  to  each  other;  in 
the  bevel  they  may  be  situated  at  any  angle ;  if  of  equal  size  and  at  right  angles, 
they  are  called  mitre  gears.  In  screw  gearing  a  toothed  wheel  is  driven  by  a 
screw  wifh  their  axes  usually  at  right  angles  to  each  other.  Spur  wheels  are 
termed  external  or  internal,  according  to  the  disposition  of  their  teeth  with  re- 
gard to  the  rim  of  the  wheel. 

Rack  gear  and  pinion  are  employed  to  convert  a  rotary  into  a  rectilinear 
motion,  or  vice  rersa.  In  this  arrangement  the  pinion  is  a  spur  wheel,  acting 
on  teeth  placed  along  a  straight  bar  (Fig.  680). 

Bevel  gearing  consists  of  toothed  wheels  formed  to  work  together  in  differ- 
ent planes,  their  teeth  being  disposed  at  an  angle  to  the  plane  of  their  faces. 

Trundle  pins  or  Avheels  (Fig.  672)  are  constructed  with  cylindrical  pieces 
called  staves  or  pins,  instead  of  teeth.  A  pinion  with  double  plates  is  called  a 
lantern ;  the  wheel,  a  face  or  crown  wheel ;  this  construction  is  very  useful 
when  iron  gears  can  not  be  easily  obtained  or  repaired. 

Fundamental  principle. — In  order  that  two  circles  A  and  B  (Fig.  673)  may 
be  made  to  revolve  bv  the  contact  of  the  surfaces  of  the  curves  m  m  and  n  n  of 


302 


MACHINE   DESIGN   AND   MECHANICAL   CONSTRUCTIONS. 


their  teeth  precisely  as  they  would  by  the  friction  of  their  circumferences,  it  is 
necessary  and  sufficient  that  a  line  drawn  from  the  point  of  contact  t  of  the 
teeth  to  the  point  of  contact  c  of  the  circumferences  (pitch-circles)  should,  in 


every  position  of  the  point  £,  be  perpendicular  or  normal  to  the  surfaces  of  con- 
tact at  that  point  to  both  the  curves  m  m  and  n  n,  a  particular  property  of  that 
curve  known  as  the  cycloid. 

When  one  wheel  conducts  the  other,  it  is  called  the  driver  or  leader,  and  the 
other  the  driven  or  follower.  The  angular  velocities  of  the  pitch  circles  is  the 
same,  but  the  number  of  revolutions  of  the  wheels  is  inversely  as  their  diam- 
eters taken  at  the  pitch  circles.  If  the  driver  is  24"  diameter,  making  120 
revolutions  per  minute,  and  the  driver  is  required  to  make  200  revolutions  per 
minute,  then  the  diameter  of  the  driven  gear  would  be 

120  x  24          4" 
200  I410 ' 

Fig.  674  gives  the  designation  of  the  various  parts  of  a  spur  wheel  by  whicli 
names  they  will  hereafter  be  called. 


Pitch  Cirple_L._ 


FIG.  074. 


MACHINE   DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 

There  is  considerable  variation  in  the  proportion  of  teeth,  as — 
Thickness  of  teeth,  from  '45  to  '48  pitch. 
Space  between  teeth,  from  -55  to  '52  pitch. 


303 


Height  of  teeth  outside  pitch  circle,  from  -2  to  -3  pitch. 

Depth  of  teeth  inside  pitch  circle,  from  *3  to  *4  pitch. 

The  above  is  for  cast  teeth,  used  without  finishing  ;  the  teeth  are  made 
narrower  than  the  space,  arid  the  height  less  than  the  depth  on  account  of  the 
irregularities  of  a  rough  casting.  The  teeth  and  space,  when  machine  cut,  may 
be  made  the  same  or  very  nearly  so. 

The  cycloid  (Fig.  675)  is  a  curve  described  by  any  point  on  the  circumfer- 
ence of  a  circle  on  a  straight  line  as  a  base  which  is  the  pitch  line  of  the  rack 
in  its  application  to  the  formation  of  teeth  of  a  rack  and  pinion. 

Divide  the  circumference  of  the  generating  or  rolling  circle  A  into  a  mini- 


304: 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


her  of  equal  parts,  say  12  ;  draw  chords  from  each  of  these  points  to  0 ;  divide 
the  base  line  into  an  equal  number  of  parts  of  the  same  length  as  the  arcs  of 
the  generating  circle  numbered  0,  1',  2',  etc.,  and  from  each  of  these  points 
erect  a  perpendicular  intersecting  the  centre  of  the  circle  A  B  at  1",  2",  etc. ; 
from  each  of  these  points  describe  arcs  with  a  radii  equal  to  the  generating 
circle.  From  the  points  1',  2',  3',  4',  etc.,  on  the  base  line,  and  with  radii  equal 
successively  to  the  chords  0  1,  0  2,  0  3,  0  4,  etc.,  describe  arcs  cutting  the  pre- 
ceding, the  intersections  will  be  points  of  the  required  curve. 

The  epicycloid  (Fig.  676)  is  a  cycloid  formed  on  the  circumference  of  a 
circle  as  base,  which,  in  its  application  to  the  teeth  of  wheels,  is  the  pitch  circle 
of  external  gearing. 

The  path  of  the  centre  of  the  generating  circle  is  concentric  with  the  base 
circle.  Divide  the  generating  circle  from  0  and  the  arc  of  the  base  circle  into 
the  same  number  of  equal  parts.  Eadiai  lines  from  C,  passing  through  1',  2', 
etc.,  and  intersecting  A  B,  give  the  points  from  which  the  arcs  of  the  generat- 
ing circle  are  described ;  from  the  points  1',  2',  3',  etc.,  on  the  base  circle,  and 
with  radii  equal  successively  to  the  chords  0  1,  0  2,  0  3,  etc.,  describe  arcs  cut- 
ting the  preceding;  the  intersections  are  points  in  the  required  curve. 

The  hypocycloid  (Fig.  677)  is  a  cycloid  with  a  base  of  the  interior  circum- 
ference of  a  circle  corresponding  to  the  pitch  circle  of  internal  gearing. 


5'  6' 


Proceed  as  in  the  previous  example  and  divide  the  generating  circle  and 
base  line  into  equal  parts,  describe  the  path  of  the  centre  of  the  generating 
circle  A  B  concentric  with  the  base  circle,  and  from  each  division  of  the  base 
line  draw  radial  lines  from  C,  intersecting  the  line  A  B  at  1",  2",  etc. ;  from 
these  centres  describe  arcs  of  a  radius  equal  to  the  generating  circle ;  from  the 
points  1',  2',  3',  etc.,  on  the  base  circle,  and  with  radii  equal  successively  to  the 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


305 


chords  0  1,  0  2,  0  3,  etc.,  describe  arcs- cutting  the  preceding;  the  intersections 
are  points  of  the  required  curve. 

INVOLUTE. 

The  involute  (Fig.  678)  is  the  curve  described  by  the  end  of  a  string  being 
unwound  from  the  circumference  of  a  circle. 


FIG.  678. 

Divide  the  circumference  of  the  given  circle  into  any  number  of  equal  parts, 
as  0,  1,  2,  etc.  At  each  of  these  points  draw  tangents  to  the  given  circle ;  on 
the  first  of  these  lay  off  the  distance  1-1',  equal  to  the  arc  0-1 ;  on  the  second 
lay  off  2-2',  equal  to  twice  the  arc  0-1  or  the  arc  0-2  ;  establish  in  a  similar 
way  the  points  3',  4',  5',  as  far  as  may  be  necessary,  which  are  points  in  the 
required  curve. 

The  involute  curve  may  be  described  mechanically  in  several  ways.  Thus, 
let  A  (Fig.  679)  be  the  centre  of  a  wheel  for  which  the  form  of  involute  teeth 
is  to  be  found.  Let  m  n  a  be  a 
thread  lapped  round  its  circum- 
ference, having  a  loop-hole  at  its 
extremity,  a;  in  this  fix  a  pin, 
with  which  describe  the  curve  or 
involute  a  b  .  .  .  .  h,  by  unwinding 
the  thread  gradually  from  the 
circumference,  and  this  curve  will 
be  the  proper  form  for  the  teeth 
of  a  wheel  of  the  given  diameter. 

In  all  the  problems  in  which 
curves  have  been  determined  by  6_9 

the  position  of  points,  the  more 
numerous  the  points  the  more  accurately  can  the  curve  be  drawn. 

Spur  Wheel  and  Rack  (Fig.  680). — The  pitch-circle  of  the  spur  wheel  is 
drawn  and  the  proper  curve  for  the  flank  and  face  of  the  teeth  obtained  by 
21 


306 


MACHINE  DESIGN  AND  MECHANICAL   CONSTRUCTIONS. 


rolling  a  generating  circle  on  the  inside  and  outside  of  the  pitch-circle ;  thus 
the  point  A'  on  the  generating  circle  gives  for  the  flank  of  the  teeth  the  hypo- 
cyeloid  A'  B',  and  for  the  face  the  epicycloid  A'  C'. 


FIG.  680. 


The  curve  for  the  teeth  of  the  rack  is  obtained  by  rolling  the  same  generat- 
ing circle  on  the  upper  and  lower  side  of  the  rack  pitch-line,  giving  two  cy- 
cloids, A  C  and  A  B,  for  the  face  and  flank  of  the  teeth.  The  diagram  showing 
the  construction  of  above  curves  is,  to  avoid  confusion,  separate  from  the  draw- 
ing of  the  spur  wheel  and  rack. 

The  diameter  of  the  generating  circle  is  to  a  certain  extent  arbitrary.  In  this 
and  the  following  examples  it  is  taken  at  a  little  less  than  the  radius  of  the 
smallest  spur  wheel ;  if  taken  at  exactly  the  radius,  the  flanks  of  the  teeth  of 
this  wheel  will  be  radial  lines,  which  is  not  usually  as  satisfactory  as  where  the 
flanks  are  of  hypocycloidal  form,  as  the  teeth,  being  narrower  at  the  root,  have 
a  tendency  to  break  at  this  point. 

When  a  number  of  wheels  are  intended  to  gear  together,  the  same  size  of 
generating  circle  and  the  same  pitch  and  dimensions  of  the  teeth  must  be  main- 
tained. The  generating  circle  should  never  be  larger  than  the  radius  of  the 
smallest  wheel  of  the  set. 

Where  a  drawing  of  a  whole  wheel  is  to  be  made,  the  circumference  can  be 
divided  by  radial  lines  into  the  same  number  of  parts  as  there  are  teeth.  The 
curve  of  one  tooth  having  been  found,  a  templet  can  be  made  and  applied 
successively;  or  find  an  arc  of  a  circle  corresponding  as  closely  as  possible 
to  the  cycloidal  curve,  and  apply  this  at  the  proper  divisions  ;  the  latter  way 
is  the  more  common. 

Spur  Wheels. — Fig.  681  shows  two  wheels  gearing  together,  one  of  ten  and 
the  other  of  thirty  teeth.  The  diameter  of  the  generating  circle  is  less  than 
the  radius  of  the  pitch-circle  of  the  smaller  wheel ;  when  the  generating  circle 
rolls  on  the  exterior  and  interior  of  both  pitch-circles,  it  will  in  the  former 
case  generate  the  faces  of  the  teeth  as  shown  at  A  C  and  A'  C',  and  in  the  latter 


MACHINE  DESIGN  AND  MECHANICAL   CONSTRUCTIONS. 


307 


case  their  flanks  A  B  and  A'  B'.     In  Bother  respects  the  construction  is  similar 
to  the  former  example. 

The  simplest  illustration  of  the  action  of  epicycloidal  teeth  is  when  they  are 
employed  to  drive  a  trundle,  as  represented  in  Fig.  672.    Let  it  be  assumed  that 


FIG.  681. 


the  staves  of  the  trundle  have  no  sensible  thickness  ;  that  the  distance  of  their 
centres  apart,  that  is  their  pitch,  and  also  their  distance  from  the  centre  of  the 
trundle,  that  is  their  pitch-circle,  are  known.  The  pitch-circles  of  the  trundle 
and  wheel  being  then  drawn  from  their  respective  centres  B  and  A,  set  off  the 
pitches  upon  these  circumferences,  corresponding  to  the  number  of  teeth  in  the 
wheel  and  number  of  staves  in  the  trundle  ;  let  five  pins,  a  b  c,  etc.,  be  fixed  into 
the  pitch-circle  of  the  trundle  to  represent  the  staves,  and  let  a  series  of  epicy- 
cloidal arcs  be  traced  with  a  describing  circle,  equal  in  diameter  to  the  radius 
of  the  pitch-circle  of  the  trundle,  and  meeting  in  the  points  klmn,  etc.,  alter- 
nately from  right  and  left.  If  motion  be  given  to  the  wheel  in  the  direction 
of  the  arrow,  then  the  curved  face  m  r  will  press  against  the  pin  b,  and  move 
it  in  the  same  direction ;  but  as  the  motion  continues,  the  pin  will  slide  up- 
ward till  it  reaches  w,  when  the  tooth  and  pin  will  quit  contact.  Before  this 
happens,  the  next  pin  a  will  have  come  into  contact  with  the  face  a  I  of  the  next 
tooth,  which,  repeating  the  same  action,  will  bring  the  succeeding  pair  into  con- 
tact ;  and  so  on  continually. 

To  allow  of  the  required  thickness  of  staves,  it  is  sufficient  to  diminish  the 


308 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


size  of  the  teeth  of  the  wheel  by  a  quantity  equal  to  the  radius  of  the  staves 
(sometimes  increased  by  a  certain  fraction  of  the  pitch  for  clearance)  by  draw- 
ing within  the  primary  epicycloids,  at  the  required  distance,  another  series  of 
curves  parallel  to  these.  In  practice,  a  portion  must  be  cut  from  the  points  of 
the  teeth,  and  also  a  space  must  be  cut  out  within  the  pitch-circle  of  the  driver, 
to  allow  the  staves  to  pass ;  but  no  particular  form  is  requisite ;  the  condition  to 
be  attended  to  is  simply  to  allow  of  sufficient  space  for  the  staves  to  pass  with- 
out contact. 

Internal  Gearing  (Fig.  682). — Draw  the  spur  wheel  as  in  the  previous  exam- 
ples ;  the  face  of  the  teeth  of  the  internally  geared  wheel  will  be  the  hypocycloid 


FIG.  682. 

A  0,  formed  by  the  generating  circle  rolling  on  the  interior  of  the  pitch-circle, 
and  the  flanks  the  epicycloid  A  B,  formed  by  the  generating  circle  rolling  on  the 
exterior  of  the  pitch-circle. 

INVOLUTE    TEETH. 

Fig.  683  is  a  pair  of  spur  wheels  showing  the  mode  of  drawing  involute  teeth. 
The  addendum,  pitch,  and  root-circles  of  both  wheels  are  first  drawn,  then  the 
base-circles  of  the  two  wheels,  which  must  bear  the  same  proportion  to  each  other 
as  the  pitch-circles.  To  arrive  at  this  proportion  a  semicircle  is  constructed  on 
the  line  A  C  B  with  a  diameter  equal  to  the  radius  A  0  of  the  pinion  ;  a  per- 
pendicular erected  where  the  larger  addendum-circle  intersects  the  line  A  C  B 
intersects  the  semicircle  at  E ;  a  line  is  then  drawn  from  A  to  E  and  a  normal  to 
it  at  E  of  indefinite  length ;  then  from  B  a  parallel  to  A  E  intersecting  the  nor- 
mal at  E' ;  circles  concentric  to  the  pitch-circles  drawn  through  E  and  E'  give 
the  base-circles. 

All  teeth  on  the  line  E  E'  will  be  in  contact  at  the  same  time,  called,  there- 
fore, the  line  of  contact.  The  involute  curves  of  the  teeth  of  both  wheels  are 
drawn  from  their  respective  base-circles,  which  correspond  to  the  given  circle  of 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


309 


Fig.  678.     Both  involutes  in  Fig.  683  start  from  the  point  of  contact  E,  hence 
one  curve  is  described  forward,  the  other  backward. 

Thus  on  the  normal  E'  E  there  are  eight  parts,  and  from  the  commencement 
of  the  next  normal  seven  parts  are  marked  off,  the  next  six,  and  so  on  until 
finally  the  involute  reaches  the  base-circle.  The  part  of  the  tooth  within  the 
base-circle  may  be  a  radius  to  it  and  tangent  to  the  involute,  and  small  fillets 
should  be  drawn  connecting  their  roots  to  the  root-circle. 


Fio.  683. 

A  pinion  gearing  into  a  rack  is  shown  in  Fig.  684.  The  faces  of  the  teeth  of 
the  rack  can  be  taken  at  an  angle  of  23°  with  the  perpendicular ;  this  angle 
gives  the  longest  line  of  contact,  which  may  be  considered  the  pitch-line  of  the 
rack,  and,  the  pitch-circle  of  the  pinion  being  indicated,  the  base-circle  for  the 
construction  of  the  involute  curves  is  obtained  by  drawing  a  line  through  the 
point  C'  where  the  two  pitch-lines  come  together  at  an  angle  of  23°  with 
the  horizontal  and  where  a  normal  from  this  line  intersects  the  centre  C  of  the 
pinion  a  line  is  drawn,  and  through  its  junction  E  of  the  line  of  contact  a 
base-circle  is  described ;  at  this  point  E  the  involute  is  drawn  as  in  the  pre- 
vious example.  As  in  cycloidal  teeth,  the  exact  curve  may  be  laid  down  for  one 
tooth,  and  an  arc  corresponding  as  closely  as  possible  to  the  involute  used  to 
describe  the  remainder. 

All  involute  wheels  whose  teeth  have  the  same  pitch  and  obliquity  to  the 
line  of  contact  work  well  together,  but  no  wheel  should  have  less  than  twelve 
teeth  to  work  well. 

Involute  wheels  can  not  be  made  with  very  long  teeth,  because  the  obliquity 
of  the  line  of  contact  will  be  too  great. 

The  diameters  of  spur  wheels  are  in  proportion  to  the  number  of  their  revo- 


310 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


lutions  per  minute,  but  the  relative  sizes  of  a  pair  of  bevel  wheels  is  determined 
by  a  division  of  the  angle  included  between  the  two  axes  inversely  as  the  ratio 


FIG.  684. 

of  their  angular  velocities.  Let  B  and  C  (Fig.  685)  be  the  position  of  the  two 
given  axes,  and  let  them  be  prolonged  till  they  meet  in  a  point  A.  Further,  let 
it  be  required  that  C  makes  seven  revolutions  while  B  makes  four.  From  any 
points  D  and  E  in  the  lines  A  B,  A  C,  and  perpendicular  to  them,  draw  D  d 
and  E  e  of  lengths  (from  a  scale  of  equal  parts)  inversely  as  the  number  of  rev- 
olutions which  the  axes  are  severally  required  to  make  in  the  same  unit  of  time. 
Thus,  the  angular  velocity  of  axis  B  being  4,  and  that  of  the  axis  C  being  7, 
the  line  D  d  must  be  drawn  =  7,  and  the  line  E  e  —  4.  Then  through  d  and  e 
parallel  with  the  axes  A  B  and  A  C  draw  d  c  and  e  c  till  they  meet  in  c.  A 
straight  line  drawn  from  A  through  c  will  then  make  the  required  division 

of  the  angle  BAG,  and  define  the 
line  of  contact  of  the  two  cones, 
by  means  of  which  the  two  rolling 
frusta  may  be  projected  at  any 
convenient  distance  from  A. 

If  the  relative  perimeters,  di- 
ameters, or  radii,  of  the  pair  have 
been  determined,  then  the  lines  D 
d  and  E  e  are  to  each  other  direct- 
ly as  these  quantities.  B  F  and 
C  F  are  radii  of  the  pitch-circle. 

The  case  in  which  the  axes  are 

FIG.  ess.  neither   parallel    nor   intersecting 

admits  of  solution  by  means  of  a 

pair  of  bevels  upon  an  intermediate  axis,  so  situated  as  to  meet  the  others  in 
any  convenient  points. 

When  the  contiguity  of  the  shafts  is  such  as  to  permit  of  their  being  con- 
nected by  a  single  pair,  skewed  bevels  (Fig.  702)  are  sometimes  employed. 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


311 


When  the  axes  are  at  right  angles  to  each  other,  and  do  not  intersect,  the 
wheel  and  screw  may  be  employed  to  connect  them.  The  velocity  of  motion  is 
in  this  arrangement  immediately  deduced  from  that  of  the  screw,  its  number 
of  threads,  and  the  number  of  teeth  in  its  gearing-wheel.  Thus,  if  it  be  re- 
quired to  transmit  the  motion  of  one  shaft  to  another,  contiguous  and  at  right 
angles  to  it — the  angular  motions  being  as  20  to  1 — then,  if  the  screw  be  a 
single-threaded  one,  the  wheel  must  have  20  teeth  ;  but  if  double-threaded,  the 
number  of  teeth  will  be  increased  to  40,  for  2  teeth  will  be  passed  at  every  revo- 
lution. If  the  screw  have  few  threads  compared  with  the  number  of  teeth  of 
the  wheel,  it  must  always  assume  the  position  of  driver  on  account  of  the  ob- 
liquity of  the  thread  to  the  axis  ;  and  in  this  respect  its  action  is  analogous  to 
that  of  a  travelling  rack,  moving  endwise  one  tooth,  while  the  screw  makes  one 
revolution  on  its  axis. 

If  the  pitch-circle  be  divided  into  as  many  equal  parts  as  there  are  teeth  to 
be  given  to  the  wheel,  the  length  of  one  of  these  parts  is  termed  the  pitch  of 
the  teeth. 

The  pitch  depends  on  the  power  to  be  transmitted  or  the  stress  on  each  tooth. 
The  diagram  (Fig.  686)  is  by  John  T.  Henthorn,  M.  E.,  in  which  pitch  and 


1,000          2,000 


3,000          4,000          5,000 
Stress  in  Pounds. 

Fio.  686. 


6,000 


7,000          8,000      9,000 


face,  represented  by  multiples  of  the  pitch,  are  proportioned  to  the  stress  in 
pounds. 

If  the  pitch  be  known,  the  number  of  teeth  in  a  wheel  can  be  determined 
approximately  by  dividing  the  circumference  of  the  wheel  by  the  pitch,  but 
there  must  be  no  remainder  in  the  quotient — there  can  be  no  fraction  of  a  pitch 
— either  the  pitch  or  diameter  of  wheel  must  be  changed  to  produce  this  re- 
sult ;  generally  the  latter,  as  gears  are  usually  made  of  determinate  inches  and 
fractions,  as  given  in  the  table,  by  which  also  calculation  for  diameters  and 
number  of  teeth  is  much  simplified. 


312 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


Example  1. — Given  a  wheel  of  88 
teeth,  2^-inch  pitch,  to  find  the  di- 
ameter of  the  pitch-circle.  Here  the 
tabular  number  in  the  second  col- 
umn answering  to  the  given  pitch  is 
•7958,  which  multiplied  by  88  gives 
70-03  for  the  diameter  required. 

2.  Given  a  wheel  33  inches  diam- 
eter, If-inch  pitch,  to  find  the  num- 
ber of  teeth.  The  corresponding 
factor  is  1-7952,  which,  multiplied 
by  33,  gives  59-242  for  the  number 
of  teeth — that  is,  59£  teeth  nearly. 
Now  59  would  here  be  the  nearest 
whole  number,  but  as  a  wheel  of  60 
teeth  may  be  preferred  for  conven- 
ience of  calculation  of  speeds,  we 
may  adopt  that  number,  and  find 
the  diameter  corresponding.  The 
factor  in  the  second  column  answer- 
ing to  If  pitch  is  -557,  and  this  mul- 
tiplied by  60  gives  33-4  inches  as  the 
diameter  which  the  wheel  ought  to 
have. 

Another  mode  of  sizing  wheels  in 
relation  to  their  pitches,  diameters, 
and  number  of  teeth,  is  adopted,  in 
some  machine  shops,  by  dividing  the 
diameter  of  the  pitch-circle  into  as 
many  equal  parts  as  there  are  teeth 
to  be  given  to  the  wheel.  To  illus- 
trate this  by  an  arithmetical  exam- 
ple, let  it  be  assumed  that  a  wheel  of 
20  inches  diameter  is  required  to  have 

40  teeth  ;  then  the  diametral  pitch, 
20       1 

77:  =  —  =  4-  inch  ; 
40       m       2 

that  is,  the  diameter  being  divided  into  equal  parts  corresponding  in  number 
to  the  number  of  teeth  in  the  circumference  of  the  wheel,  the  length  of  each 
of  these  parts  is  %  an  inch,  consequently  m  =  2 ;  and  according  to  the  phrase- 
ology of  the  workshop,  the  wheel  is  said  to  be  one  of  two  pitch. 

A  decided  advantage  is  obtained  by  the  use  of  the  diametral-pitch  sys- 
tern,  since  circular  pitch  =  di*™-*  f^6,  diam.  =  circ.  pitch  X  No.  of  teeth 


D  =  —  x  N. 

N  =  -p-  x  D. 

PITCH  IN 

RULE.—  To  find  the 

RULE.—  To  flnd  the 

INCHES 
AND 

diameter  in    inches. 

number    of   teeth, 

PARTS  OF 

multiply  the  number 

multiply    the    given 

AN  INOII. 

of  teeth  by  the  tabu- 

diameter  in    inches 

lar  number  answer- 

by the  tabular  num- 

ing   to    the    given 

ber  answering  to  the 

pitch. 

given  pitch. 

Values  of 

p. 

P 

Values  of  — 

Values  of-p- 

6 

1-9095 

•5236 

5 

1-5915 

•6283 

4| 

1-4270 

•6981 

4 

1-2732 

•7854 

3* 

1-1141 

•8976 

3 

•9547 

1-0472 

2f 

•8754 

1-1333 

2^ 

•7958 

1-2566 

2* 

•7135 

1-3963 

2 

•6366 

1-5708 

i| 

•5937 

1-6755 

If 

•5570 

1-7952 

If 

•5141 

1-9264 

H 

•4774 

2-0944 

If 

•4377 

2-2848 

IJ 

•3979 

2-5132 

H 

•3568 

2-7926 

i 

•biss 

3-1416 

1 

•2785 

3-5904 

i 

•2387 

4-1888 

i 

•1989 

5-0266 

i 

•1592 

6-2832 

i 

•1194 

8-3776 

* 

•0796 

12-5664 

No.  of  teeth 

which  always  brings  out  the  diameter  as  a  number  with  an  inconvenient  frac- 
tion if  the  pitch  is  in  even  inches  or  simple  fractions  of  an  inch.  By  the  di- 
ametral-pitch system  the  diameter  may  be  in  even  inches  or  convenient  frac- 
tions, and  the  number  of  teeth  is  usually  an  even  multiple  of  the  number  of 
inches  in  the  diameter. 


MACHINE  DESIGN  AND    MECHANICAL   CONSTRUCTIONS.  313 

RELATION  OP   DIAMETRAL   TO   CIRCULAR   PITCH. 


Diametral 
pitch. 

Circular 
pitch. 

Diametral 
pitch. 

Circular 
pitch. 

Circular 
pitch. 

Diametral 
pitch. 

Circular 
pitch. 

Diametral 
pitch. 

In 

In. 

In. 

In 

1 

3-142 

11 

0-286 

3 

1-047 

fl 

3  "SSI 

H 

2-094 

12 

0-262 

24 

1-257 

1 

3-590 

2 

1-571 

14 

0-224 

2 

1-571 

IS 

3-867 

2i 

1-396 

16 

0-196 

11 

1-676 

1 

4-189 

24 

1-257 

18 

0-175 

If 

1-795 

« 

4-570 

dt 

1-142 

20 

0-157 

If 

1-933 

f 

5-027 

3 

1-047 

22 

0-143 

H 

2-094 

A 

5-585 

8| 

0-898 

24 

0-131 

We 

2-185 

4 

6-283 

4 

0-785 

26 

0-121 

If 

2-285 

ft 

7-181 

5 

0-628 

28 

0-112 

1A 

2-394 

t 

8-378 

6 

0-524 

30 

0-105 

1* 

2-513 

A 

10-053 

7 

0-449 

32 

0-098 

1A 

2-646 

* 

12-566 

8 

0-393 

36 

0-087 

H 

2-793 

A 

16-755 

9 

0-349 

40 

0-079 

1A 

2-957 

i 

25-133 

10 

0-314 

48 

0-065 

1 

3-142 

A 

50-266 

To  find  the  outside  diameter  of  spur-gear  blanks,  add  two  parts  of  the  pitch  to 
the  pitch  diameter.  Thus  for  an  8-pitch  gear  of  40  teeth  the  outside  diameter 
of  blank  is  ^-,  equal  to  5£  inches ;  for  a  12-pitch  gear  of  36  teeth  the  outside 
diameter  of  blank  is  ^f ,  equal  to  3£  inches ;  for  a  16-pitch  gear  of  46  teeth  the 
outside  diameter  of  blank  is  ff,  equal  to  3  inches. 

To  obtain  the  distance  between  the  centres  of  two  gears,  add  the  number  of 
teeth  together  and  divide  half  the  sum  by  the  diametral  pitch.  Thus  if  two 
gears  have  40  and  30  teeth  respectively  and  are  5  pitch,  add  40  and  30,  making 
70,  divide  by  2,  and  then  divide  this  quotient  35  by  the  diametral  pitch  5,  and 
the  result,  7  inches,  is  the  distance  between  centres. 

It  is  a  common  practice  of  shops  to  take  as  the  diameter  of  the  rolling  circle 
the  radius  of  the  smallest  pinion  which  will  ever  be  used  for  gears  of  this  pitch, 
and  constructing  the  epicycloids  for  different  diameters  of  this  pitch,  and  allow- 
ing arcs  of  circles  corresponding  very  closely  to  these  epicycloids.  On  this 
principle  Robert  Adcock,  C.  E.,  constructed  a  table  of  radii  for  these  arcs,  for 
rolling  circles  of  pinions  of  8,  10,  and  12  teeth.  We  give  the  last  only  as  best 
suited  to  the  usual  conditions  of  practice  : 

TABLE   OP  RADII  OP   ARCS  OP   CIRCLES   FOR  GEAR  TEETH. 


•3 

CJ 

SMALLEST   PINION, 

•3 

0) 

SMALLEST   PINION, 

3 

<u 

SMALLEST  PINION, 

I 

*s2 

TWELVE  TEETH. 

3 

=1 

TWELVE   TEETH. 

« 
jjj 

*! 

TWELVE   TEETH. 

o 

aa 

Radii  of  the  Eadii  of  the 

"3 

V 

.2^ 

Radii  of  the 

Radii  of  the 

s| 

Radii  of  the 

Radii  of  the 

X 

'•3  £ 

faces  of    i     flanks  of 

,-; 

^5  -ij 

faces  of 

flanks  of 

^s 

faces  of 

flanks  of 

st 

So, 

teeth.             teeth. 

£ 

a  -a 

teeth. 

teeth. 

1 

Mft 

teeth. 

teeth. 

12 

1-93 

1-88  0-75 

27 

4-31 

4-23 

0-84 

4-63 

1-41 

42 

6-69 

6-60!0'89 

6-91 

1-20 

13 

2'09 

2-040-76    7-45 

7-14 

28 

•46 

•39 

•85 

•37 

•38 

43 

•85 

•76 

•89 

7-06 

•20 

14 

2-25 

•19    '77    4-86 

4-27 

29 

•62 

•55 

•85 

•92 

•36 

44 

7-01 

92 

•89 

•22 

•19 

15 

2-40 

•35 

•78    3-92 

3-04 

30 

•78 

•70 

•86 

5-07 

•34 

45 

•17 

7-07 

•89 

•38 

•18 

16 

2-56 

•50 

•78      -62 

3-53 

31 

•94 

•86 

•86 

•21 

•32 

46 

•33 

•23 

•90 

•53 

•18 

17 

2-72 

•66 

•79      -58 

2-22 

32 

5-10 

5-02 

•86 

•37 

•30 

47 

•49 

•39 

•90 

•09 

•17 

18 

2-88 

•82    -80      -59 

2-02 

33 

•26 

•18 

•86 

•52 

•29 

48 

•64 

•55 

•90 

•84 

•16 

19 

3-04 

•97    -81  1     -63 

1-87 

34 

•42 

•34 

•87 

•67 

•28 

49 

•80 

•71 

•90 

8-00 

•16 

20 

3-20 

3-13 

•81  1      -73 

1-76 

35 

•58 

•49 

•87 

•82 

•26 

50 

•96 

•86 

•90 

•96 

•16 

21 

3-35 

•29 

•82      -83 

1-68 

36 

•74 

•65 

•87 

•97 

•25 

51 

8-12 

8-02 

•91 

•31 

•16 

22 

3-51 

•44 

•82      -95 

1-61 

37 

•90 

•81 

•88 

6-13 

•24 

52 

•28 

•18 

•91 

•47 

•If 

23 

3-67 

•60 

•83'  4-07 

1-56 

38 

6-05 

•97 

•88 

•29 

•23 

53 

•44 

•34 

•91 

•63 

•11 

24 

3-83 

•76 

•83      -21 

1-51 

39 

•21 

6-13 

•88 

•44 

•23 

54 

•60 

•50 

•91 

•79 

•14 

25 

3-99 

•91 

•84      -34 

1.47 

40 

•37 

•28 

•88 

•60 

•22 

55 

•76 

•66 

•91 

•95 

•14 

26 

4-15 

4-07J  -84J     -48 

1-44 

41 

•53 

•44 

•89 

•75 

•21 

56 

•92 

•81 

•91 

9-10 

•14 

314          MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


jj 

,2                SMALLEST   PINION, 

^              _®     |           SMALLEST  PINION,          ||    £ 

,2'               SMALLEST   PINION, 

I 

fc.  g                 /TWELVE   TEETH. 

°o   ! 

!  J 

V.  g     !             TWELVE   TEETH. 

»-  g                  TWELVE   TEETH. 

•53 

6 

j».g    Radii  of  the 
•g  *;       faces  of 

Radii  of  the 
flanks  of 

4-1 

O 

o 

II 

Radii  of  the 
faces  of 

Radii  of  the      *S 
flanks  of 

J  .g    Radii  of  the 
"3  *j        faces  of 

Radii  of  the 
flanks  of 

(2  °-         teeth. 

teeth. 

£ 

""      '-' 

teeth. 

teeth.            szj 

K  A         teeth. 

teeth. 

67 

9-08    8-97 

0-91 

9-26    1-13 

120  19-10 

18-99 

1910 

183  29-13  29-00 

•97 

29-27 

68 

•23    9-13 

•91 

•42 

•13 

121 

•26 

1915 

•42 

1-06 

184 

•28:     -IB 

i 

•43 

1-03 

69 

•37|     '29 

•92 

•57 

•13 

122 

•42 

•30 

•95 

•57 

185        -44      -32 

•59 

60 

•55      -45 

•92 

•73 

•13 

123 

•58 

•46 

•73 

•06 

186       -60 

•48 

•97 

•74 

1-03 

61 

•71     -61 

•92 

•89 

•12 

124 

•74 

•62 

•89 

187 

•76 

•64 

•90 

62 

•87 

•77 

•92 

10-05 

•12 

125 

•90 

•78 

•95 

20-05 

•06 

188 

•92 

•80 

30-06 

63 

10-03      -92 

•92 

•20 

•12 

126 

20-05 

•94 

•21 

189 

30-08 

•96 

•98 

•22 

1-03 

64 

•19  10-08 

•92 

•36 

•12 

127 

•21 

2010 

•37 

•05 

190 

•24 

3012 

•38 

65 

•35      -24 

•92 

•62 

•12 

128 

•37 

•26 

•96 

•53 

191 

•40 

•28 

•98 

•54 

1-02 

66 

•51       -40 

•92 

•68 

•11 

129 

•53 

•42 

•69 

•05 

192 

•55 

•48 

•70 

67 

•67      '56 

•92 

•84 

•11 

130 

•68 

•58 

•84 

193 

•71 

•59 

•86 

6S 

•83 

•72 

•92 

•99 

•11 

131 

•84 

•74 

•96 

21-00 

•05 

194 

•87 

•75 

•98 

31-02 

1-02 

69 

•98 

•88 

•93 

11-15 

•11 

132 

21-00 

•89 

•16 

196 

31-03 

•91 

•18 

70 

11-14  11-04 

•93 

•31 

•11 

133 

•17 

21-05 

•32      -05 

196 

•19 

31-07 

•83 

1-02 

71 

•30  11-20 

•93 

•47 

1-10 

!l34 

•33 

•21 

•96 

•48 

197 

•86 

•23 

•98 

•49 

72 

•46      -35 

•93 

•63 

•10  135 

•49 

•37 

•64      -05  '  198 

•61 

•39 

•65 

1-02 

73 

•62      -51 

•93 

•79 

•10,1136 

•65 

•53 

•96 

•80 

199 

•67 

•55 

•81 

74 

•78 

•67 

•93 

•95 

•10  137 

•81 

•69 

•96      -05 

200 

•83 

•71 

•98 

•97 

75 

•94 

•83 

•93 

12-10 

•10   138 

•96 

•85 

22-11 

201 

•99 

•87 

3213 

76 

12-1011-99 

•93 

•26      -09  139 

2212 

22-01    -96 

•27      -05  202 

32-15 

32-02 

•29 

77 

•26  12-15 

•42 

•09 

140 

•28 

•17 

•43      -05 

203 

•30 

•18 

•45 

78 

•42      -30 

•93 

•58 

•09  141 

•44 

•33 

•59 

204 

•46 

•34 

•61 

79 

•58 

•47 

•74 

•09  142 

•60 

•48    -96 

'    -75      -05  1  205 

•62 

•50 

•77 

80 

•73 

•63 

•93 

•90 

•09  143 

•76 

•64 

•911 

206 

•78      -66 

•92 

81 

•89 

•79 

13-06 

•09  144 

•92 

•80 

23-07 

•05 

207 

•94 

•82 

33-08 

82 

13-05 

•94 

•93 

•22 

•09  145 

23-08 

•96    -96 

•23 

208 

33-10 

•98 

•24 

83 

•21 

13-10 

•38 

•09  146 

•24 

2312 

•38    1-04  209 

•26 

33-14 

•40 

84 

•37 

•26 

•94 

•53 

•08 

147 

•40 

•28 

•64            |210 

•42 

•30 

•56 

85 

•53 

•42 

•94 

•69 

•08  148 

•56 

•44 

•70      -04;'211 

•58 

•46 

•72 

86 

•69 

•58 

•85 

•08  149 

"7*2 

•60    -96 

•86             212 

•74 

•61 

•88 

87 

•85 

•74 

•94 

14-01 

•08I|150 

•87 

•76 

24-02;      -04  213 

•90 

•77 

34-04 

88 

14-01      -90 

•94 

•17 

•08 

151 

24-03 

•92 

18             1214 

34-06 

•93 

•20 

89 

•1714-06 

•33 

•08 

152 

•19 

24-07    '96 

•34 

215 

•21 

34-09 

•36 

90 

•33      -22 

•94 

•49 

•08 

153 

•35 

•23 

•50 

•04   216 

•37 

•25 

•51 

91 

•49      -38 

•94 

•65 

•08 

154 

•51 

•39 

•65 

217 

•53 

•41 

•67 

92 

'  -64      -53 

•81 

•08 

155 

•67 

•55    '96 

•81 

•04  218 

•69 

•57 

•83 

93 

•80      -69 

•94 

•97 

•08 

156 

•83 

•71 

•98 

219 

•85 

•73 

•99 

94 

•96      -85 

•94 

15-12 

•07 

|157 

•99 

•87 

2513 

•04  220 

35-01 

•89 

3515 

95 

15-14  15-01 

•30 

•07 

158 

25-15 

25-03    -97 

•29 

221 

•17'35'05 

•31 

96 

•28|     -17 

•94 

•44 

•07 

159 

•31 

19 

•45 

•04  222 

•33      -20 

•47 

47 

•44      -33 

•60 

•07 

160 

•47 

•35 

•61 

223 

•40 

•36 

•63 

98 

•60      -49 

•94 

•76 

•07 

161 

•62 

•51    '97 

•77 

i  224 

•65 

•52 

•79 

99 

•76 

•65 

•92 

-07 

162 

•78 

•66 

•93 

•04  225 

•80 

•68 

•95 

100 

•92 

•81 

•95 

16-08 

•07 

163 

•94 

•82 

26-09 

226 

•96 

•84 

3610 

101 

16-08 

•97 

•24 

•07 

164 

26-10 

•98    -97 

•25 

•04  227 

3612 

36'00 

•26 

102 

•24 

16-13 

•40 

165 

•262614 

•42 

:228 

•28 

16 

•42 

103 

•39 

•28 

•95 

•56 

•07 

166 

•42      -30 

•56 

•04:  229 

•44 

•32 

•58 

104 

•55 

•44 

•72 

167 

•58 

•46 

•72 

230 

•59 

•48 

•74 

105 

•71 

•60 

•87 

•07 

168 

•74 

•62    -97 

•88 

•03 

231 

•75 

•64 

•90 

106 

•87 

•76 

•95 

17-03 

169 

•90 

•78 

27-04 

232 

•9! 

•79 

37-06 

107 

17-03 

•92 

•19 

•06 

170 

27-06 

•94: 

•22 

•03 

233 

37-08 

•95 

•22 

108 

•19 

17-08 

•35 

Ijl71 

•2227-10    -97 

•36 

234 

•24 

3711 

•58 

109 

•35 

•24 

•95 

•51 

•06 

172 

•38      -25 

•62 

•03 

235 

•40 

•27 

•54 

110 

•51 

•40 

•67 

173 

•53 

•41 

•68 

236 

•56 

•43 

•69 

111 

•67 

•66 

•83 

•06 

174 

•69 

•57 

•97 

•84 

237 

•72 

•59 

•85 

112 

•83 

•71 

•95 

•99 

175 

•85 

•73 

1-00 

•03 

1238 

•87 

•75 

38-01 

113 

•99 

'   -87 

18-15 

•06 

176 

28-01 

•89 

28-16 

239 

38-03 

•91 

•17 

114 

18-1518-03 

•95 

•80 

177 

•17 

28-05 

•97 

•31 

•03 

240 

19 

38-07 

•33 

L15 

•30      -19 

•46 

•06 

178 

•33 

•21 

•47 

241 

•85 

•23 

•69 

116 

•46      -35 

•26 

179 

•48 

•37 

•63 

242 

•51 

•88 

•fc5 

117 

•62      -51 

•95 

•62 

•06 

180 

•64 

•53 

•97 

•79 

•03 

243 

•67 

•54 

39-01 

118 

•78      -67 

•78 

181 

•80 

•69 

•95 

244 

•83 

•70 

•17 

119       -94      -83 

•95 

•94 

1-06 

182 

•97      '84 

2911 

1-03 

245 

•99 

•86 

•33 

MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


315 


No.  of  teeth.  ' 

Radius  of 
pitch-circle. 

SMALLEST   PINION, 
TWELVE  TEETH. 

No.  of  teeth. 

Radius  of 
pitch-circle. 

-SMALLEST  PINION, 
TWELVE   TEETH. 

•3 
§ 

*o 

I 

Radius  of 
pitch-circle. 

SMALLEST  PINION, 
TWELVE  TEETH. 

Radii  of  the 
faces  of 
teeth. 

Radii  of  the 
flanks  of 
teeth. 

Radii  of  the 
faces  of 
teeth. 

Radii  of  the 
flanks  of 
teeth. 

Radii  of  the 
faces  of 
teeth. 

Radii  of  the 
flanks  of 
teeth. 

246 

39-15 

3902 

39-28 

265 

42-17  42-04 

42-31 

284 

45-19 

45-06 

45-33 

247 

•31 

•18 

•44 

266 

•33      -20 

•46 

285 

•35 

.22 

•49 

248 

•47 

•34 

•60 

267 

•49      '36 

•62 

286 

•51 

•38 

•64 

249 

•64 

-50 

•76 

268 

•64      '52 

•78 

287 

•67 

•54 

•80 

250 

•78 

•86 

•92 

269 

•80 

•68 

•94 

288 

•83 

•70 

•96 

251 

•94 

•82 

40-08 

270 

•97 

•84 

43-10 

289 

•99 

•86 

46-12 

252 

40-10 

•97 

•24 

271 

43-13 

1-00 

•26 

290 

46-15 

46-02 

•28 

253 

•26 

40-13 

•40 

272 

•28 

43-15 

•42 

291 

•30 

•17 

•44 

254 

•42 

•30 

•56 

273 

•44 

•31 

•58 

292 

•46 

•33 

•60 

255 

•59 

•45 

•72 

274 

•60 

•47 

•74 

293 

•62 

•49 

•76 

256 

•74 

•61 

•87 

275 

•76 

•63 

•90 

294 

•78 

•65 

•82 

257 

•90 

•77 

41-03 

276 

•92 

•79 

44-05 

295 

•94 

•81 

•98 

258 

41-06 

•93 

•20 

277 

44-08 

•96 

i 

•21 

296 

47-10 

•97 

47-13 

259 

•22 

41-09 

•36 

278 

•24 

44-11 

•37 

297 

•25 

47-13 

•29 

260 

•38 

•25 

•51 

279 

•40 

•27 

•53 

298 

•42 

•29 

•45 

261 

•53 

•41 

•67 

280 

•56 

•43 

•69 

299 

•58 

•45 

•61 

262 

•69 

•56 

•83 

281 

•71 

•59 

•85 

300 

•74 

•61 

•77 

263 

•85 

•72 

•99 

282 

•87 

•74 

45-01 

Rack 

•129 

1-00 

0-129 

1-00 

264 

42-01 

•89 

42-15 

283 

45-03 

•90 

•17 

Rule. — Seek  in  the  first  column  of  the  table  for  the  number  of  teeth  it  is 
proposed  that  the  wheel  shall  contain.  In  a  line  with  such  number  of  teeth 
take  from  columns  2,  3,  4,  5,  and  6  the  numbers  that  are  in  them ;  and  in 
every  case  multiply  such  numbers  by  the  pitch.  The  products  will  be  the 
number  of  inches  and  parts  of  inches  to  which  the  compasses  must  be  opened 
to  describe  the  circles  and  parts  of  circles  that  are  required. 

Example. — Suppose  that  a  wheel  (Fig.  687)  is  to  be  made  to  contain  thirty 
teeth,  and  that  the  pitch  of  the  teeth  is  to  be  2£  inches,  proceed  as  follows : 


FIG.  687. 


Seek  in  column  1  for  30,  the  number  of  proposed  teeth,  and  take  from  col- 
umn 2  the  numbers  4-78,  which  multiplied  by  2£  inches,  the  product  will  be 
11-957".  Open  the  compasses,  therefore,  to  this  radius  and  describe  a  circle, 
which  will  be  the  "  pitch-circle."  On  an  arc  of  this  circle  lay  off  2'5  X  '48  = 
1-2"  for  the  thickness  of  a  tooth,  and  2 -5  x  -52  =  1-3"  for  the  space.  Having 


316 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


determined  the  number  of  teeth  and  pitch,  next,  in  column  3,  and  in  the  same 
line  with  30  teeth,  will  be  found  the  numbers  4'70,  which  multiply  by  2£ 
inches — the  product  will  be  11'75.  With  the  compasses  opened  to  this  dis- 
tance, and  from  the  same  centre  as  the  last,  describe  another  circle,  which  will 
be  the  paths  of  centres  for  the  curves  of  the  faces  of  the  teeth.  From  column 
4  similarly  take  the  numbers  0'86  and  multiply  by  2£  inches.  The  product  is 
2-15,  to  which  distance  the  compasses  must  be  opened  to  describe  the  faces  of 
the  teeth. 


FIG.  688. 

Again,  in  column  5,  multiply  5-07  X  2-5  =  12-675",  and  from  the  centre, 
with  this  radius,  describe  another  circle  for  the  paths  of  centres  of  flanks  of  the 
teeth,  from  column  6,  1'34  X  2'5  =  3'35,  the  radius  of  the  flanks  of  the  teeth. 

For  the  height  of  a  tooth  a  common  proportion  is  -fa  of  pitch  outside  of 
pitch-circle,  and  ^  of  pitch  within,  which  leaves  -fo  pitch  for  clearance  at  the 
bottom,  where  usually  small  arcs  are  described  to  connect  the  teeth  with  the 
wheel. 

Having  described  a  few  teeth  of  any  gear  to  its  full  size,  the  rest  may  be  laid 
off  from  a  templet,  or  cutters  made  by  which  the  teeth  may  be  accurately 
formed.  In  the  illustration  the  teeth  and  spaces  are  proportioned  to  a  common 
form  (see  page  303). 

It  is  not  uncommon  to  make  one  of  the  set  of  gears  with  wooden  teeth, 
mortices  being  cast  in  the  periphery  of  the  wheel  for  the  insertion  of  these 
teeth — hence  called  mortise  or  core  ;  the  elasticity  of  the  wood  diminishes  the 
effect  of  shocks,  and  they  run  with  less  noise. 

The  usual  proportions  and  construction  of  mortise  wheels  are  shown  in  Fig. 
688,  a  section  across  and  with  the  rim  of  the  wheel.  The  figures  represent  the 
proportions  to  pitch  as  unity  ;  b  is  from  2  to  3  p.  The  teeth  are  held  in  posi- 
tion by  wooden  dovetailed  keys. 

Fig.  689  is  a  section  across  the  rim  of  mortised  bevel-gear ;  the  figures  are 


FIQ.  689. 


n 


\ 

MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS.  317 

as  before  in  ratios  to  p.     In  this  illustration  the  teeth  are  held  in  by  pins,  com- 
mon also  to  spur-mortise-gears. 

It  is  unusual  in  drawings  to  complete  gears  with  teeth  according  to  the  ex- 
amples given  ;  it  is  sufficient  for  the  purposes  of  pattern-making  that  the  pitch- 
circle,  pitch  and  form  of  one  tooth  be  given.  For 
lines  of  shafting,  spur-gears  may  be  represented,  like 
plain  pulleys,  tangent  to  each  other,  of  the  diameters 
of  the  pitch-circle,  with  the  pitch  and  number  of 
teeth  written  in :  bevel-gears,  as  in  Fig.  690.  In  fin- 
ished drawings,  detail  is  necessary.  The  following 
simple  forms  of  describing  spur-and  bevel-gears  will 
in  general  answer  the  purpose,  but  if  more  accuracy 
is  required  use  Adcock's  tables. 

Projections  of  a  Spur  Wheel. — To  draw  side  ele-  FtG  690 

vation  (Fig.  691),  an  edge  view  (Fig.  692),  and  a  ver- 
tical section  (Fig.  693)  of  a  spur  wheel  with  54  teeth  and  a  pitch  of  two  inches : 

Determine  the  radius  of  the  pitch-circle  from  the  table,  page  312 
(-6366  X  54  =  34-376  =  D.  E  =  17-19) ;  draw  the  central  line  A  C  B  and  the 
perpendicular  D  E;  on  C  as  a  centre,  with  a  radius  17-19,  describe  the  pitch- 
circle,  and  divide  it  into  54  equal  parts.  To  effect  this  division,  without  defa- 
cing by  repeated  trials  that  part  of  the  paper  on  which  the  teeth  are  to  be  repre- 
sented, describe  from  the  same  centre  ci  with  any  convenient  radius,  a  circle 
abed]  with  the  same  radius  divide  its  circumference  into  six  equal  parts,  and 
subdivide  each  sixth  into  nine  equal  parts,  and  draw  radii  to  the  centre  c ;  these 
radii  will  cut  the  pitch-circle  at  the  required  number  of  points.  Divide  the 
pitch  (2  inches)  into  10  equal  parts ;  mark  off  beyond  the  pitch-circle  a  dis- 
tance equal  to  3  of  these  parts,  and  within  it  a  distance  equal  to  4  parts,  and 
from  the  centre  C  describe  circles  passing  through  these  points ;  these  circles 
are  projections  of  the  cylinders  bounding  the  points  of  the  teeth  and  the  roots 
of  the  spaces  respectively. 

In  forming  the  outlines  of  the  teeth,  the  radii,  which,  by  their  intersections 
with  the  pitch-circle,  divide  into  the  required  number  of  parts,  may  be  taken 
as  the  centre  lines  of  each  tooth.  The  thickness  of  the  tooth,  measured  on  the 
pitch-circle,  is  -46  pitch  x  2*  =  -92,  and  the  width  of  the  space  is  equal  to 
'54:  p  x  2"  =  1-08.  These  distances  being  set  off,  take  in  the  compasses  the 
length  of  the  pitch,  and  from  the  centre  g  describe  a  circular  arc  h  i ;  and  from 
the  centre  j,  with  the  same  radius,  describe  another  arc  h  k  touching  the 
former ;  these  arcs,  being  terminated  at  the  circles  bounding  the  points  of  the 
teeth  and  the  bottoms  of  the  spaces  respectively,  form  the  curve  of  one  side  of 
a  tooth.  The  other  side  is  formed  in  a  similar  manner,  by  drawing  from  the 
centre  I  the  arc  m  n,  and  from  the  centre  p  the  arc  m  0,  and  so  on  for  all  the 
rest  of  the  teeth. 

The  teeth  having  been  completed,  proceed  to  the  delineation  of  the  rim, 
arms,  and  eye  of  the  wheel.  The  thickness  of  the  rim  is  usually  made  equal  to 
that  of  the  teeth,  say  one  half  of  the  pitch,  which  distance  is  accordingly  set  off 
on  a  radius  within  the  circle  of  the  bottoms  of  the  spaces,  and  a  circle  is  de- 
cribed  from  the  centre  C  through  the  point  q  thus  obtained.  Within  the  rim, 
a  strengthening  feather  q  r,  in  depth  about  three  fourths  of  the  thickness  of  the 


318  MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 

JB 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS.  319 

rim,  is  generally  formed,  as  shown  in  the  plate.  Describe  the  eye,  or  central 
aperture  for  the  reception  of  the  shaft,  to  the  specified  diameter,  as  also  the 
circle  representing  the  thickness  of  metal  round  the  eye,  usually  equal  to  the 
pitch  of  the  teeth. 

To  draw  the  arms,  from  the  centre  C,  with  the  radius  C  u  equal  to  the 
pitch,  describe  a  circle ;  draw  all  the  radii,  as  C  L,  which  are  to  form  the  centre 
lines  of  the  arms,  and  set  off  the  distance  L  #,  equal  to  one  third  pitch,  on  each 
side  of  these  radii  at  the  inner  circumference  of  the  rim ;  and  through  all  the 
points  thus  obtained  draw  tangents  to  the  circle  passing  through  u.  The  con- 
tiguous arms  are  rounded  off  into  each  other  by  arcs  of  circles  (Fig.  691). 
Draw  the  central  web  of  the  arm  by  lines  parallel  to  their  radii,  making  the 
thickness  about  f  inch  for  wheel  of  about  this  size. 

Having  completed  the  elevation  for  the  edge  view  and  vertical  section, 
draw  the  perpendiculars  F  G  and  H  I  (Figs.  692  and  693)  as  central  lines  in 
the  representations  ;  set  off  on  each  side  of  these  lines  half  the  breadth  of  the 
teeth,  and  draw  parallels ;  project  the  teeth  of  Fig.  691  upon  Fig.  692,  by 
drawing  through  all  the  visible  angular  points  straight  lines  parallel  to  A  B, 
and  terminated  at  either  extremity  by  the  verticals  representing  the  outlines  of 
the  breadth  of  the  wheel ;  project  in  like  manner  the  circles  of  the  hub ;  lay 
off  half  length  on  each  side  of  F  G-,  and  draw  parallels  to  it.  The  section  (Fig. 
693)  is  made  on  the  line  D  E  of  the  elevation ;  project,  as  in  Fig.  692,  those 
portions  which  will  be  visible  in  this  section,  and  shade  those  parts  which  are 
in  section.  The  arms  are  made  tapering  in  width,  and  somewhat  less  than  the 
face  of  the  wheel  (Fig.  694) ;  a  cross-section  of  one  of  them  is  made  by  a  plane 
passing  through  XX'  and  Y  Y'.  The  points  y,  z,  in  Fig.  691,  and  correspond- 
ing lines  in  Fig.  693,  represent  the  edges  of  key-seat. 

Oblique  Projection  of  a  Spur  Wheel. — In  drawing  an  object  in  an  oblique 
position  with  respect  to  the  vertical  plane  of  projection,  lay  down  in  the  first 
place  the  elevation  and  plan  as  if  it  were  parallel  to  that  plane  (Figs.  695  and 
696).  Then  transfer  the  plan  to  Fig.  698,  giving  it  the  same  inclination  with 
the  ground  line  which  the  wheel  ought  to  have  in  relation  to  the  vertical  plane  ; 
and  assuming  that  the  horizontal  line  A  B  represents  the  axis  of  the  wheel, 
both  in  the  parallel  and  oblique  positions,  the  centre  of  its  front  face  in  the 
latter  position  will  be  determined  by  the  intersection  of  a  perpendicular  raised 
from  the  point  C'  (Fig.  697)  with  that  axis.  Take  any  point,  as  a  in  Fig.  695, 
and  the  projection  of  that  point  on  Fig.  696  must  be  in  the  line  a  a,  parallel  to 
A  B ;  this  point  being  projected  at  a'  (Fig.  698),  must  be  in  the  perpendicular 
a'  a ;  therefore  the  intersection  of  these  two  lines  is  the  point  required.  Thus 
all  the  remaining  points  J,  c,  d,  etc.,  may  be  obtained  by  the  intersections  of  the 
perpendiculars  raised  from  the  points  #',  c',  d',  etc.  (Fig.  698),  respectively,  with 
the  horizontals  drawn  through  the  corresponding  points  in  Fig.  695.  Since  the 
points  e  and/,  in  the  further  face  of  the  wheel,  have  their  projections  in  a  and 
b  (Fig.  695),  their  oblique  projections  will  be  situated  in  the  lines  a  a  and  b  J, 
but  they  are  also  at  e  and/;  consequently  the  lines  e  a  and  fb  are  the  oblique 
projections  of  the  edges  a'  e'  and  b'f. 

All  the  circles  which,  in  the  rectangular  elevation  (Fig.  695),  have  been  em- 
ployed in  the  construction  of  this  wheel  are  projected  in  the  oblique  view  into 
ellipses ;  thus,  since  the  plane  F'  G',  in  which  these  circles  are  situated,  is  verti- 


320  MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS.  321 

oal,  the  major  axes  of  all  the  ellipses  in  question  are  perpendicular  to  the  line 
A  B,  and  equal  to  the  diameters  of  the  circles  of  which  they  are  respectively  the 
projections ;  and  the  minor  axes,  representing  the  horizontal  diameters,  will  all 
coincide  with  the  line  A  B. 

To  obtain  the  ellipse  into  which  the  pitch-circle  is  projected,  set  off  upon 
the  vertical  D  E  (Fig.  697)  above  and  below  C  the  radii  of  the  pitch-circle  for 
the  major  axis,  and  project  i' f  (Fig.  698)  to  the  horizontal  axis  at  i  and/  (Fig. 
697)  for  the  minor  axis. 

The  intersection  of  the  horizontal  lines  g  g,  h  h,  etc.,  with  the  projection  of 
the  pitch-circle  gives  the  thickness  of  the  teeth  at  the  pitch-line ;  in  the  same 
manner  the  circles  bounding  the  extremities  and  roots  of  the  teeth  may  be  de- 
termined. If  strict  accuracy  is  required,  a  greater  number  of  points  is  neces- 
sary for  the  construction  of  the  curvature  of  the  teeth,  and  two  additional  cir- 
cles, 77i  n  and  op,  may  be  drawn  on  Fig.  695  and  projected  to  Fig.  697,  and  the 
points  of  their  intersection  with  the  curves  of  the  teeth  projected  to  correspond- 
ing points  as  indicated  by  the  same  letters. 

Projections  of  a  Bevel  Wheel. — Fig.  699  is  an  edge  view,  Fig.  700  a  face  view, 
and  Fig.  701  a  vertical  transverse  section.  For  the  determination  of  the  divi- 
sion of  the  angle  of  inclination  of  the  axes  of  a  pair  of  bevel  wheels,  see  Fig. 
685  ;  for  their  size  and  proportion,  the  rules  given  for  spur  wheels  ;  thus,  con- 
sider the  base  of  the  cone  A  B  (Figs.  700  and  701)  as  the  diameter  of  the  pitch- 
circle  of  a  spur  wheel,  and  proportion  the  pitch,  form,  and  breadth  of  teeth,  ac- 
cording to  the  stress  to  which  they  are  to  be  subjected. 

Having  determined  and  laid  down,  according  to  the  required  conditions,  the 
axis  0  S  of  the  primitive  cone,  the  diameter  A  B  of  its  base,  the  angle  A  S  0 
which  the  side  of  the  cone  makes  with  the  axis,  and  the  straight  lines  A  0,  D  o', 
perpendicular  to  A  S,  and  representing  the  sides  of  two  cones,  between  which 
the  breadth  of  the  wheel  (or  length  of  the  teeth)  is  comprised,  the  first  opera- 
tion is  to  divide  the  primitive  circle,  described  with  the  radius  A  C,  into  a  num- 
ber of  equal  parts  corresponding  to  the  number  of  teeth  or  pitch  of  the  wheel. 
Then  upon  the  section  (Fig.  701)  draw  with  the  radius  o  A  or  o  B,  moving  par- 
allel to  itself,  outside  the  figure,  a  small  portion  of  a  circle,  upon  which  con- 
struct the  outlines  of  a  tooth  M,  and  of  the  rim  of  the  wheel,  with  the  same 
proportions  and  after  the  same  manner  in  reference  to  spur  wheels  ;  set  off  from 
A  and  B  the  points  a,  d,  and  /,  denoting  respectively  the  distances  from  the 
pitch-line  to  the  points  and  roots  of  the  teeth,  and  to  the  inside  of  the  rim,  and 
join  these  points  to  the  vertex  S  of  the  primitive  cone,  terminating  the  lines  of 
junction  at  the  lines  D  o',  E  o' ;  the  figure  a  1)  c  d  will  represent  the  lateral  form 
of  a  tooth,  and  the  figure  c  dfe  a  section  of  the  rim  of  the  wheel,  by  the  aid  of 
which  the  face  view  (Fig.  700)  is  constructed. 

The  points  a,  J,.c,  d,  and  e,  having  been  projected  upon  the  vertical  diame- 
ter A'  B',  describe  from  the  centre  C'  a  series  of  circles  passing  through  the 
points  thus  obtained,  and  draw  any  radius,  as  C'  L,  passing  through  the  centre 
of  a  tooth.  On  either  side  of  the  point  L  set  off  the  distances  L  &,  L  I,  making 
the  thickness  of  the  tooth  M  at  the  point,  and  indicate,  in  like  manner,  upon 
the  circles  passing  through  the  points  B'  and  d',  its  thickness  at  the  pitch-line 
and  root ;  then  draw  radii  through  the  points  i,  /,  k,  g,  m,  etc.,  terminating 
them  respectively  at  the  circles  forming  the  projections  of  the  corresponding 
22 


322  MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


323 


parts  at  the  inner  extremity  of  the  teeth  ;  these  radial  lines  will  represent  the 
rectilinear  edges  of  all  the  teeth.  The  curvilinear  outlines  may  be  delineated 
by  arcs  of  circles,  tangents  to  the  radii  g  C'  and  i  C',  and  passing  through  the 
points  obtained  by  the  intersections  of  the  radii  and  the  various  concentric  cir- 
cles. The  radii  of  these  circular  arcs  may  in  general,  as  in  the  case  of  spur 
wheels,  be  taken  equal  to  the  pitch,  and  their  centres  upon  the  interior  and  ex- 
terior pitch-circles ;  thus  the  points  g  and  i,  n  and  o,  for  example,  are  the  centres 
for  the  arcs  passing  through  the  corresponding  points  in  the  next  adjacent  teeth, 
and  vice  versa. 

The  drawing  of  the  teeth  in  the  edge  view  (Fig.  699),  and  of  such  portions 
of  them  as  are  visible  in  the  section  (Fig.  701),  are  explained  by  inspection  of 
the  lines  of  projection.  In  the  construction  observe  that  every  point  in  the 
principal  figure  from  which  they  are  derived  is  situated  upon  the  projection  of 
the  circle  drawn  from  the  centre  C',  and  passing  through  that  point.  Thus  the 
points  g  and  i,  for  example,  situated  upon  the  exterior  pitch-circle,  will  be  de- 
termined in  Fig.  699  by  the  intersection  of  their  lines  of  projection  with  the 
base  A  B  of  the  primitive  cone  ;  and  the  points  k  and  I  will  be  upon  the  straight 
line  passing  through 
a  a  (Fig.  701),  and  so 
on.  Further,  as  the 
lateral  edges  of  all  the 
teeth  in  Fig.  699  are 
radii  of  circles  drawn 
from  the  centre  0',  so 
in  Fig.  700  they  are 
represented  by  lines 
drawn  through  the  va- 
rious points  found  as 
above  for  the  outer  ex- 
tremities of  the  teeth, 
and  converging  toward 
the  common  apex  S  ;  while  the  cen- 
tre lines  of  the  exterior  and  interior 
extremities  themselves  all  tend  to 
the  points  o  and  o'  respectively. 

Skew- Bevels. — When  the  axes  of 
wheels  are  inclined  to  each  other, 
and  yet  do  not  meet  in  direction, 
and  it  is  proposed  to  connect  them 
by  a  single  pair  of  bevels,  the  teeth 
must  be  inclined  to  the  base  of  the 
frusta  to  allow  them  to  come  into 
contact.  Set  off  a  e  (Fig.  702)  equal 
to  the  shortest  distance  between  the 

axes   (called  the   eccentricity),   and  Fm  702 

divide  it  in  e,  so  that  a  c  is  to  e  c  as 

the  mean  radius  of  the  frustum  to  the  mean  radius  of  that  with  which  it  is  to 
work ;  draw  cm  d  perpendicular  to  a  e.  The  line  cm  d  gives  the  direction  of 


324 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


the  teeth ;  and,  if  from  the  centre  a,  with  radius  a  c,  a  circle  be  described,  the 
direction  of  any  tooth  of  the  wheel  will  be  a  tangent  to  it,  as  at  c.  Draw  the 
line  d e  perpendicular  to  cm  d,  and  with  a  radius  d e  equal  to  c  e  describe  a 
circle ;  the  direction  of  the  teeth  of  the  second  wheel  will  be  tangents  to  this 
last,  as  at  d. 

System  composed  of  a  Pinion  driving  a  Rack  (Fig.  703). — The  pitch-line 
M  N  of  the  rack  and  the  pitch-circle  A  B  D  of  the  pinion  being  laid  down 
touching  one  another,  divide  the  latter  into  twice  the  number  of  equal  parts 
that  it  is  to  have  teeth,  and  set  off  the  common  distance  of  these  parts  upon 
the  line  M  N,  as  many  times  as  may  be  required  ;  this  marks  the  thickness  of 


FIG.  703. 

the  teeth  and  width  of  the  spaces  in  the  rack.  Perpendiculars  drawn  through 
all  these  points  to  the  solid  part  of  the  rack  will  represent  the  flanks  of  the  teeth 
upon  which  those  of  the  pinion  are  to  be  developed  in  succession.  The  curva- 
ture of  these  latter  should  be  an  involute  A  c  of  the  circle  A  B  D.  The  teeth 
might  be  cut  off  at  the  point  of  contact  d  upon  the  line  M  N,  for  at  this  posi- 
tion the  tooth  A  begins  its  action  upon  that  of  the  rack  E  ;  but  it  is  better  to 
allow  a  little  more  length  ;  in  other  words,  to  describe  the  circle  bounding  the 
points  of  the  teeth  with  a  radius  somewhat  greater  than  C  d. 

For  the  form  of  the  spaces  in  the  rack,  set  off  from  M  N,  as  at  the  point  e, 
a  distance  slightly  greater  than  the  difference  A  a  of  the  radius  of  the  pitch- 
circle,  and  that  of  the  circle  limiting  the  points  of  the  teeth,  and  through  this 
point  draw  a  straight  line  F  G-  parallel  to  M  N.  From  this  line  the  flanks  of 
all  the  teeth  of  the  rack  spring,  and  their  points  are  terminated  by  a  portion 
of  a  cycloid  A  5,  which,  however,  may  in  most  instances  be  replaced  by  an  arc  of 
a  circle.  As  the  depth  of  the  spaces  in  the  pinion  depends  upon  the  height 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


325 


of  this  curved  portion  of  the  teeth ;  their  outline  is  formed  by  a  circle  drawn 
from  the  centre  C,  with  a  radius  a  little  less  than  the  distance  from  this  point 
to  the  straight  line  bounding  the  upper  surface  of  the  teeth  of  the  rack. 

System  composed  of  a  Rack  driving  a  Pinion. — In  this  case  the  construc- 
tion is  identical  with  that  of  the  preceding  example,  except  that  the  form 
proper  to  be  given  to  the  teeth  of  the  rack  is  a  cycloid  generated  by  a  point  A 
in  the  circumference  of  the  circle  A  E  C  rolling  on  the  line  M  N.  The  curva- 
ture of  the  teeth  is  an  involute  as  before. 

System  composed  of  an  Internal  Spur  Wheel  driving  a  Pinion  (Fig.  704). — 
The  form  of  the  teeth  of  the  driving-wheel  is  in  this  instance  determined  by 
the  epicycloid  described  by  a  point  in  the  circle  A  E  C,  rolling  on  the  concave 


FIG.  704. 

circumference  of  the  primitive  circle  MAN.  The  points  of  the  teeth  are  to 
be  cut  off  by  a  circle  drawn  from  the  centre  of  the  internal  wheel,  and  passing 
through  the  point  E,  indicated  by  the  contact  of  the  curve  with  the  flank  of 
the  driven  tooth. 

The  wheel  being  supposed  to  be  the  driver,  the  curved  portion  of  the  teeth 
of  the  pinion  may  be  very  small.  This  curvature  is  a  part  of  an  epicycloid 
generated  by  a  point  in  the  circle  MAN  rolling  upon  BAD. 

System  composed  of  an  Internal  Wheel  driven  T)y  a  Pinion. — Fig.  705 
involves  a  different  mode  of  treatment  from  that  employed  in  the  preceding 
cases.  The  epicycloidal  curve  A  a,  generated  by  a  point  in  the  circle  having 
the  diameter  A  0,  the  radius  of  the  circle  MAN,  and  which  rolls  upon  the 
circle  BAD,  can  not  be  developed  upon  the  flank  A  5,  the  line  described  by 
the  same  point  in  the  same  circle  in  rolling  upon  the  concave  circumference 


326 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


MAN;  and  for  the  reason  that  that  curve   is  situated   without  the  circle 
BAD,  while  the  flank,  on  the  contrary,  is  within  it.     In  order  that  the  pinion 


FIG.  705. 


may  drive  the  wheel  uniformly  according  to  the  required  conditions,  form  the 
teeth  so  that  they  shall  act  always  upon  one  single  point  in  those  of  the  wheel. 
By  taking  for  the  curvature  of  the  teeth  of  the  pinion  the  epicycloid  A  rf,  de- 
scribed by  the  point  A  in  the  circle  MAN  rolling  over  the  circle  B  A  D,  as  in 
the  preceding  examples,  the  tooth  E  of  the  pinion  begins  its  action  upon  the 
tooth  F  of  the  wheel  at  the  point  of  contact  of  their  respective  primitive  cir- 
cles, and  it  is  unnecessary  to  be  continued  beyond  the  point  c,  because  the  suc- 
ceeding tooth  H  will  then  have  been  brought  into  action  upon  G  ;  consequently 
the  teeth  of  the  wheel  might  be  bounded  by  a  circle  passing  through  the  point 
c.  One  of  the  practical  advantages  which  this  species  of  gearing  has  over 
wheels  working  externally  is  that  the  surfaces  of  contact  of  the  wheel  and 
pinion  admit  of  being  more  easily  increased ;  and,  by  making  the  teeth  some- 
what longer  than  simple  necessity  demands,  the  strain  may  be  distributed  over 
two  or  more  teeth  at  the  same  time.  The  flanks  of  the  teeth  of  the  wheel  are 
formed  by  radii  drawn  to  the  centre  0,  and  their  points  are  rounded  off  to  en- 
able them  to  enter  freely  into  the  spaces  of  the  pinion. 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


327 


DRAWING    OF  SCREWS. 


Projections  of  a  Triangular-threaded  Screw  and  Nut  (Fig.  706). — Draw  the 
ground  line  A  B,  and  the  centre  lines  C  c'  of  the  figures,  from  0  as  a  centre, 
with  a  radius  equal  to  that  of  the  exterior  cylinders,  describe  the  semicircle 


C 

FIG.  ror. 


#36;  and  with  the  radius  of  the  interior  cylinder  the  semicircle  bee.  Draw 
the  perpendiculars  a  a"  and  6  6',  b  b"  and  e  e" ,  to  represent  the  vertical  projec- 
tions of  the  exterior  and  interior  cylinders ;  divide  the  semicircle  a  3  6  into  any 


328 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


number  of  equal  parts,  say  6,  and  through  each  part  draw  radii  to  divide  the 
interior.  On  the  line  a'  a"  set  off  the  length  of  the  pitch  as  many  times  as  re- 
quired ;  and  through  the  points  of  division  draw  lines  parallel  to  the  ground 
line  A  B.  Divide  the  pitch  into  twice  the  number  of  equal  parts  that  the 
semicircles  have  been  divided  into,  and  following  instructions  laid  down  (page 
140),  construct  the  helix  a!  3'  6  both  in  the  screw  and  nut. 

Having  obtained  the  point  #',  by  the  intersection  of  the  horizontal  line  pass- 
ing through  the  middle  division  of  a'  a  with  the  perpendicular  b  b",  describe  the 
helix  b'  c'  e',  which  will  represent  the  bottom  of  the  groove.  The  apparent  out- 
lines of  the  screw  and  its  nut  will  then  be  completed  by  drawing  the  lines  b'  a', 
a'  £',  etc.,  to  the  curves  of  the  helices ;  these  are  not,  strictly  speaking,  straight 
lines,  but  their  deviation  from  the  straight  line  is,  in  most  instances,  so  small 
as  to  be  imperceptible. 

When  a  long  series  of  threads  have  to  be  delineated,  they  should  be  drawn 
mechanically,  by  means  of  a  templet  constructed  in  the  following  manner  :  Take 
a  small  slip  of  thin  wood  or  pasteboard,  and  draw  upon  it  the  helix  a'  3'  6  to  the 
same  scale  as  the  drawing,  and  cut  the  slip  carefully  and  accurately  to  this  line. 
Applying  this  templet  upon  Fig.  706,  so  that  the  points  a'  and  6  on  the  plate 
shall  coincide  with  a'  and  6  on  the  drawing,  the  curve  a'  3'  6  can  be  drawn 
mechanically,  and  so  on  for  the  remaining  curves  of  the  outer  helix.  The  same 
templet  may  be  employed  to  draw  the  corresponding  curves  in  the  screw-nut 
by  simply  inverting  it;  but  for  the  interior  helix  a  separate  one  must  be  cut, 
its  outlines  being  laid  off  in  the  same  manner. 

Projections  of  a  Square-threaded  Screw  and  Nut  (Fig.  707).— The  depth 
of  the  thread  is  equal  to  its  thickness,  and  this  latter  to  the  depth  of  the 
groove.  The  construction  is  similar  to  the  preceding ;  the  same  letters  and 
figures  mark  relative  parts.  The  parts  of  the  curve  concealed  from  view  are 
shown  in  dotted  lines. 


M 


FIG.  708. 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


329 


System  composed  of  a  Wheel  and-  Tangent,  or  Endless  Screw. — In  laying  out 
the  work,  the  pitch  of  the  teeth  is  to  be  determined  by  the  required  stress,  as 
for  spur  wheels,  and  the  number  of  the  teeth  in  the  wheel  by  the  number  of 
turns  of  the  screw  for  each  revolution  of  the  wheel.  With  these  determined, 
take  C  (Fig.  708)  to  be  the  centre  of  the  wheel,  E  F  the  axis  of  the  screw,  C  A  the 
radius  of  the  pitch-circle  of  the  wheel,  and  G  A  that  of  the  pitch-cylinder  of 
the  screw ;  the  line  M  N  drawn  through  A,  parallel  to  E  F,  will  be  the  gen- 
eratrix of  that  cylinder,  which  will  serve  the  purpose  of  determining  the  form 
of  the  teeth.  The  section  is  made  through  the  axis,  and  is  the  case  of  a  rack 
driving  a  pinion ;  consequently  the  curve  of  the  teeth,  or  rather  thread,  of  the 
screw  should  be  simply  a  cycloid  generated  by  a  point  in  the  circle  AEG,  de- 
scribed upon  A  C  as  a  diameter,  and  rolling  upon  the  straight  line  M  N".  The 
outlines  of  the  teeth  are  helical  surfaces  described  about  the  cylinder  forming 
the  screw,  with  the  pitch  A  b  equal  to  the  distance,  measured  upon  the  primi- 
tive scale,  between  the  corresponding  points  of  two  contiguous  teeth.  These 
curves  are  expressed  by  dotted  lines.  The  teeth  of  the  wheel  are  set  at  angle 
to  the  plane  of  its  face,  and  with  surfaces  corresponding  to  the  inclination  and 


FIG.  709. 


FIG.  710. 


helical  form  of  the  thread  of  the  screw.     Usually  the  points  of  the  teeth  and 
bottoms  of  the  spaces  are  formed  of  a  concave  outline,  adapted  to  the  convexity 


330 


MACHINE  DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


of  the  screw,  in  order  to  pre- 
sent as  much  bearing  surface 
as  possible  to  its  action.  In 
this  kind  of  gearing  it  is  al- 
most invariably  the  screw  that 
imparts  the  motion. 

A  screw  is  designated  as 
right  or  left  hand,  according  as 
the  forward  motion  is  imparted 
by  turning  the  screw  to  the 
right  or  left. 

In  the  proportions  adopted 
by  the  Yale  &  Towne  Manu- 
facturing Co.  for  worm  gear- 
ing, the  wheel  under  the  weight 
will  revolve  the  screw  slowly.. 
This  angle  (slightly  less  than 
the  angle  of  quiescence,  see 
Morin's  table,  page  199)  of  the 
teeth  is  found  to  be  the  best 


FIG.  711. 


FIG.  712. 


adapted  for  economy  of  power.     In  the  wheel  the  teeth  in  section  are  those  of 
a  spur  wheel,  cut  with  a  chasing  cutter,  and  in  the  screw  turned  in  a  lathe. 

Figs.  709  and  710  are  two  views,  worm  and  wheel,  with  such  lines  of  con- 
struction dotted  as  will  explain  the  manner  of  drawing. 


Fig.  711  is  the  Albro  worm  and  worm  wheel  as  used  on  the  cruisers  of  the 
United  States  Government  for  ship  steering  and  for  heavy  windlass  work. 


MACHINE  DESIGN   AND  MECHANICAL   CONSTRUCTIONS. 


331 


Frictional  Gearing. — When  motion  is  not  continuous  for  a  long  time,  but 
frequently  stopped  and  started  or"  reversed,  frictional  gearing  is  very  often 
used.  The  starting  is  with  as  little  shock  as  with  belting,  as  by  the  usual  ap- 
pliances this  pressure  may  be  applied  gradually  and  is  fully  as  positive.  The 
simplest  form  of  frictional  gearing  is  that  in  which  the  surfaces  in  contact  cor- 
respond to  that  of  the  pitch-circles  (Fig.  712). 

Fig.  713  is  a  plan  of  a  bevel  frictional  gear.  One  half  is  shown  in  section. 
The  surface  of  the  large  or  driven  gear  is  of  cast-iron,  that  of  the  pinion  of 
paper,  in  washers  compressed  by  a  hydraulic  press  and  firmly  held  together  by 
bolts.  The  bevel  in  section  is  in  contact  with  the  large  wheel-surface,  the  other 
is  disengaged.  A  slight  motion  to  the  right  will  throw  the  one  in  contact  out, 
and  not  throw  in  the  other,  and  motion  ceases  in  the  large  driven  wheel ;  a  still 
further  motion  throws  in  the  left  pinion,  and  the  motion  of  the  driven  wheel  is 
reversed. 

The  mode  in  which  this  is  done  is  shown  in  the  elevation  (Fig.  714).     The 
shipper   consists  of  a  bell-crank,  controlled  by  a 
screw.     The  screw  works  in  a  stand,  on  the  top  of 
which  is  a  hand  wheel ;   the  hand  wheel  can  be 
moved  in  either  direction,  and  any  desirable  pres- 
sure can  be  brought  upon  the  frictional  surfaces 
by  means  of  the  screw.     It  is  not  unusual,  instead 
of  two  pinions  to  have  one  pinion,  with  a  little 
clearance   on   each  side,   revolving  between  two 
wheels,  a  slight  lateral  motion,  in  either  direction, 
bringing     it     iji 
contact  with  one 
or  the  other  of 
the  wheels.  Some 
provision,    by    a 


loose  coupling  or  otherwise,  must  be  made  to  admit  of  this  lateral  movement 
in  the  pinion  shaft.  Straight  pulleys,  or  what  would  correspond  to  spur-gears 
without  teeth,  are  constructed,  as  in  the  example  given,  and  are  thrown  in  or 
out  of  gear  by  a  lateral  motion  of  the  pinion. 

In  proportioning  the  face  of  the  pulleys  it  has  been  found  safe  to  consider 
it  the  same  as  belts,  given  in  the  table  (page  292).  The  pressure  can  be  ap- 
plied according  to  the  requirements  of  driving,  and  there  is  no  falling  off  in 
the  friction.  The  frictional  surfaces  are  not  always  paper  ;  wood,  leather,  and 
prepared  rubber  are  frequently  used. 


332 


MACHINE   DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


Wedge  Gearing,  or  Robertson  Grooved- Surf  ace  Frictional  Gearing. — Fig. 
715  is  the  cross-section  of  the  rims  of  two  wheels  of  this  gearing.     The  angle 

recommended  by  Robertson  is  50°  (usually  not 
over  30°  in  our  practice),  and  the  pitch  to  vary 
somewhat  with  the  velocity  and  power  to  be 
transmitted.  For  the  adhesion,  it  is  safe  to 
make  the  horizontal  face  equal  to  that  of  a  belt 
under  the  same  circumstances  of  transfer  of 
power. 

Fig.  716  shows  the  application   of   wedge 
gearing  to  a  hoist  drum  d.     The  power  is  ap- 
Fl°- 715-  plied  through  the  shaft  s ;  one  end  of  the  drum 

shaft  rests  in  a  swivel  box,  the  other  in  an  eccentric  box.     Motion  is  given 
through  the  eccentric  handle  by  which  the  drum  gear  can  be  engaged  with  that 


FIG.  716. 


of  the  pinion  of  the  driving  shaft ;  the  drum  is  revolved  and  the  load  raised. 
In  lowering,  the  drum  is  thrown  out  by  the  eccentric,  and  the  brake  b  applied, 
which  is  controlled  by  a  system  of  levers  brought  within  reach  of  the  man  at 
the  eccentric  lever. 

When  applied  to  the  driving  of  a  rotary  fire  pump,  the  friction  pinion  on 
the  pump  shaft  is  thrown  into  gear  with  the  friction  wheel  of  the  main  shaft 
by  a  sliding  frame  of  iron  with  a  screw  and  hand  wheel.  With  this  apparatus 
the  pump  can  be  started  without  shock  or  jar  and  without  reducing  the  speed 
of  the  main  shaft. 

For  large,  straight  pulleys,  wooden  rims  from  6"  to  8"  deep,  and  built  up  in 
segments  from  1*  to  2'  thick,  so  placed  that  the  direction  of  the  fibres  shall 
follow  the  circumference  of  the  wheel  as  nearly  as  possible.  The  segments  are 
firmly  clamped  together  and  secured  by  glue  joints,  nails,  and  bolts,  and  the 
rim  is  bolted  to  the  arms  of  the  pulley  with  additional  outside  and  deeper  rings 
secured  to  the  rim.  The  whole  is  then  turned  and  finished.  This  pulley  may 
be  used  with  a  belt  as  a  friction  gear. 

Figs.  717  and  718  are  sections  of  wooden  bevel  friction  gears,  showing  the 
way  in  which  they  are  formed  by  wooden  disks  planed  and  fitted,  glued,  nailed, 
and  bolted,  and  then  turned  to  the  proper  angle  and  face. 


MACHINE   DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


333 


For  the  transmission  of  small  powers,  the  combination  of  one  conical  wheel 
and  one  narrow  disk  wheel  with  rounded  edges,  both  of  iron,  is  sometimes  used 


FIG.  717. 


FIG.  718. 


FIG.  719. 


(Fig.  719).     The  pressure  is  applied  to  the  disk  wheel,  and  is  so  arranged  that 
it  can  be  shifted  along  its  axis  for  a  variable  speed  motion.     The  surfaces  in 

contact  are  limited,  the  diameters,  therefore,  should 
be  as  large  as  possible,  with  high  velocity. 

Another  variable  speed 
gear  is  made  by  using,  instead 
of  a  cone,  a  crown  plate  on 
which  the  disk  rests  which 
can  be  moved  inward  or  out- 
ward from  the  centre  of  the 
driving  plate. 

Rope  for  running  rigging 
for  derricks  and  general  hoist- 
ing work  is  made  of  hemp  or  manilla,  but  rope  of  iron  or  steel  wire,  mostly 
with  hemp  centres,  is  preferred  for  many  positions. 

The  shells  of  the  common  and  lighter  blocks  are  made  of  solid  wood,  mor- 
tised for  the  reception  of  the  sheaves,  and  rope-strapped  (Fig.  720).  Larger 
and  better  blocks  are  made  of  separate  pieces  of  wood,  riveted  or  bolted  to- 
gether top  and  bottom,  and  iron-strapped  (Fig.  721) ;  the  sheaves  (Fig.  722)  are 

usually  of  lignurn-vitae,  metal-bushed ; 
the  pin  is  fastened  to  the  shell,  and 
the  sheaves  revolve  on  the  pin.  To 
diminish  friction  under  heavy  weights, 
friction  rolls  are  introduced  (Fig.  723). 


FIG.  720. 


FIG.  721. 


FIG.  722. 


To  strengthen  the  pin,  blocks  are  inside-strapped  (Fig.  724),  or  with 
wrought-iron  straps  or  malleable-iron  shells  (Fig.  725)  and  cast-iron  sheaves, 
entirely  without  woodwork.  Most  blocks  (Figs.  724  and  725)  have  beckets 
attached. 

In  the  Appendix  will  be  found  a  table  of  the  strength  and  weight  of  hemp, 
steel-,  and  iron- wire  rope  and  chain ;  but  as  a  simple  rule  of  their  working 
strength,  multiply  the  square  of  the  girth  or  circumference  of  a  hemp  rope  by 


334: 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


100,  of  an  iron-wire  rope  by  600,  of  steel-wire  rope  by  1,000,  and  the  square  of 
the  diameter  of  the  rods  of  which  a  chain  is  made  by  12,000. 


FIG.  723. 


FIG.  724. 


FIG.  725. 


The  following  table  of  sizes  are  from  the  Boston  and  Lockport  Block  Com- 
pany : 


DIMENSIONS. 

DIMENSIONS. 

Size  sheave. 

For  dia.  rope. 

Size  shell. 

Size  sheave. 

For  dia.  rope. 

Size  shell. 

Six   fxf 

i 

4  inches. 

8    xlfxf 

li 

12  inches. 

3    x   fxf 

$ 

5       " 

9    xl|xf 

li 

13       " 

3£xl    x£ 

i 

6       " 

9ixl£xf 

If 

14      " 

4jxl    xj 

i 

7      " 

10   xlfxl 

H 

15      " 

4fx.lixf 

i 

8      " 

11    x2|xl 

2 

16       " 

5£  x  1£  x  | 

i 

9      " 

12   x2fxl 

2f 

18      " 

6ixl*xi 

H 

10      " 

14   x2fxli 

21 

20      " 

7J  x  1±  x  f 

H 

11      " 

15   x3£xli 

3 

22      " 

16   x3£xl£ 

3| 

24      " 

Gin-blocks  (Fig.  726)  are  made  with  wrought-  and  malleable-iron  frames 
and  wrought  swivel-hook. 

Winding-drums  or  barrels  must  have  their  'diameters  pro- 
portioned to  the  diameters  of  the  rope  or  chain  to  be  used  (see 
table  of  sheaves  above),  and  their  length  to  the  length  of  rope 
or  chain  to  be  taken  in,  and  when  the  coils  or  turns  of  the  rope 
are  numerous,  provision  must  often  be  made  for  keeping  the 
rope  or  chain  so  that  one  coil  may  not  ride  on  another.  This 
is  done  by  spiral  grooves  in  the  barrel,  or  shifting  the  barrel  or 
the  rope-guide  automatically. 

FIG.  726.  Fig.  1806  shows  the  way  in  which  a  chain  cable  is  taken  in 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


335 


with  but  few  coils  on  the  barrel.  The  coils  are  sufficient  for  the  friction  of 
taking  up  the  cable ;  the  tight  cable  is  wound  on  the  larger  part  of  the  barrel, 
and  as  the  coils  are  unwound  on  the  slack  side  the  tight  coil  slips  down  to  a 
smaller  diameter ;  the  weight  of  the  chain  on  the  slack  side,  as  it  drops  into 
the  locker,  is  sufficient  to  preserve  the  friction ;  but  with  a  rope  and  a  few 
turns  on  the  barrels  the  force  of  a  man  is  sufficient,  and  he  can  readily  slack 
and  hold  the  load  in  position  or  lower  without  changing  the  direction  of  mo- 
tion or  the  speed  of  the  barrel. 


FIG.  728. 


FIG.  727. 


Chain-wheels  with  pockets  are  especially  applicable  to  the  purpose  of  hoist- 
ing, requiring  a  width  only  slightly  greater  than  that  of  the  chain,  and  a  diam- 
eter sufficient  to  give  the  proper  engagement  with  it. 

Yule  &  Towne  Manufacturing  Company  have  made  a  pitch  chain,  of  com- 
mon form  but  of  uniform  links,  especially  adapted  to  hoists,  and  Figs.  727, 
728,  and  729  illustrate  the  construction  of  their  chain-wheel.  A  is  a  pocketed 
chain-wheel,  made  of  soft  cast-iron,  mounted  on  a  frame  B.  C  is  the  chain- 
guide  enveloping  the  lower  half  of  the  chain-wheel.  The  inner  curved  surface 
of  the  chain-guide  is  grooved,  and  is  of  such  a  shape  as  to  leave  a  space  be- 
tween it  and  the  periphery  of  the  chain-wheel  merely  sufficient  to  admit  the 


FIG.  730. 


FIG.  731. 


FIG.  732. 


FIG.  7:33. 


FIG.  734. 


FIG.  735. 


chain ;  it  must  then  enter  properly  and  continue  engaged  with  the  chain-wheel. 
E  is  a  chain-guide  roller,  that  delivers  the  slack  chain  into  the  box  or  locker. 


336 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


FIG.  736. 


D  is  the  chain-stripper,  bolted  also  to  the  plate  B,  with  a  tongue  or  rib  pro- 
jecting into  the  centre  groove  of  the  wheel  which  disengages  the  chain. 

Forms  of  chain-cables  are  rep- 

,  resented  by  the  open  circular  link 

(Fig.  730),  the  open  oval.  (Fig.  731), 
oval  with  pointed  stud  (Fig.  732), 
oval  with  broad-headed  stud  (Fig. 
733),  an  obtuse  -  angled  stud-link 
(Fig.  734),  and  the  parallel-sided 
stud-link  (Fig.  735).  The  usual 
proportions  of  chain  -links  are  6 
diameters  of  the  iron  in  length  by 
3£  in  width.  The  end  links,  which 
terminate  each  15  fathoms  of  chain, 
are  6-5  in  length  to  4'1  in  breadth, 
and  the  iron  about  1*2  the  diameter 
of  the  rest  of  the  chain. 

Chain  Couplings.  —  Fig.  736  is 
an  ordinary  coupling  link  of  an 
anchor  chain.  The  link  is  of 
wrought-iron,  the  bolt  and  pin  of 
steel,  both  galvanized.  The  next 
link  ig  made  somewhat  longer  than 

FIG  737.  other  links  of  the  chain,  so   that 

the   coupling    link    may   be   more 

readily  introduced.     Fig.  737  is  a  coupling  link  in  which  one  part  is  a  swivel, 
so  that  the  chain  may  have  a  rotation  about  its  axis  of  length  without  twist- 


-4,5  —  e~*0~*«!»**fc«-»f*—  -a* 


FIG.  738. 


FIQ.  739. 


FIG.  740. 


FIG.  741. 


ing.  Figs.  738,  739,  and  741  are  sockets  for  wire-rope  connections,  shown  in 
section,  Fig  739,  with  a  wrought-iron  conical  key ;  often  the  wires  of  the  rope 
are  spread  with  wrought-iron  wedges  or  nails,  and  in  addition  lead  is  poured  in. 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


337 


In  Fig.  739  the  conical  cone  is.  formed  over  an  iron  core  by  unravelling  the 
rope,  passing  the  wires  over  it,  and  serving  the  ends  to  the  rope  below  ;  an  iron 

socket  fits  over  the  core.  Fig.  740  is 
a  thimble  in  which  the  end  of  the 
rope  is  either  spliced  in  or  loose  and 
served  to  the  rope,  with  the  end 
wires  turned  down.  Fig.  741  is  an 
open  socket  with  a  swivel  hook,  to 
prevent  the  twisting  and  untwisting 
of  the  rope  and  thereby  weakening  it. 
Fig.  742  is  a  loop-clamp. 

Hooks.— Figs  743  and  744  (from 
Kedtenbacher)  represent  two  wrought-iron  hooks.  The  proportions  of  Fig. 
743  are :  assuming  the  neck  of  the  hook  as  1,  the  diameter  of  journals  of  the 


FIG. 


FIG.  743. 


FIG.  744. 


FIG.  745. 


traverse  are  I'l ;  width  of  traverse  at  centre,  2 ;  distance  from  the  centre  of  the 
hook  to  the  centre  of  the  traverse,  7'5 ;  interior  circle  of  the  hook,  3-4;  great- 
est thickness  of  the  hook,  2'8.  Assuming  (Fig.  744)  the  diameter  of  the  wire 
of  the  chain  as  1 :  interior  circle  of  hook  is  3'2,  and  greatest  thickness'  of 
hook  3-5. 

Fig.  745  represents  a  hook  of  the  Yale  &  Towne  Manuf'g  Company  as  fitted 
for  a  cross-head ;  the  diameter  at  A  is  that  of  iron  from  which  the  hook  is 
forged,  and  the  section  shown  hatched  is  equal  to  that  of  the  round  iron.  Hooks, 
of  the  proportions  but  with  a  much  greater  load  than  given  in  the  table  below, 
yield  by  the  gradual  opening  of  the  jaw,  giving  ample  notice  before  rupture. 


Ton. 

Ton. 

Ton. 

Ton. 

Ton. 

Ton. 

Ton. 

Ton. 

Ton. 

Ton. 

Ton. 

Ton. 

Capacity  of  hook  

-1- 

\ 

1 

1 

H 

9, 

8 

4 

5 

6 

8 

10 

In. 

In. 

In. 

In. 

ID. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

Dimensions  of  A  

4 

if 

4 

1A 

1} 

1ft 

If 

2 

<H 

n 

2£ 

3* 

Dimensions  of  D  

li 

1* 

H 

13- 

9 

H 

?,£ 

3* 

•H 

4} 

51- 

6* 

23 


338 


MACHINE   DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


All  parts  of  the  hook  are  drawn  in  parts  of  A. 

Levers. — Figs.  746  and  747  are  side  and  front  elevations  of  an  ordinary 
straight  lever  on  a  shaft ;  both  are  shown  broken,  either  because  the  length  is 
indefinite,  or  because  it  is  inconvenient  to  put  on  the  p#per.  The  handle 
should  be  from  5  to  6  inches  long,  and  1£*  diameter.  The  bar  beneath  the 


T 

X. 


i 

-   ( 

i.    FIG 

cr: 

0 

.  r-i 

FIG.  741 

to-1  © 


FIG.  748. 


FIG.  749. 


FIG.  750. 


FIG.  751. 


handle  to  be  square,  and  of  uniform  width  on  one  side  of  the  lever  and  a  taper 
on  the  other,  as  shown,  of  about  •£"  in  4  feet  on  each  side.  The  sides  of  the 
square  at  the  handle  to  be  £  \f  length  in  inches,  or  say  f"  for  30"  lever,  £"  for 
4  feet,  and  1*  for  5  feet.  The  neck  of  the  shaft  to  be,  as  proportioned  in  the 
drawing,  about  ^  of  the  greatest  width  of  the  lever,  and  the  diameter  of  hub 
1-j^-.  The  stress  exerted  by  a  man  may  be  from  75  to  100  pounds,  and  the  size 
of  the  shaft  will  depend  on  the  torsional  stress  between  the  hub  of  the  lever 
and  the  point  of  resistance. 

Fig.  748  is  a  hand-lever  forming  one  arm  of  a  bell-crank — a  bolt  passing 
through  a  slot  in  the  frame  and  the  arm  of  the  lever,  and  the  two  are  clamped 
together  by  a  thumb-nut,  n,  by  which  the  lever  can  be  held  in  any  position. 

The  same  purpose  is  often  effected  by  notches  in 
/•  ^    the  frame,  into  which  the  arm  of  the  lever  is  caught, 

or  by  spring  latches,  as  in  Fig.  749. 

Figs.  750  and  751  are  side  view  and  plan  of  a 
foot-lever.  The  foot-plate  is  8"  X  5"  X  f",  and  as 
the  lever  is  subject  to  double  the  stress  of  the  hand- 
lever  above,  the  dimension  should  be  somewhat  in- 
creased. The  side  of  square  next  the  foot-plate 
should  be,  say  for  a  lever  of  30",  1";  of  4  feet,  \\'\ 
of  5  feet,  14/;  the  form  and  taper  as  in  the  hand- 
lever. 

Figs.  752  and  753  are  views  of  a  hand-crank.  The  diameter  of  the  handles, 
for  convenience  in  grasping,  should  not  be  less  than  1  £•"  ;  if  for  the  force  of  two 
men,  1|",  and  from  the  diameter  of  the  handle  the  rest  may  be  proportioned  as 


FIG.  752. 


FIG.  753. 


MACHINE   DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


339 


fe  1.4- 


in  the  figure.  The  length  of  handle  for  a  single  man  should  be  from  10"  to 
12";  for  two  men,  from  20"  to  24";  the  crank  from  15"  to  18",  and  the  height 
of  shaft  above  the  foot  support  for  the  men  from  2'  10"  to  3'  2". 

In  the  construction  of  steam  engines  the  makers  adopt  simple  rules  of  pro- 
portion between  the  diameter  of  cylinder  and  its  connections.     Thus,  if  that  of 
the    diameter    of 
cylinder  be  1,  that 
of  the  crank-shaft 
at  the  journal  is 
•50,  of  crank-pin 
•25,  of  crank-pin 
eye  *6,  that  of  the 
cylinder   may  be 
altered  moderate- 
ly without  change  in  that  of  con- 
nections which    may    be    kept   in 
stock.     In  large  quick-running  en- 
gines (Fig.  791)  the  crank-pin  is  of 
larger  proportions  than  above. 

Figs.  754  and  755  are  two  views 
of  a  wrought-iron  crank,  and  Figs. 
756  and  757  of  a  cast-iron  crank,* 
both  proportioned  in  their  parts  to 
the  diameter  of  the  large  eye  as 
unity,  but,  as  shown  by  the  diagram 
and  rule  following,  these  figures  can  only  apply  to  a  single  throw  of  crank,  as 
the  diameters  of  the  two  eyes  vary  as  their  distances  apart. 

Taking  the  diameter  of  the  large  eye  of  the  crank  as  the  unit,  Eedtenbacher 
gives  in  the  table  the  relative  sizes  of  cen- 
tral and  end  eyes  of  cranks,  depending  on 
the  proportion  between  the  length  of  crank 
and  the  diameter  of  central  eye.  The  first 
column  exhibits  the  number  of  times  the 
diameter  of  eye  is  contained  in  the 'length 
of  crank ;  the  second  and  third  columns 
give  the  suitable  diameters  of  crank-pins. 

The  diameters  of  crank-pins  as  above 
given  are  on  the  basis  of  a  length  of  from  1 
to  1-J  of  the  diameter ;  if  the  length  be  in- 
creased beyond  this,  the  diameter  should  be 
increased  in  the  ratio  of  1  to  the  square  root 
of  the  diameter. 

Disk-cranks  are  circular  disks  of  cast- 
iron,  with  crank-pins  of  iron  or  steel,  and 
as  much  strength  of  metal  around  the  pin  as  in  the  crank.     They  are  better 
than  the  crank,  in  that  there  is  no  unbalanced  crank,  and  part  of  the  weight 


FIG.  754. 


FIG.  755. 


DIAMETER  OF  EYE,  BEING  UNITS. 


I 

d 

For  wrought- 
iron  shafts. 

Cast-iron 
shafts. 

2 

0-85 

0-62 

8 

0-69 

0-51 

4 

0-60 

0-44 

5 

0-54 

0-39 

6 

0-49 

0-36 

7 

0-45 

0-33 

8 

0-42 

0-31 

9 

0-40 

0-29 

10 

0-38 

0-28 

11 

0-36 

0-26 

12 

0-34 

0-25 

13 

0-33 

0-24 

*  "  Elements  of  Machine  Design,"  Unwin. 


340 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


I.ZF 
IS 
1..5 


of  the  connection  can  be  balanced  by  a  proper  disposition  of  metal  within 
the  area  of  the  disk. 

Fig.  758  is  a  plan  of  a  double  crank-axle,  although  by  the  projection  the 
lower  axle  A  appears  as  a  straight  shaft.     The  dimensions  given  are  from  an 
axle  in   use.      In 
construction    the 
cranks  are  rectan- 
gular  in   section, 
of      which      the 
width   is    TV  the 
depth,     and     the 
depth  1-5  the  di- 
ameter of  crank- 
journal.    Double  cranks  are  usually 
forged  solid,  and  the  slot  for  the 
crank  cut  out ;  that  shown  in  the 
figure  was  cast  in  steel  for  a  double 
compound  engine,  7  X  15  X  15,  and 
has  long  worked  satisfactorily. 

Fig.  759  is  a  drawing  of  a  crank- 
axle  adapted  to  a  machine. 

Fig.  760  is  an  elevation  and  sec- 
tion of  the  driving  wheel  of  a  loco- 
motive, with  a  counterbalance  op- 
posite the  crank-pin,  and  Fig.  761  is  a  section  of  the  trailing  wheel.  The  crank- 
pin  of  the  driver  has  two  journals — one  for  the  main  connecting  rod,  the 
other  for  the  coupling  rod,  for  which  there  is  a  journal  on  the  trailing  wheel. 

Fig.  762  is  a  front  and  side  elevation  of  a  return  crank,  returning  back  and 


FIG.  756. 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS.  341 


342 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


having  rotation  about  the  main  crank-shaft,  used  on  small  steam  engines  in- 
stead of  an  eccentric  to  give  motion  to  the  valve-rod.     With  its  centre  on  the 


FIG.  759. 

central  line  of  the  main  shaft  there  will  be  no  motion,  and  used  for  the  posi- 
tion of  an  oil  cup,  the  oil  flowing  down  the  moving  arm  for  the  lubrication  of 
the  crank- journal. 

Eccentrics. — An  eccentric  is  a  modified  crank  ;  the  crank-pin  is  enlarged  so 

as  to  include  the  crank-shaft ;  motion 
is  conveyed  through  the  crank  to  the 
eccentric,  and  not  through  the  eccen- 
tric to  the  shaft. 

Fig.  763  represents  a  front  view, 
Fig.  764  the  side  view,  and  Fig.  765  a 
section,  of  a  form  of  eccentric  usually 
adopted  in  steam  engines  for  giving 
motion  to  the  valves  regulating  the  ac- 
tion of  the  steam  upon  the  piston. 
A  ring  or  hoop,  eccentric  strap,  is  ac- 
curately fitted  within  projecting  ledges 
on  the  outer  circumference  of  the  eccentric,  so  that  the  latter  may  revolve 
freely  within  it ;  this  ring  is  connected  by  an  inflexible  rod  with  a  system  of 
levers,  by  which  the  valve  is  moved.  By  the  revolution  of  the  shaft  to  which 


FIG.  762. 


FIG.  7G3. 


FIG.  765. 


MACHINE   DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


343 


the  eccentric  is  fixed  an  alternating  rectilinear  motion  is  impressed  upon  the 
rod,  its  amount  being  determined-  by  the  eccentricity,  or  distance  between  the 
centre  of  the  shaft  and  that  of  the  exterior  circle.  The  throw  of  the  eccentric 
is  twice  the  eccentricity  C  E  ;  or  the  diameter  of  the  circle  described  by  the 
point  E.  The  alternating  motion  is  identical  with  that  of  the  crank. 

The  term  eccentric  is  generally  confined  to  the  circular  eccentric,  all  others, 
with  exception  of  that  last  described,  being  called  cams  or  wipers,  but  eccentric 
is  often  applied  to  curves  composed  of  points  situated  at  unequal  distances 
from  a  central  point  or  axis. 

Fig.  766. — To  draw  the  eccentrical  symmetrical  curve  called  the  heart,  which, 
when  revolving  with  a  uniform  motion  on  its  axis,  communicates  to  a  movable 
point  A,  a  uniform  rectilinear  motion  of  ascent  and  descent. 

Let  C  be  the  axis  or  centre  of  rotation  upon  which  the  eccentric  is  fixed,  and 
which  is  supposed  to  revolve  uniformly  ;  and  let  A  A'  be  the  distance  which  the 
point  A  is  required  to  traverse  dur- 
ing a  half  revolution  of  the  eccen- 
tric. From  the  centre  C,  with  radii 
respectively  equal  to  C  A  and  C  A', 
describe  two  circles  ;  divide  the 
outer  one  into,  say,  16  equal  parts, 
and  through  these  points  of  divis- 
ion draw  the  radii  C  1,  C  2,  C  3,  etc. ; 
divide  the  line  A  A'  into  the  same 
number  of  equal  parts  as  in  the 
semicircle,  and  through  all  the 
points  1',  2',  3',  etc.,  draw  circles 
concentric  with  the  former  ;  the 
points  of  their  intersection  B,  D,  E, 
etc.,  with  the  respective  radii  C  1, 
C  2,  C  3,  etc.,  are  points  in  the 
curve  required,  its  vertex  being  at 
the  point  8. 

When  the  axis,  in  its  angular  motion,  shall  have  passed  through  one  division, 
the  radius  C  1  coincides  with  C  A',  the  point  A,  urged  upward  by  the  curvature 
of  the  revolving  body  on  which  it  rests,  takes  the  position  indicated  by  1' ;  and 
further,  when  the  succeeding  radius  C  2  shall  have  assumed  the  same  position, 
the  point  A  will  have  been  raised  to  2',  and  so  on  till  it  arrives  at  A',  after  a 
half  revolution  of  the  eccentric.  The  remaining  half,  A  G  F  8,  of  the  eccen- 
tric, symmetrical  with  the  other,  enables  the  point  A  to  descend  in  the  same 
manner  as  it  was  elevated. 

If  the  eccentric  is  turned  vertically  and  the  point  of  a  weighted  lever  rests 
upon  the  curve,  the  lever  will  take  a  uniform  motion  from  the  curve ;  but  if  a 
groove  be  cut  in  the  face  of  a  wheel  with  its  outer  edge  like  that  of  the  curve 
and  its  inner  one  parallel  to  the  outer  one  and  a  friction  roll  be  inserted  in  the 
groove  and  attached  to  a  lever  or  rod,  the  motion  of  roller  and  rod  will  be  similar 
to  that  of  the  weighted  lever  resting  on  the  eccentric.  This  construction  is  of 
frequent  use,  applicable  to  a  great  variety  of  motions,  and  is  designated  as  agrooved 
cam.  The  grooves  may  be  cut  either  in  the  face  of  a  plate  or  of  a  cylinder. 


344 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


In  the  "  Transactions  of  the  American  Society  of  Mechanical  Engineers  "  is 
an  illustration  of  a  grooved  cam  cut  on  a  machine  of  W.  A.  Gabriel,  M.  E.,  the 
motions  being  first  laid  out  on  paper  and  transferred  to  wooden  or  metallic  forms, 
which  act  as  guides  to  the  cutting  out  of  the  grooves.  The  difficulty  for  the 

draughtsman  is  to  comprehend 
the  motions  required  and  lay 
them  out  on  the  paper,  which  in 
lack  of  a  machine  may  be  trans- 
ferred to  the  metal  surface  and 
cut  by  hand,  with  the  aid  of 
drills,  chisels,  and  files. 

Fig.  767. —  To  draw  a  double 
and  symmetrical  eccentric  curve, 
such  as  to  cause  the  point  A  to 
move  in  a  straight  line,  and  with 
an  unequal  motion  ;  the  velocity 
of  ascent  being  accelerated  in  a 
given  ratio  from  the  starting- 
point  to  the  vertex  of  the  curve, 
and  the  velocity,  of  descent  being 
retarded  in  the  same  ratio. 

As  in  Fig.  76G,  take  C.as  the 

centre  of  motion  and  A  A'  the  distance  to  which  the  point  A  is  to  be  moved  by 
a  half  revolution;  with  C  as  centre  and  a  radius  C  A'  describe  a  circle  and  di- 
vide the  semicircle  into  eight  equal  arcs,  and  draw  the  radii  C  1,  C  2,  C  3,  etc. 
On  A  A'  as  a  diameter  describe  a  semicircle  and  divide  it  also  into  eight  equal 
arcs  and  project  the  points  of  division  1',  2',  3',  and  4' ;  on  the  diameter  A  A', 
with  C  as  a  centre  through  the  several  points  projected,  describe  circles ;  the 


FIG.  767. 


FIG.  769.     FIG.  770. 


intersection  severally  of  these  circles  with  the  radii  C  1,  02,  C  3,  will  give 
points  of  the  eccentric  curve  required. 

Fig.  768. —  To  construct  a  double  and  symmetrical  eccentric,  which  shall  pro- 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS.  345 


FIG.  771. 


:0* 


346 


MACHINE  DESIGN   AND  MECHANICAL  CONSTRUCTIONS. 


duce  a  uniform  rectilinear  motion,  with  periods  of  rest  at  the  points  nearest  to, 
and  farthest  from,  the  axis  of  rotation. 

The  lines  in  the  figure  above  referred  to  indicate  the  construction  of  the 


FIQ.  772. 

curve  in  question,  which  is  simply  a  modification  of  the  eccentric  represented 
at  Fig.  766.  In  the  present  example  the  eccentric  is  adapted  to  allow  the  mov- 
able point  A  to  remain  in  a  state  of  rest 
during  the  first  quarter  of  a  revolution 
B  D  ;  then,  during  the  second  quarter,  to 
cause  it  to  traverse,  with  a  uniform  mo- 
tion, a  given  straight  line  A  A',  by  means 
of  the  curve  D  G  ;  again,  during  the  next 
quarter  E  F  G,  to  render  it  stationary  at 
the  elevation  of  the  point  A' ;  and  finally, 
to  allow  it  to  subside  along  the  curve  B  E, 
with  the  same  uniform  motion  as  it  was 
elevated,  to  its  original  position,  after  hav- 
ing performed  the  entire  revolution. 

Fig.  769  represents  an  edge  view  of 
this  eccentric,  and  Fig.  770  a  vertical  sec- 
tion of  it. 

If  but  one  side  of  this  were  constructed, 
and  the  motion  only  equal  to  that  of  the 
arc  and  reciprocating,  it  would  raise  and 
lower  every  point  resting  on  it,  and  would 
be  called  a  wiper.  The  wiped  surface  is 
generally  flat,  an  arm  extending  out  from 
the  rod  to  be  raised,  and  a  curve  D.  G  may 
be  formed  adapted  to  the  height  of  lift, 
and  action  during  the  lift. 

Fig.  771  is  a  partial  vertical  section  of 
the  valve  motion  of  one  of  the  high-service 
pumping  engines  at  St.  Louis,  Mo.,  show- 
ing the  wiper  W,  or  lifting  toe,  with  its 
connection  with  the  valves.  The  wiper 
shaft  has  a  reciprocating  motion  by  which 
the  valve  stem  is  raised  and  dropped.  The  valves  are  double-beat  balanced  ; 
the  cut  shows  the  arrangement  of  the  steam  jacket  J,  a  space  for  live  steam  in- 
closing the  cylinder,  to  aid  in  preserving  the  temperature  and  pressure  within  it. 


FIG. 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


347 


Fig.  772  exhibits  on  a  larger  scale  a  portion  of  a  section  in  plan  and  eleva- 
tion of  the  steam  piston  and  mode~of  packing  of  the  above  engine. 

Fig.  773  is  the  elevation  of  a  stamp  mill  in  which  a  double  wiper  on  a  rotary 
shaft  raises  the  stamp  by  its  contact  with  a  hub  or  collar  on  its  shaft,  and  lets 
it  fall  suddenly  by  its  weight. 

Machines  like  the  above  are  often  used  in  bleacheries  to  give  a  watered 
finish  to  goods.  The  battery  of  stamps  is  equal  to  the  width  of  the  cloth  which 
turns  in  a  roll  beneath  it,  and  the  blows  follow  in  quick  succession. 

Connections. — Figs.  774  and  775  are  sections  of  cottered  joints  of  wrought- 
iron  bars,  the  first  made  with  a  socket  and  the  end  of  one  of  the  bars ;  the 


latter  by  a  sleeve  connecting  the  two  bars.  The  bars  in  the  socket  and  sleeve 
are  upset,  to  give  more  section  than  the  bars  themselves,  so  that  the  slots  cut 
for  the  cotters  c  c  will  not  reduce  the  strength  below  that  of  the  bars.  The 
cotters  must  have  sufficient  shearing  strength  and  bearing  surface,  and  at  the 
same  time  diminish  as  little  as  possible  the  section  of  the  parts  connected. 
The  proportions  given  in  the  figures  are  drawn  to  a  scale  of  the  diameter  of 
the  enlarged  part  as  the  unit,  and  the 
proportions  given  in  figures  are  such  as 
obtain  in  practice  for  wrought-iron. 
If  the  cotter  be  of  steel,  its  breadth 
may  be  three  fourths  of  that  given, 
preserving  the  other  dimensions  the 
same ;  the  thickness  is  '25  of  the  unit. 

The  knuckle-joint  (Fig.  776)  is 
given  in  dimensions  of  the  bar  as  a 
unit,  and  adapted  to  usual  work.  If 
there  is  much  motion  at  the  joint,  the 
wearing-surface  should  be  larger,  by 
increasing  the  width  of  the  eyes  and  Fio 

the  length  of  the  pin.     The  pin  in  the 
drawing  is  through  the  collar ;  usually  the  pin  is  extended,  and  the  pin  passes 
through  the  bolt  outside  the  collar. 

Connecting-rods,  in  their  application  to  steam  engines,  are  the  rods  connect- 
ing the  piston  through  the  cross-head  to  the  crank.  When  two  cranks  are 
connected  it  is  called  a  coupling-rod. 


34:8 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


Fig.  777  is  the  side  elevation  of  the  eccentric  and  strap  of  a  Reynold's 
20*  X  48*  Corliss  engine.  The  eccentric  rod  is  made  with  a  shoulder,  the  stem 
is  fitted  to  the  If*  socket,  and  held  firmly  by  a  nut  in  the  4"  groove. 

Fig.  778  is  a  double  eccentric,  used 
in  giving  motion  to  the  link  in  the  cut- 
off. The  eccentrics  are  made  in  halves 
for  convenience  in  putting  them  on  the 
shaft. 

Governors  are  used  on  quick-run- 
ning engines  (page  407)  to  control  the 
cut-off  through  movable  eccentrics,  but 
eccentrics  adjustable  by  hand  are  con- 
venient as  applied  to  pumps  in  modi- 
fying the  stroke.  With  a  uniform  ac- 
tion of  the  motor  the  stroke  of  the 
pump  is  reduced,  giving  greater  pres- 
sure on  the  plunger,  say  from  a  domes- 
tic to  a  fire  pressure. 

Figs.  779  and  780  are  plan  and  sec- 
tion of  such  an  eccentric.  The  crank-pin  is  fastened  on  a  slide-rest  moving  in 
guides  attached  to  the  power  shaft  by  a  long  hub.  To  hold  the  slide  firmly  to 
the  shaft-hub  there  are  three  key-bolts,  n  n  n.  To  move  the  crank-pin  slide 
these  bolts  must  be  slacked,  and  by  means  of  a  hand  lever  (Fig.  781),  using  as 
a  fulcrum  the  pins  on  one  of  the  guides,  and  bringing  the  short  end  of  the 
lever  against  a  projection,^,  attached  to  the  crank-pin,  it  may  be  moved  to  any 
desirable  position  or  stroke  and  clamped  to  the  hub  firmly  by  the  key-nuts. 


FIG.  777. 


1 

;  i 

t-f--+ 

'-'v-A  j  

1 

t  i 

L/    * 

i    'N_    '         - 

^ 

T  

,        . 

l  n-1  1  — 

i         | 

1              i      T 

i_J                          1 

f*~~\~t    T  rf" 

--;-- 

n-i"-:<rVvii 

• 

»--- 

FIG.  T78. 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


349 


FIG.  779. 


FIG. 


Fig.  782  is  the  elevation,  plan,  and  section  of  an  eccentric  strap  of  a  locomo- 
tive engine,  of  cast-iron,  with  very  long  bolts,  and  a  very  rigid  construction. 
The  strap  forms  a  cup-section  over  the  projecting  ring  on  the  eccentric,  and 
retains  the  oil  at  the  bottom  for  more  efficient  lubrication  and  prevents  drip. 

Figs.  783,  784,  and  785  is  another  cast-iron  eccentric  strap,  in  which  a  box 
is  inserted,  fitted  with  metallic  disks,  to  prevent  frequent  oiling.  The  bolts  at 
the  large  end  are  bored  up  to  a  sectional  area  of  that  of  the  screwed  portion  to 
secure  equal  elasticity. 


FIG.  782. 


350 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


FIG.  784. 


U 


MACHINE   DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


351 


In  many  marine  engines  the  boxes  of  both  crank  and  cross-head  pins  are 
connected  with  strong  and  heavy  bolts  without  any  other  rod. 

Fig.  786  is  a  strap-end  of  a  connecting-rod,  from  the  Corliss  Steam-Engine 
Company.  The  peculiarity  is  the  adjusting-screws  connected  with  the  boxes. 

Fig.  787  is  the  strap-end  of  a  locomotive  connecting-rod  in  which  the  wear 
of  the  boxes  is  taken  up  by  a  cotter  at  the  end  of  the  strap. 


t2T 


FIG.  788. 


FIG.  78 


In  Fig.  788  the  key  is  between  the  bolts ;  the  weakness  from  bolt-holes  or 
cotter-slot  is  compensated  by  the  width  of  the  strap. 

Fig.  789  is  the  box-end  of  a  locomotive-rod,  in  which  the  strap  gives  place 
to  a  box  forged  on  the  end  of  the  connecting-rod. 


352  MACHINE   DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


353 


Figs.  790,  791,  and  792  are  side,  plan,  and  end  views  of  a  connecting-rod  of 
the  Southwark  Foundry,  of  Philadelphia,  used  on  their  fast-running  Porter- 
Allen  engines. 

The  cross-head  end  is  a  strap-end,  while  that  of  the  crank  is  a  box-end,  and 
of  larger  diameter  than  the  former  on  account  of  the  extra  wear  and  size  of  the 
crank-pin.  The  length  of  the  page  does  not  admit  of  the  representation  of  the 
full  length  of  the  connecting-rod  on  the  scale ;  it  is  therefore  shown  broken, 
with  the  dimensions  figured  in.  The  sections  of  the  two  ends  are  drawn  in  on 
the  rods ;  the  circular  section  A  is  the  same  as  that  of  the  piston-rod,  and  both 
are  represented  in  the  conventional  hatching  of  cast-iron,  but  it  is  of  wrought- 
iron.  The  gib  g  and  key  or  cotter  v  at  the  strap-end  are  of  steel,  and  the  key 
is  fastened  when  in  position  by  a  set-screw  through  the  head.  At  the  box- 
end,  a  wedge  and  screw  forces  the  box  into  position. 


354:  MACHINE  DESIGN  AND  MECHANICAL  CONSTEUCTIONS. 

Figs.  793  and  794  are  the  sides  and  top  elevations  of  the  connecting-  and 
coupling-rods  of  the  express  locomotives  of  the  New  York  Central  and  Hud- 
son Eiver  Kailroad,  designed  by  Mr.  Buchanan,  and  built  at  the  Schenectady 
Locomotive  Works,  of  which  the  drawing  of  driving  wheels  will  be  found 
at  Fig.  760,  of  the  frame  Fig.  1301,  and  the  boiler  Fig.  926,  with  the  gen- 
eral weights  and  dimensions  of  the  locomotive.  Fig.  795  is  a  section  of  the 
coupling-rod. 

Fig.  796  is  a  connecting-rod  of  the  Eider  hot-air  engine,  in  which  the  ends, 
made  of  gun  metal,  are  connected  together  by  a  tube  in  which  is  fitted  a  rod, 
extending  from  the  upper  to  the  lower  brass,  and  so  arranged  that  one  key,  E, 
capable  of  nice  adjustment  by  nuts,  at  once  takes  up  the  lost  motion  on  both 
upper  and  lower  brasses. 


FIG.  796. 


Fig.  797  is  the  stub  end  of  a  coupling-rod.  The  bushes  are  solid,  of  brass, 
and  kept  from  turning  round  by  taper-pins,  which  are  secured  by  set-screws 
pressing  on  the  larger  end  ;  taper,  -fa  in  3  inches. 

Cast-iron  connecting-rods  are  now  very  seldom  used.  In  some  cases  of 
vertical-beam  pumping  engines  it  is  necessary  that  the  weight  of  the  steam 
pistons  should  be  counterbalanced  by  some  mass  of  material,  and  it  may  be 
convenient  to  make  use  of  a  heavy  pump-connection. 

The  wrought-iron  crank  connections  of  American  river-boat  engines  are 
peculiar  in  their  construction.  They  are  made  as  light  as  possible,  with  very 
great  stiffness.  Fig.  798  represents  the  side  elevation  of  such  a  connecting- 
rod.  The  means  adopted  to  give  the  required  stiffness  consist  of  a  double- 
truss  brace,  a  a,  of  round  iron,  which  is  fastened  by  bolts  to  the  rod  near  each 
end  ;  struts  b  b,  cut  with  a  screw,  and  furnished  with  nuts,  pass  through  the 
centre  of  the  brace,  by  which  means  the  braces  are  tightened.  The  connecting- 
rod  at  its  smallest  part  near  the  extremities  is  of  the  same  diameter  as  the  pis- 
ton-rod ;  the  boss  in  the  centre  is  from  one  to  two  inches  more. 

Fig.  799  is  the  front  view  of  the  forked  end  of  the  rod,  which  is  fitted  with 
the  usual  straps,  gibs,  and  cotters.  Fig.  800  is  the  side  view  of  the  brace-rod. 

The  working-beam  (Figs.  801  and  802),  of  similar  framed  construction,  was 
at  one  time  largely  used  for  river  boats,  but  may  still  be  applicable  in  many 
places  for  its  lightness  and  stiffness.  It  is  composed  of  a  skeleton  frame  of 
cast-iron  round  which  a  wrought-iron  strap  is  fitted  and  fastened.  The  strap 
is  forged  in  one  piece,  and  its  extreme  ends  are  formed  into  large  eyes,  which 
are  bored  to  receive  the  end-pins  or  journals.  The  skeleton  frame  is  a  single 
casting,  and  contains  the  eyes  for  the  main  centre  and  air-pump  journals ;  the 


MACHINE   DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


355 


centre  hub  is  strengthened  by  wrought-iron  hoops  shrunk 
upon  it.     At  the  points  of  contact  of  the  strap  and  skele- 
ton, key-beds  are  prepared.     Small  straps  connect  the  frame 
and  main-strap  at   these  points,  keyed  to  the  frame — keys 
riveted  over.     The  frame  is  further  braced  by  wrought-iron 
straps,  C  C,  which  tie  the  middle  of  the  long  arms  to  the 
extremities  of  the  shorter  ones.     The  following  are  the  gen- 
eral dimensions :  From  centre  to  centre  of  end-journals,  26 
feet;  this  is  somewhat  less  than  the  usual  proportion  to 
length  of   stroke,   being  slightly  less   than  double  the 
stroke ;    length    of   centre   hub,  26",  a  a ;   diameter   of 
main  centre  eye  c,  15|" ;  of  air-pump  journal-eye  d,  6f; 
of  end-journals  e  e,  8£". 

Double  plates  or  flitches  of  wrought-iron  are  often 
used  in  the  construction  of  working-beams  and  side-levers. 
Fig.  803  is  the  section  between  the  two  plates  of  a  beam 


FIG.  79 


FIG.  797. 

of  this  kind,  attached  to  the  compound  pumping  engines 
at  Milwaukee,  Wis.  The  plates  are  each  30  feet  long, 
by  6'  4"  deep  at  centre,  by  If"  thick.  The  connections 
between  the  two,  shown  in  section  in  the  figupe,  are 

cast-iron  pipes  with  wide  flanges  at 

each  end  riveted  or  bolted  to  the 

plates.     The  main  centre  and  other 

small    journal  -  pins    are    rods    of 

wrought-iron,  passing  through  the 

pipes,   and    extending   outside    the 

plates  to  form  the  journals ;   c  is 

the  section  of   the  pin   for  crank 

connection,  p  for  that  of  pump,  h 

for  that  of  high- pressure  cylinder,  I 

for  that  of  low-pressure  cylinder,          FIG.  799. 


FIG.  800. 


356 


MACHINE   DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


m  for  main  centre-pin,  and  g  for  the  parallel-motion  links.     This  last  is  usu- 
ally the  position  of  the  air-pump  centre,  but  in  this  engine  the  air-pump  is 


FIG.  802. 


below  the  high-pressure  cylinder,  and  its  piston-rod  is  extended  to  the  air- 
pump  piston.     The  dimensions  are — H.  P.,  cylinder  36"  X  62" ;  L.  P.,  cylin- 


FIG.  803. 


der  58"  X  8  feet.     The  heads  of  the  two  cylinders  are  kept  at  the  same  levels 
by  increasing  the  length  of  the  H.  P.  piston. 

Working-beams  with  vertical  steam  engines  are  now  seldom  used  except  in 


Fia.  804. 


connection  with  large  pumps.  For  power  the  horizontal  engine  is  now  sub- 
stituted and  connected  closely  with  the  fly-wheel.  Fig.  804  represents  such 
an  engine  and  frame. 


MACHINE  DESIGN  AND   MECHANICAL   CONSTRUCTIONS.  357 


The  pin  p  is  the  connection  in.the  cross-head  (Fig.  804)  between  the  piston- 
rod  of  the  steam  engine  and  the  connecting-rod  to  the  crank. 

Figs.  805,  806,  and  807  represent  the  plan,  end  view,  and  section  of  the 
cross-head  adopted  by  the  Southwark  Foundry  for  their  high-speed  engines.  It 
is  of  cast-iron,  with  large, 
flat  faces,  the  pin  p  for 
the  connecting-rod  being 
in  the  middle  of  the 
length.  This  pin  is  of 
wrought-iron,  large  and 
flattened  on  top  and  bot- 
tom, so  that  the  boxes  of 
the  rod  can  never  bind  on 
the  pin  at  the  extreme  of 
the  vibrations  of  the  rod  ; 
usually  these  pins  are 
round.  The  pin  is  formed 
with  large  squares  at  the 
ends,  by  which  it  is  fitted 
into  the  jaws  of  the  cross- 
head,  where  it  is  secured  FIG.  so?. 
by  a  steel  pin  passing 

through  the  cross-head.  The  bearing  surfaces  of  the  head  and  those  of  the 
guide-bars  are  finished  by  scraping  to  true  planes ;  there  are  no  means  of  ad- 
justment, as  there  is  no  wear  if  kept  clean. 


FIG.  808. 


1 


FIG.  809. 


It  is  to  be  understood  that  the  piston-rod  moves  in  a  straight  line,  and  that 
the  stress  on  the  connecting-rod  pin  is  mostly  oblique.  Guides  are  to  be  pro- 
vided, between  which  the  cross-head  slides,  to  take  the  oblique  stress  off  the 
piston-rod. 


358 


MACHINE  DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


Pigs.  808  and  809  are  elevation  and  plan  of  guide-bars  suited  to  the  cross- 
head  above,  which  are  in  common  use  for  both  vertical  and  horizontal  engines. 
Lugs  or  ears  are  cast  on  the  steam-cylinders,  and  on  the  frames  to  which  the 
bars  are  bolted,  and  between  which  the  cross-head  slides.  The  grooves  or 
notches  across  the  guide-bars,  at  the  ends  of  the  stroke,  are  to  throw  off  any 
grease  or  dirt  that  may  be  carried  along  by  the  head  and  prevent  their  accumu- 
lation. The  stress  on  the  guide-bars  is  due  to  the  pressure  of  the  steam  on  the 
piston  acting  obliquely  on  the  crank  through  the  connecting-rod,  and  is  the 
greatest  when  the  crank  is  at  right  angles  to  the  piston.  It  can  be  determined 
by  multiplying  the  pressure  on  the  piston  by  the  length  of  the  crank,  and  divid- 
ing the  product  by  the  length  of  the  connecting-rod,  which  will  be  the  stress 
tending  to  separate  the  guides.  If  the  connecting-rod  be  3  times  the  stroke,  or 
6  times  that  of  the  crank,  which  is  the  usual  proportion,  then  the  stress  is  £ 
the  pressure  on  the  piston.  Sometimes  the  proportion  of  connecting-rod  to 


FIG.  810. 


stroke  is  2£  to  1.     When  a  portion  of  the  force  of  the  steam  is  opposed  directly 
to  the  resistance,  as  in  direct-acting  pumps,  and  only  the  irregularities  in  the 

steam-pressure  are  transmitted  through  the  connect- 
ing-rods, the  proportion  of  rod  to  stroke  may  be  still 
smaller. 

Fig.  810  is  the  cross-head  of  the  Harris-Corliss 
engine  in  which  the  bearing  surfaces  of  guides  are 
adjusted  by  bolts  passing  through  wedges. 

On  locomotives  it  is  not  unusual  to  have  the 
guide  on  one  side,  as  in  Fig.  811,  where  the  side-bars  are  of  wrought-iron  and 
the  slide-block  is  fastened  between  the  two  plates  of  the  cross-head  by  bolts. 
It  is  the  most  common  practice  in  this  country  to  use  guides  with  vertical  en- 
gines, even  when  the  connection  is  with  working-beams. 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


359 


Steam- Cylinders. — Fig.  812  is  a  sectional  plan  of  a  common  form  of  small 
steam-cylinder.  A  is  the  cylinder,  B  the  piston,  b  the  piston-rod,  D  the  slide- 
valve,  d  the  valve-rod,  C  the  valve- 
chest,  c  the  chest-cover,  s  s  the 
steam-ports,  e  the  exhaust-port,  S  the 
stuffing-box  of  the  piston-rod,  s'  that 
of  the  valve-rod.  H  is  the  front 
head  and  H'  the  back  head  of  the 
cylinder.  The  bolts  attaching  the 
heads  to  the  body  of  the  cylinder  are 
not  shown. 

Length  of  Cylinder. — It  is  the 
present  practice,  in  the  construction 
of  stationary  engines  for  driving  ma- 
chinery, to  make  the  stroke  not  over 
twice  the  diameter  of  the  cylinder,  and  for  diameters  above  24"  about  1£  time  the 
diameter  of  the  cylinder,  and  invariably  to  place  the  cylinders  horizontally  with 
a  direct  connection  with  the  crank,  without  the  intervention  of  a  working-beam. 

Fig.  813  is  a  front  view  partly  in  section,  and  Fig.  814  is  a  transverse  section 
through  the  centre  of  a  Fishkill  Corliss  steam-engine  cylinder,  giving  the  steam- 


Fia.  812. 


FIG.  813. 


valves  in  section  and  outside  view  showing  their  connection  with  the  wrist-plate 
and  its  motion,  also  the  piston-rod  and  stuffing-box  with  a  scale  of  reference. 
The  thickness  of  shell  Mr.  Henthorne  finds,  by  many  examples  in  Corliss's  large 
practice,  to  conform  to  the  formula  t  =  -268  Vd,  t  and  d  being  in  inches. 


360 


MACHINE   DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


Thus  the  thickness  of  the  shell  of  a  16"  cylinder  will  be  V 16  X  '268  =  4  X  '268  = 
1-072,  a  little  more  than  1".  The  thickness  of  flanges  should  exceed  that  of 
the  shell  by  |  to  %  its  thickness.  The  bolts  should  not  be  less  than  f "  and  sel- 
dom more  than  1".  It  is  better  to  increase  the  number  of  bolts  than  their  di- 


Fio.  814. 

ameter,  the  breadth  of  flange  to  be  about  3  times  the  diameter  of  the  bolts,  and 
the  pitch  of  the  bolts,  or  the  distance  between  centres,  about  6  times  the  diam- 
eter of  the  bolts. 

Cast-iron  is  the  material  chiefly  used  for  pistons,  but  those  of  wrought-iron, 
brass,  bronze,  and  cast-steel  are  common.  The  wrought-iron  pistons  recently 
introduced  in  American  locomotive  practice  follow  the  designs  of  the  older 
cast-iron  pistons. 

Fig.  815  is  the  cast-iron  piston  of  a  locomotive.  The  spring  or  snap-rings 
forming  the  packing  are  of  cast-iron,  1^-"  wide  by  %"  thick,  of  uniform  section. 
The  split  is  made  with  a  half  lap,  and 
the  splits  of  the  two  rings  are  on  oppo- 
site sides  of  the  piston.  The  outsides  of 
the  rings  are  turned  to  a  diameter  slightly 
in  excess  of  that  of  the  cylinder,  and  are 
sprung  into  recesses  of  the  piston  fitted 
to  receive  them. 

Fig.  816  is  a  half  plan  and  half  sec- 
tion and  Fig.  817  a  full  cross-section  of 
piston   of   a   steam-cylinder  of   Leavitt's 
design  ;  the  packing  is  Wheelock's,  in  which  the  rings  are  in  sections  joined  to 
adjust  themselves  to  cylinders  that  have  become  worn. 


MACHINE   DESIGN  AND  MECHANICAL  CONSTRUCTIONS.  361 


FIG.  816. 


SECTION   E  F 


FIG.  817. 


Large  cast-iron  pistons  are  made  hollow  and  strengthened  by  internal  radial 
ribs.  In  Fig.  772  is  shown  the  packing  of  the  steam  piston  of  the  cylinder  of 
one  of  the  St.  Louis  pumping-engines.  Fig.  818  is  a  design  from  an  English 
manual  for  a  large  cast-iron  piston.  The  dimensions  marked  on  the  figure  are 

in  terms  of  the  unit     **    ,  in  which  D  is  the  diameter  of  the  piston  in  inches 


362 


MACHINE  DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


and  P  the  initial  pressure  per 
square  inch.  The  junk-ring  is 
secured  by  wrought-iron  or  steel 
bolts  and  brass  nuts.  The  diam- 
eter of  the  junk-ring  bolts  may  be 

•28TVP 

— ^-~ 1- 1  inch,  and  they  may 

be  placed  at  a  pitch  of  seven  to 
ten  times  their  diameter.  The 
number  of  ribs  or  webs  may  be 

about  -=r  +  2  and  their  thickness 


•4D.yp 

100     ' 


The  size  of  the  space 


FIG.  818. 


for  the  packing  will  depend  on 
the  design  of  packing  adopted. 
Fig.  819  is  a  sectional  plan  and  Fig.  820  is  a  sectional  elevation  of  the  inte- 
rior of  a  piston-ring,  showing  another  common  form  of  ring  packing,  which 
consists  of  a  single  interior  ring  r  and  two  exterior  rings  r"  r",  and  each  cut  in 


FIG.  819. 


FIG.  820. 


two  and  so  fastened  that  the  joints  are  always  broken.  The  packing  is  set  out 
by  springs  s  s,  one  of  which  is  shown.  F  is  the  follower,  which  can  be  taken 
off  for  the  admission  of  the  rings  and  springs,  and  then  replaced  and  bolted  to 
the  piston,  making  a  close  joint  with  the  end  of  the  rings.  The  depth  of  the 
piston  at  the  exterior  is  from  3"  to  9",  varying  with  the  diameter  of  the  piston. 
Figs.  821,  822,  and  823  are  sections  of  the  exterior  rings  of  pistons  adapted 


FIG.  821. 


FIG.  822. 


FIG.  823. 


more  particularly  to  water-pumps.  Fig.  821  depends  on  the  closeness  of  fit  of 
the  exterior  of  the  piston  with  the  inner  surface  of  the  cylinder,  and  when  accu- 
rately turned  and  fitted  the  leak  is  very  inconsiderable,  and  by  the  use  of  grooves 


MACHINE   DESIGN   AND   MECHANICAL   CONSTRUCTIONS. 


363 


(Fig.  822)  it  is  still  less.  In  Fig.  823  the  joint  between  the  piston  and  the  cyl- 
inder is  made  tight  by  a  gasket,  usually  of  hemp,  compressed  by  a  joint  ring  or 
follower,  a,  in  the  pocket  between  piston  and  cylinder. 

Wood-packing  put  in  short  staves,  as  shown  in  Fig.  824,  is  often  used  for 
pump-pistons  and  buckets.  Make  the  diameter  of  the  wood-packing  a  little 
less  than  the  diameter  of  the  barrel  of  the  pump,  to  allow  for  the  swelling 
which  takes  place  when  the  wood  becomes  saturated  with  water. 


FIG.  825. 


FIG.  824. 


FIG.  826. 


Fig.  825  is  a  cup  leather  packing,  and  Fig.  826  is  a  U-packing  for  small 
cylinders  of  hydraulic  presses.  The  application  of  the  first  will  be  understood 
from  Fig.  827,  in  which  the  piston  is  packed  with  two  cup  leathers,  in  this  case 
to  withstand  pressure  in  both  directions.  Were  the  piston  single-acting,  but 
one  cup  would  be  necessary — and  if  from  beneath  the  piston,  this  would  be  the 
lower  cup.  The  flexible  flange  is  pressed  against  the  inside  of  the  cylinder,  and 
the  joint  is  perfectly  tight. 


FIG.  827. 


FIG.  829. 


364: 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


Fig.  828  shows  the  application  of  the  U-packing  ;  it  is  put  into  a  recess  in 
the  cylinder  by  bending  the  packing  into  a  saddle-bag  form,  and  then  allowing 
it  to  spring  back  into  the  recess.  In  English  practice  hemp  packings  serve 
the  same  purpose,  and  are  necessary  when  the  temperature  of  the  water  ex- 
ceeds 90°. 

Packings  can  be  obtained  from  hydraulic-pump  and  press  manufacturers, 
and  are  kept  in  stock  of  all  the  usual  sizes.  Their  depths  are  from  1"  to  1£" 
for  diameters  varying  from  4"  to  14",  and  the  space  occupied  by  the  thickness 
in  the  U  from  \"  to  f ".  A  filling  of  flat  braided  hemp  is  placed  inside  the  U 
to  keep  it  tight  when  not  under  pressure.  The  packings  are  made  by  steeping 
the  leather  in  warm  water,  forcing  them  into  a  mould,  and  leaving  them  to  dry 
and  harden.  The  moulds  (Fig.  829)  are  made  of  either  metal  or  wood  ;  fre- 
quently the  rings  are  of  metal,  and  the  piston  over  which  the  cup  is  formed,  of 
wood. 


The  outer  cylinder  forming  the  exterior  shell  of  the  steam-jacket  is  fastened 
to  the  steam-cylinder,  but  is  allowed  to  move  under  changes  of  temperature. 
In  Figs.  830  and  831  are  given  longitudinal  and  transverse  sections  of  a  steam- 
cylinder  with  jacket,  as  constructed  by  E.  D.  Leavitt,  M.  E.,  in  which  the  upper 
and  lower  end  of  jacket  is  cast  with  the  cylinder,  and  the  connection  between 
the  two  is  by  a  copper  U-ring,  which  admits  the  necessary  expansion  and  con- 
traction. All  steam-cylinders,  whether  with  or  without  jackets,  should  be 
clothed — that  is,  covered  with  some  preparation  to  prevent  the  escape  of  heat 


MACHINE  DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


365 


from  contact  with  air.     The  usual  clothing  is  hair  felt,  with  a  lagging — that  is, 
an  exterior  shell  of  some  wood,  usually  black  walnut. 


FIG.  832. 


Fig.  832  is  a  section  and  partial  elevation  of  the  air-chamber  of  one  of 
Leavitt's  pumps.  It  is  of  the  Thames  Ditton  variety,  in  which  the  whole  charge 
of  water  is  drawn  into  the  lower  chamber,  and  a  portion  corresponding  to  the 
difference  between  the  two  plungers  raised  to  the  full  head  in  the  upper  cham- 
ber j  in  the  down  stroke  a  quantity  of  water  equal  to  the  displacement  of  the 
upper  plunger  is  raised  to  the  full  head.  The  packing  of  the  lower  plunger  is 
by  grooves  in  the  exterior  ring ;  this  form  of  packing  by  proper  fitting  makes  a 
tight  joint  without  friction.  With  this  packing  the  lower  chamber  of  the  pump 
can  be  drawn  off  and  examined,  leaving  the  water-load  in  the  upper  piston.  The 
dash-pot  of  a  Fishkill  Landing  Corliss  engine,  with  a  similar  groove  packing, 


366 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


was  tested  to  a  water  pressure  of  140  pounds  and  leaked  very  little.    Like  pack- 
ings are  used  in  air-pump  pistons  with  satisfaction. 

The  pump-valves  are  not  shown  in  the  drawing,  but  are  Riedler's  controlled 
valves,  which  are  opened  by  the  movement  of  the  water  and  closed  positively  by 
a  mechanical  connection. 


Fio.  834. 


FIG.  833. 

Fig.  833  is  a  section  of  a  single  Worth- 
ington  steam-pump,  one  of  a  pair  always 
placed  side  by  side  (hence  called  duplex), 
combined  to  act  reciprocally  on  the  steam- 
valves  of  each  other. 

In  the  form  of  pump  shown,  the  length 
of  barrel  is  about  equal  to  the  diameter 
of  the  piston,  but  the  length  of  the  piston 
is  equal  to  that  of  the  stroke  of  the  pump 
plus  that  of  the  length  of  the  barrel. 

In  Fig.  834  the  pump  barrel  is  long 
and  the  piston  short. 

The  duplex  was  H.  R.  Worthington's 
invention  and  is  now  the  general  type  of 
most  makers  for  boiler  feed  pumps  and 
small  water  supplies.  For  the  boiler  feed 
especially  of  locomotives  the  injector  is 
largely  used,  and  as  supplementary  to  the 
pump. 

The  injector  is  an  apparatus  in  which 
the  momentum  of  a  jet  of  steam  issuing 
from  the  boiler  is  transferred  to  a  body 
of  water,  producing  a  resulting  velocity 
sufficient  to  force  the  water  into  the  same 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


367 


boiler.  Many  shops  manufacture,  injectors.  The  section  shown  (Fig.  835)  is 
from  William  Sellers  &  Co.,  one  of  the  earliest  makers,  and  the  explanation  of 
its  working  illustrates  the  principles  of  a  good  and  successful  machine. 

To  start  the  injector  the  valve  G  is  raised  to  permit  the  admittance  of  water 
into  the  chamber  J  ;  the  lever  F  is  then  opened  sufficiently  to  allow  the  steam 
through  the  opening  d  of,  while  the  plug  //  still  keeps  the  forcing  nozzle  a 
closed,  thus  admitting  steam  into  the  annular  steam  nozzle  i,  which,  passing 
into  the  water-chamber  J  and  the  combining  tube  through  the  overflow  cham- 
ber I  and  into  the  overflow  E,  producing  a  strong  vacuum  in  the  water-chamber 
J,  into  which  the  water  from  the  source  of  supply  is  forced  by  the  atmospheric 
pressure,  the  characteristic  of  a  lifting  injector.  The  combined  jet  of  water 
and  steam  passes  through  the  combining  tube ;  the  valve  F  is  then  fully  raised, 
admitting  steam  into  the  forcing  nozzle  a ;  this  steam,  uniting  with  the  jet  in 
the  combining  tube,  accelerates  its  velocity  to  such  an  extent  that  the  valve  g 
is  forced  down,  thus  allowing  the  passage  of  water  to  the  boiler. 


n 
1 

i 

FIG.  835. 


The  issuing  steam  and  water  maintains  its  velocity  by  reduction  of  the  areas 
of  channel  discharge  till  the  last  channel  in  connection  with  the  boiler,  which 
increases  till  it  meets  the  valve  g. 

The  lower  the  temperature  of  the  feed-water  the  greater  the  capacity  of  the 
injector.  As  the  steam  strikes  the  water  its  momentum  is  checked  and  trans- 
ferred to  heat  and  at  once  absorbed  by  the  feed,  all  the  energy  apparently 
wasted  reappearing  in  the  latent  and  sensible  heat  transferred  to  the  feed.  It 
is  this  absorption  of  heat  that  gives  the  great  economy  over  the  feed-pump,  but 
for  raising  water  it  is  not  to  be  used  except  where  simplicity  of  construction 
and  convenience  of  application  may  offset  the  waste  of  power. 

To  use  the  injector  as  a  heater  to  prevent  the  freezing  of  the  water  in  the 
water-tank,  the  valve  G  is  opened  and  the  eccentric  lever  H  closed ;  the  steam 
will  then  have  free  admittance  into  the  chamber  I  and  the  water-tank. 


368 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


Each  size  of  injector  is  named  from  the  diameter  of  the  delivery  tube  in 
millimetres.  In  the  table  given  by  Strickland  L.  Kneass  the  diameter  runs 
from  3'2  to  11'5  millimetres;  the  steam  pressure  from  30  to  150  pounds,  and 
the  discharge  23'5  to  550  cubic  feet  per  hour ;  height  of  lift,  1  foot ;  tempera- 
ture of  water,  60°. 

Ejectors  are  also  used  as  pumps  for  the  raising  of  water  by  suction  and 
pressure,  of  which  Figs.  836  and  837  are  of  the  simplest  form.  The  steam  is 


FIG.  836. 


FIG.  837. 


FIG.  838. 


ejected  through  a  central  nozzle  a,  while  the  water  is  raised  and  discharged 
through  the  pipe  inclosing  it.  The  same  principle  of  induced  current  is 
applied  through  a  current  of  water,  steam,  or  air  in  discharging  earth  from  a 
caisson,  the  ashes  from  the  boiler  hold  of  a  marine  engine,  water  from  founda- 
tions or  from  driven  wells. 

Fig.  838  is  a  section  of  a  Korting  blower  to  improve  the  draft  in  the  ash- 
pit, fire-box,  or  chimney  of  a  boiler,  and  Fig.  839  is  that  of  a  larger  size,  show- 
ing the  construction  of  the  jet  in  which  the  force  of  the  steam  drawing  the 
air  through  compound  nozzles  reduces  the  intensity  of  its  flow,  but  increases 
its  quantity  to  suit  the  purposes  of  draft. 

M.  Mondesir,  in  the  French  Exhibition  of  1867,  effected  the  ventilation  by 
means  of  reservoirs  of  compressed  air.  Around  the  exterior  of  the  building 
there  was  a  large  underground  gallery  into  which  the  exterior  air  was  intro- 
duced by  sixteen  vertical  shafts  symmetrical  in  position,  and  from  the  main 
gallery  the  air  was  distributed  by  radial  galleries  into  the  interior  of  the  build- 
ing, into  which  the  air  current  was  introduced  by  numerous  jets  of  condensed 
air  from  the  reservoirs.  The  air  was  supplied  to  the  jets  at  a  pressure  of  29|  to 
3l£  inches  of  water.  The  vitiated  air  escaped  through  a  ventilator  in  the  roof. 

Clearances  in  cylinders' include,  in  general  signification,  not  only  the  spaces 
between  the  piston  and  cylinder-heads  at  the  ends  of  the  stroke,  but  also  the 
spaces  between  the  cylinder  and  the  valves  ;  and  as  those  spaces  are  voided  in 
a  steam-cylinder  at  each  stroke  for  which  adequate  work  from  the  steam  is  not 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


369 


obtained,  they  are  usually  made  as  small  as  possible.  If 
the  steam  is  fairly  dry,  from  %'  to'-l"  will  be  sufficient 
for  end-clearances — that  is,  minimum  distance  between 
piston  and  cylinder-head. 

Piston-rods  are  proportioned  to  the  stress  on  them, 
usually  one  square  inch  of  section  to  each  5,000  pounds 
of  stress.  In  Fig.  815  the  tapered  end  fits  a  taper  hole 
in  the  piston,  and  is  riveted  over.  It  is  more  usually 
held  by  a  nut,  some  use  a  shoulder  on  the  inner  end  of 
the  piston-rod  instead  of  a  taper,  and  the  nut  brings  the 
piston  strongly  up  against  this  shoulder. 

Piston-rods  are  made  either  of  steel  or  hammered 
iron,  some  makers  of  engines  preferring  one  and  some 
the  other  material. 

Stuffing-boxes  are  the  mechanisms  to  prevent  the 
leakage  of  steam,  air.  or  water,  in  the  movement  of  the 
piston  or  other  rod  out  of  the  cylinder  or  chest.  They 
consist  of  an  annular  chamber  around  the  rod,  general- 
ly filled  with  gaskets  of  hemp,  which  is  forced  down  by 
a  ring  or  gland  into  close  contact  with  the  rod  and  the 
sides  of  the  box.  In  Fig.  812  there  are  two  stuffing- 
boxes  shown,  one  for  the  main  piston-rod,  the  other  for 
the  valve-rod.  In  the  latter  the  cap  of  the  gland  is 
fitted  with  a  screw  to  connect  it  with  the  side  of  the 
stuffing-box,  by  which  the  gasket  may  be  more  or  less 
compressed.  This  is  the  general  form  of  stuffing-box 
for  small  stems  or  rods,  sometimes  with  a  ring  or  follower  on  the  top  of  the 
gasket,  which  is  forced  down  by  the  gland  without  turning  the  ring  or  gasket. 

In  the  figure  the  stuffing-box  is  made  of  brass, 
and  screwed  into  the  end  of  the  steam-  or  valve- 
chest. 

The  stuffing-box  to  the  piston  is  cast  with  the 


FIG.  839. 


FIG.  841. 


370 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


head  of  the  cylinder,  and  is  bored  out,  .and  a  brass  bushing  fitted  and  driven 
into  the  end  of  the  box.     The  hole  through  the  bushing  in  most  boxes  fits  the 

piston-rod  accurately.  The  gland  is  of  cast- 
iron,  turned  to  fit  the  stuffing-box,  and  bored 
to  fit  the  piston-rod ;  after  packing  the  box 
the  gland  is  forced  in  and  retained  by  screws. 
Fig.  840  is  the  plan  and  section  of  a  com- 
mon stuffing-box,  in  which  the  thickness  of 
packing  is  from  £"  to  l£",  and  the  depth  from 
1£  to  2  times  the  diameter  of  the  piston-rod. 
The  number  of  bolts  vary  with  the  diameter 
of  the  piston — seldom  more  than  four,  and 
usually  but  two. 

Fig.  841  is  the  section  of  a  stuffing-box  of 
the  proportions  adopted   by   the    Southwark 
Foundry.     Taking  the  diameter  of  piston-rod 
A  as  the  unit,  B  is  2,  C  3,  D  2,  all  scant  up 
Fl°- 842-  to  a  3"  rod,  or  22"  cylinder.     For  a  28"  X  42' 

A  =  4,  with  an  allowance  of  -fa"  for  clearance,  B  6|,  0  9,  D  6£". 

Fig.  842  is  a  modification  with  double-cone  grooves  in  the  glands  and  stuf- 
fing-box by  which  the  loose  fibrous  packing  is  prevented  from 
getting  into  the  joint  spaces. 


Besides  hemp   gaskets,  there  are  a  very  great  variety  of 
packings,  patented  or  otherwise,  which  are  very  good,  adapted 
to  common  stuffing-boxes,  and  easily  procured. 

Valves — Steam-cylinder  Valves. — The  simplest  and  most  common  is  the 
slide  D,  of  which  the  action  is  described  under  the  chapter  on  Motion,  pages 
216-218. 


MACHINE  DESIGN   AND  MECHANICAL   CONSTRUCTIONS. 


3Y1 


Of  the  Size  of  Ports  or  Openings. — Under  "  Steam-pipes  "  will  be  given  the 
formula  for  the  flow  of  steam,  but  the  general  rule  of  proportioning  the  ports 
of  a  cylinder  is  to  consider  the  velocity  of  steam  100  feet  per  second,  and  of  the 
exhaust  80  feet  per  second.  With  the  slide-valve  the  opening  and  closing  are 
made  gradually,  thereby  throttling  the  flow  of  the  steam.  To  avoid  this,  Mr. 
Corliss  in  his  engine  has  made  the  ports  long  and  narrow  ;  the  steam-valves  open 
quickly  and  close  at  once  by  a  drop ;  the  exhaust- valves  move  rapidly  from  the 
wrist  connection.  From  the  great  size  and  form  of  the  common  slide-valve  there 
ensues  a  great  pressure  on  the  surface ;  various  expedients  have  been  adopted 
to  relieve  this  pressure,  which  is  especially  desirable  in  quick-running  engines. 

Fig.  843  is  a  horizontal  section  of  cylinder,  through  steam-  and  exhaust- 
valves,  of  a  Porter- Allen  engine,  and  Fig.  844  a  vertical  cross-section  through 


FIG.  844. 

cylinder  and  valves.  The  valves  are  four  in  number,  one  for  admission  and  one 
for  exhaust,  at  each  end  of  the  cylinder,  and  on  opposite  sides.  They  stand 
vertically  to  drain  the  cylinder.  The  valves  work  between  opposite  parallel 
seats  ;  the  exhaust-valves  nearly  and  the  admission-valves  wholly  in  equilibrium. 
The  action  of  the  back  plate,  and  how  the  wear  is  taken  up,  will  be  understood 
from  the  section  (Fig.  844),  which  passes  through  the  middle  of  one  pressure- 
plate.  It  is  made  hollow,  and  most  of  the  steam  supplied  to  two  of  the  open- 
ings passes  through  it.  It  is  arched  to  resist  the  pressure  of  the  steam  without 
deflection.  It  rests  on  two  inclined  supports,  one  above  and  the  other  below 
the  valve.  These  inclines  are  so  steep  that  the  plate  will  move  down  under 
steam  pressure ;  and  that  it  may  be  closed  up  to  the  valve  with  only  a  small 
vertical  movement,  the  pressure-plate  is  held  in  its  correct  position  by  projec- 
tions in  the  chest  on  one  side  and  tongues  from  the  cover  in  the  other,  which 
bear  against  it  at  the  near  end,  as  shown.  Between  these  guides  it  is  capable 
of  motion  up  and  down  and  back  and  forth  from  iy  to  |".  The  pressure  of 
the  steam  on  this  plate  tends  to  force  it  down  the  inclines  to  rest  on  the  valve. 
By  the  means  of  the  screw  the  plate  is  forced  up  and  away  from  the  valve,  and 


372 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


can  be  so  nicely  adjusted  that  the  valve  works  freely  and  perfectly  steam-tight. 
When  the  pressure  is  greater  in  the  cylinder  than  in  the  chest,  the  pressure- 
plate  is  forced  back,  to  the  instant  relief  of  the  cylinder. 

Cylindrical  Valves. — Fig.  845  represents  the  section  of  the  steam-cylinder 
of  an  Armington  &  Sims  steam  engine  with  a  cylindrical  valve.     The  steam- 


JTI 


FIG.  845. 


chest  S  is  central  and  incloses  the  valve  ;  the  exhaust  chambers  E  E  are  at  the 
ends  of  the  valve,  and  are  connected  through  the  hollow  stem  or  body  of  the 
valve.  The  valve  depends  on  its  accuracy  of  fit  for  its  tightness.  The  valve- 
chamber  is  bored  out  and  ground,  the  valve  is  turned,  ground,  and  carefully 
worked  by  hand,  to  so  close  a  fit  that  there  is  no  loss  of  steam  in  action,  and 
the  valve  is  completely  balanced. 

There  is  a  form  of  balanced  valves,  called  the  double-beat,  much  used  both 
for  steam  and  water  valves.     Fig.  846  is  a  sectional  elevation  of  a  steam  valve 


Fia.  846. 


FIG.  847. 


MACHINE   DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


373 


of  this  kind,  and  Fig.  847  a  plan  of  the  lower  seat  a,  with  the  valve-guides  g  g 
in  section.  There  are  two  seats,  flf  and  b,  and  two  faces  on  the  valve  corre- 
sponding to  them.  The  balance  depends  upon  the  relative  diameters  of  the 
bearing-lines  of  the  two  faces.  In  the  figure,  if  the  exterior  of  the  bearing  at 


y*j     ^j     i^j    y,j 

FIG.  848. 

\' 

Z>  and  the  interior  at  ft  are  both  tight,  the  valve  is  balanced  under  any  pressure, 
except  as  to  its  own  weight ;  s  is  the  valve-stem,  and  the  hole  r  is  for  a  bolt  to 
fasten  the  valve-seat  to  the  casting  of  the  steam- chest.  The  scale  is  £  full  size. 
Fig.  848  is  another  form  of  balance,  consisting  of  two  equal  poppet-valves 
connected  together — the  steam  passage  to  the  cylinder  being  central,  and  the 
steam-chest  at  each  end,  connected. 

Automatic  valves,  that  are  moved  by  the  action  of  the  fluid  in  which  they  are 
placed. 

The  double-beat  valve  (Fig.  846)  is  sometimes  used  in  large  pumping-en- 
gines.  From  its  two  beats,  the  lift  is  about  one  half  that  of  a  plain  valve. 
There  must  be  difference  enough  in  the  faces  to  admit  of  the  lift  of  the  valve 

by  the  pressure  of  water  acting  on  this 
difference.  The  seats  of  the  valves  are 
often  made  of  wood,  set  endways. 

Large  valves,  from  their  great  weight 
and  flow  of  water  through  them,  are  noisy 
in  both  seating  and  lifting.  This  is  met 
in  the  balanced  valves  by  slower  move- 
ments of  the  piston  ;  but  present  practice 
is  to  obtain  outlets  by  increasing  the  num- 
ber of  valves,  the  total  area  of  the  aper- 
tures, and  the  speed. 

Fig.  849  is  a  single-beat  direct  lift- valve 
guided  by  three  feathers  on  its  under  side, 

which  slide  in  the  cylindrical  part  of  the  pipe.  The  feathers  are  of  a  screw 
form,  by  which  a  rotary  motion  is  given  to  the  valve  through  the  flow  of  the 
water,  which  prevents  its  beating  on  the  same  parts  of  the  seat ;  usually  the 


FIG.  849. 


FIG.  8so. 


374 


MACHINE   DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


FIG.  851. 


FIG.  852. 


feathers  are  straight,  and  often  four  instead  of  three.  Fig.  850  is  a  poppet-valve 
guided  by  a  central  stem  ;  both  these  valves  have  conical  faces  and  seats,  with 
generally  an  inclination  of  45°  to  the  axis  of  the  valve.  In  many  valves  the 
faces  and  seats  are  flat,  one  or  the  other  of  which  is  of  soft  metal  or  rubber. 

Figs.  851  and  852  are  elevation  and  section  of  a  rubber  disk- valve  in  very 
common  use  in  direct-acting  pumps  and  small  pumping- engines ;  sometimes 

with  a  thimble  in  the  rubber  as  a 
guide ;  usually,  as  in  the  figure, 
with  a  metallic  plate  on  top  of 
the  rubber  for  the  bearing  of  the 
spring  ;  valve-seat  generally  of 
composition,  with  spindle  riveted 
or  screwed  into  it.  Sometimes 
the  rubber  is  held  in  a  metallic 
plate  or  cup.  The  springs  at 
their  backs  cushion  the  blow  on 
the  lift,  and  start  the  valve  down- 
ward promptly  on  the  check  of 
the  waterflow  at  the  end  of  the 
stroke.  The  great  desideratum 
of  water  -  valves  is  that  there 
should  be  little  lift,  but  ample 
water-way. 

Fig.  853  is  a  section  of  Field's  pump-valves,  an  English  design  for  high-water 
service,  as  fire-pumps,  of  which  the  flaps  are  rubber  disks.  For  lower  pressures, 
as  for  the  pumping  of  half-stuff  in  paper-mills,  valves  are  made  in  the  shape 
of  a  bishop's  mitre  slit  lengthwise 
at  the  top  and  partly  down  the 
sides.  The  bottom  flanges  should 
be  held  loosely  without  bolts 
through  them. 


FIG.  853. 


FIG.  854. 


FIG.  855. 


Fig.  854  is  a  ball- valve,  guided  in  its  movement  by  an  open  guide-cage,  c, 
which  is  held  down  by  a  set  screw  in  the  cover.  Globe-valves  with  this  form 
are  on  sale.  Ball- valves  are  usually  small  metallic  balls  on  metallic  or  wooden 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


375 


seats,  or  rubber  balls  on  metallic  seats ;  and  cylindrical  valves  have  been  made 
of  the  same  section  as  in  the  figure  4  the  body  of  the  valves  of  brass  pipes  with 
rubber  jackets. 

In  Fig.  855  the  ball  is  of  rubber  and  the  seat  is  of  composition,  screwed 
into  the  pipe  with  a  cage  of  the  same  metal,  screwed 
to  the  seat. 

Fig.  856  is  a  section  of  a  poppet-valve;  the  body 
is  of  cast-iron,  but  the  valve  and  seat  are  of  brass. 
The  valve  is  guided  by  three  feathers.  The  lift  of 
the  valve  may  be  controlled  by  a  set  screw  in  the 
cover  which  admits  of  adjustment  to  varied  lifts. 

Figs.  857  and  858  are  the  plan  and  section  of  a 
disk- valve  for  the  air  pump  of  a  condensing  steam 
engine.  The  valve  consists  of  a  disk  of  rubber  ly- 
ing on  a  flat  grating  or  perforated  plate  of  brass, 
held  in  position  between  the  grating  and  a  spheri- 
cal guard  by  a  central  bolt.  The  shape  of  the  guard 
gives  a  uniform  flexure  to  the  rubber  in  lifting,  and 
an  easy  flow  to  the  current  of  air  and  water.  The  rubber  is  not  closely  clamped 


FIG.  856. 


between  the  guard  and  plate,  as  will  be  seen  in  the  figure, 
being  screwed  home,  is  riveted,  and 
the  upper  nut  usually  pinned  to  pre- 
vent turning.  The  size  of  the  aper- 
tures in  the  grating  are  adapted  to  the 
thickness  of  the  rubber.  With  an  ex- 
ternal diameter  of  opening  of  6",  and 


The  lower  nut,  after 


°,w«ga 

>WG' 


FIG  857. 


FIG.  858. 


rubber  £"  thick,  the  exterior  ring  of  openings  may  be  f  "  by  f  ",  the  lands  or 

spaces  between  openings  £"  wide,  and  exterior  lap  of  the  rubber  %  inch.     With 

larger  diameters  and  larger  openings  thicker  rubber  must  be  used.     This  valve 

is  often  made  of  a  long  strip  or  flap  of  rubber,  on  a  suitable  grating,  with  a 

curved  guard  attached  on  one  side.     For 

the  common  air-pump  pressure,  f"  rubber 

is  sufficient  for  apertures  1"  X  4".     With 

the  use  of  backing  and  face  plates  on  the 

rubber  or  leather  flaps,  gratings   may  be 

dispensed  with  (Fig.  859).     Valves  of  this 

description — duplicate  (Fig.  860)  beneath 

the  central  pin  and  half  circular  in  plan 

— are  often  used  in  pumps,  and  are  called 

butterfly  valves.     It  is  the  best  practice  to 

insert  thimbles  in  the  rubber  (Fig.  859),  FIG.  859. 


376 


MACHINE  DESIGN  AND  MECHANICAL   CONSTRUCTIONS. 


and  the  rivets  connecting  the  plates  pass  through  these  thimbles,  so  that  the 
rubber  may  be  held  but  not  tightly  fastened — a  rule  applicable  to  all  such  valves. 
Check-valves  (Figs.  861  and  862)  are  placed  outside  of  large  pumps  to  pre- 
vent the  return  of  water  in  cases  of  accident  to  the  pumps,  and  for  facility  of 


SPACE  OCCUPIED   BY  THE 
VALVES. 


FIG.  860. 


Measure- 

Measure- 

SIZE. 

ment  from 
face  to  face 

ment  from 
end  to  end 

of  flange. 

of  hub. 

Inches. 

4 

11* 

1*| 

5 

iif 

16 

6 

-14| 

16 

8 

17f 

19 

10 

ail 

24 

12 

24i 

26| 

16 

29 

31 

18 

33 

35 

20 

35J 

38 

24 

39f 

39 

their  examination.  Valves  of  this  kind  open  from  the  pressure  of  water  be- 
neath, and,  from  a  state  of  rest,  with  some  suddenness  and  shock.  To  prevent 
this  in  large  valves,  there  is  a  valve  and  small  by-pass  pipe,  from  one -side  to 
the  other  of  the  valves,  by  opening  which  the  pressure  on  the  two  sides  of  the 
valve  may  be  equalized,  and  the  excess  due  to  the  starting  of  the  pump  dis-' 
tributed.  At  many  pumping  works  the  by-pass  is  kept  open  except  when 
necessary  to  get  at  the  pumps.  In  case  of  accident  to  the  pumps  the  flow 
through  the  by-pass  would  be  comparatively  small,  and  readily  shut  off. 


FIG.  861. 


FIG.  862. 


Valves  controlled  by  Hand. — Fig.  863  represents  a  side  view  of  a  water  bib- 
cock, called  a  hose-bib,  because  the  outlet  end  is  fitted  with  a  screw  to  adapt  it 
to  a  hose.  Without  this  screw  it  is  a  plain  bib.  If  both  ends  of  the  cock  are 
in  the  same  line,  it  is  called  a  stop-cock.  The  ends  may  not  be  fitted  with 
screws,  as  in  the  figure ;  the  screws  are  sometimes  female  screws,  and  often 
with  taper  ends,  to  solder  lead  pipe  to,  or  to  drive  into  a  cask.  These  cocks 
come  under  the  common  designation  of  plug-cocks,  from  their  interior  con- 
struction, which  will  be  readily  understood  from  the  section  given  in  Fig.  864. 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


377 


FIG.  863. 


FIG.  864. 


FIG.  865. 


They  are  used  in  both  steam  and  water  pipes,  but  not  in  the  former  when  the 
use  is  frequent  and  daily,  and  then  usually  not  over  2"  in  diameter  of  passage. 


FIG.  866. 


FIG.  867. 


Fig.  865  is  the  side  view  of  a  compression  water-bib,  used  when  the  pres- 
sure of  the  water  is  great.  The  section  is  somewhat  similar  to  that  of  Fig. 
870,  in  which  a  rubber  disk  is  forced  against  a  metallic  seat  to  shut  off  the 
flow. 

Fig.  866  is  a  side  view  of  a  common  air-cock  for  boilers  and  steam  work ; 
they  are  plugs  in  their  construction,  as  are  the  cocks  used  in  gas-fitting ;  size  of 
vent  of  air-cocks,  £  to  \  inch  diam- 
eter. 

Fig.  867  is  an  air-cock  in  which 
the  valve  is  a  plug  of  Jenkins's  pat- 
ent composition,  mostly  rubber  and 
graphite,  on  a  flat  seat  of  small  sur- 
face. 

Figs.  868  and  869  are  front 
views  of  globe  -  valves,  so  called 
from  the  shape  of  the  body  inclos- 
ing the  valve.  Fig.  868  is  an  an- 
gle globe- valve ;  Fig.  869,  a  cross 
globe- valve  used  for  cutting  off  the 
steam  supply  through  the  vertical  FIG.  scs.  FIG.  seo. 


378 


MACHINE   DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


pipe  from  the  horizontal  one  ;  the  same  purpose  is  attained  by  putting  a 
straightway  valve  on  the  vertical  pipe.  The  valve  seats  of  all  globe-valves, 
kept  in  stock  and  on  sale,  are  now  made  of  soft  metal  or  of  rubber,  or  of  some 
mixture  of  it  vulcanized  ;  soft  rubber  for  cold  water,  hard  rubber  for  hot  water 
or  steam.  Fig.  870  is  a  front  view  of  a  globe- valve,  with  one  side  turned  off 


DIMENSIONS  OF  GLOBE-VALVES 
IN  COMMON  USE,  WITH  SOFT 
SEATS. 


Diameter 
of  opening 
in  seat. 

Length 
over  all. 

Diameter 
of  globe. 

Body 
metal. 

4 

24 

If 

Brass. 

i 

2i 

If 

1 

24 

14 

4 

2f 

2* 

1 

3f 

24 

H 

4i 

3 

14 

4f 

if 

a 

5f 

4| 

24 

8 

Iron. 

3 

9f 

7* 

34 

10 

4 

114 

9* 

5 

13f 

10£ 

6 

14| 

124 

7 

16* 

14 

8 

17i 

14 

c 


FlG. 


to  show  its  interior   construction. 

The  diaphragm  d  d  is  in  the  form 

of  a  |  —  l,which  divides  the  interior 

of  the  globe  ;  through  the  flat  part 

is  the  aperture  for  the  passage  of 

the  fluid  covered  by  the  valve,  controlled  by  the  handle  and  screw  on  its  stem. 

The  arrows  show  the  direction  of  flow. 

Fig.  871  is  a  perspective  of  the  valve,  showing  the  grooves  through  which 
it  is  slipped  on  to  the  head  on  the  stem  and  held.  The  composition  or  rubber 
is  in  the  form  of  a  ring  slipped  into  a  circular  groove  in  the  bottom  of  the 
valve.  In  some  valves  the  rubber  ring  is  slid  into  a  straight  groove  and  re- 
tained by  a  nut  on  the  stem,  and  the  head  of  the  stem  is  held  to  the  valve  by  a 
nipple. 

When  the  seat  is  of  soft  metal  it  is  run  into  a  groove  in  the  case,  faced,  and 
the  valve  formed  with  a  circular  chisel  edge  is  forced  down  by  the  hand  wheel 
into  the  soft  metal.  On  account  of  the  loss  of  head  by  the  change  of  direction 
in  flow  —  through  the  valve  aperture  —  it  is  better  to  make  it  of  a  little  larger 
diameter  than  that  of  the  pipe. 

Figs.  872  and  873  are  the  plan  and  section  of  a  steam  valve  of  the  South- 
wark  Foundry  pattern  ;  the  seats  and  faces  are  of  metal  ground  to  a  fit.  The 
valve  is  guided  by  three  wings,  w  w.  The  flow  through  globe-valves,  as  will  be 
seen  by  their  sections,  have  three  changes  of  direction  ;  to  avoid  this,  straight- 
way gates  are  almost  invariably  used  on  water  mains. 

If  the  double-beat  valve  (Fig.  846  or  848)  be  mounted  with  a  screw  (like  the 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS.  379 


380 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


above),  as  the  pressure  on  the  valve  may  be  nearly  balanced  throughout  its 
movement,  it  can  be  made  of  large  area,  and  still  be  under  the  control  of  a 
hand  wheel. 

GATE-VALVES. 

When  the  pressure  is  always  on  one  side  of  the  valve,  it  may  be  made  as  a 
plain  gate,  sliding  in  grooves,  and  raised  up  into  a  chamber ;  but  it  is  the  usual 
practice  to  make  these  gates  double,  each  being  forced  positively  against  faces. 

The  earliest  of  these 
forms  of  gates  are  the 
Peet  (Fig.  874)  and  the 
Coffin  valve  (Fig.  875). 

The  first  were  usually 
made  of  small  sizes,  and 
for  steam  -  pipes,  it  is 
shown  in  the  figure  shut ; 


FIG.  874. 


the  two  side  valves  or  disks  are  forced  against  their  respective  faces  by  the  cone 
suspended  between  the  disks,  forced  upward  by  its  stem  coming  in  contact  with 
the  bottom  of  the  case ;  as  the  gate  is  raised,  the  cone  drops,  the  pressure  is  re- 
leased, and  the  valve  easily  drawn  up  into  the  chamber  above,  giving  an  un- 
obstructed passage  through  the  body  of  the  valve. 

In  the  Coffin  valve  the  disks  are  suspended  by  two  pivots  in  their  backs  to 
a  wedge  connected  with  the  same.  The  wedge  by  its  downward  movement 
forces  the  disks  outward  against  the  seats,  while  by  the  upward  motion  this 
pressure  is  relieved. 

In  the  Pratt  and  Cady  valve  (Fig.  876)  the  seats  are  of  soft  metal  which 
are  cast  in  a  mould  and  forced  into  position,  making  a  tight  fit  with  the  body 
of  the  valve  and  a  seat  for  the  valve  with  smooth  faces.  In  case  of  a  cutting 
of  the  soft  metal,  it  can  be  readily  withdrawn  and  replaced  by  a  new  one. 

The  above  forms  of  gates,  especially  those  of  large  sizes,  are  used  as  water 
gates.  Steam-valves  are  mostly  of  the  globe  pattern. 

Between  the  boilers  and  the  steam-chest  of  an  engine  there  should  be  a 
valve  that  can  be  shut  promptly.  The  simplest  is  the  damper-valve  (Fig.  877), 
which  is  also  used  for  the  control  of  the  draft  in  the  smoke-pipe,  but  for  a 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


381 


steam-pipe  it  is  made  with  a  closer 
fit;  it  never  can  be  close,  but 
sufficiently  so  to  control  or  slow 
down  the  engine.  A  better  valve 
is  the  usual  Corliss  steam-cylin- 
der valve,  moved  by  a  handle,  or 
the  register  -  valve  (Fig.  878), 
which  is  held  down  by  a  spring, 
and  is  opened  and  shut  like  a 
register.  These  valves  may  be 
connected  to  a  governor. 

Fig.  879  is  a  valve  used  in 
Nasmyth's  works  for  steam  ham- 
mers. Opposite  the  ports  there 
are  false  ports  or  slight  recesses 
in  the  shell.  The  steam  enters 
at  the  end  of  the  valve  into  the 
spaces  a  a ;  the  endwise  pressure 
is  received  by  a  thrust  bearing. 
This  valve  is  so  nearly  balanced 
that  it  is  readily  moved  by  hand. 
To  prevent  excessive  pres- 
sures, either  of  steam  or  water,  a 
safety-valve  is  used  (Fig.  880), 
which  consists  of  a  poppet-valve 
held  down  by  a  lever  and  weight. 
To  determine  the  weight  coun- 
terbalancing the  pressure,  put 
the  valve  and  lever  in  position, 
attach  the  valve  to  the  stem,  and 
with  a  spring  balance  attached  to 
the  lever  at  its  connection  with 
the  stem,  find  how  much  weight  it  takes  to  lift  the  valve-stem  and  lever ;  this 
is  a  constant,  which  if  divided  by  the  area  of  valve  at  its  lowest  bearing  diame- 


Fia.  877. 


FIG.  878. 


382 


MACHINE   DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


ter  will  give  the  constant  pressure  per  square  inch.     The  movable  weight  is  the 

P  of  a  steelyard,  and  is  to  be  estimated  by  multiplying  fp  by  the  weight  and 

dividing  it  by  fs  and  the 

area  of  the  valve,  to  which 

is  to  be  added  the  constant 

weight     per    square    inch 

found  above. 


FIG.  879. 


FIG.  880. 


The  safest  and  simplest  way  is  to  put  a  blank  flange  on  below  the  valve  and 
with  a  force  pump  inject  water  to  certain  pressure,  as  shown  by  a  steam  gauge ; 
balance  this  pressure  by  a  weight  P  on  the  lever  and  mark  its  distance  from 
the  fulcrum,  which  will  give  the  weight  per  square  inch  on  the  valve  at  the 
position  of  the  P ;  in  the  same  way  determine  other  points  on  the  lever. 

Fig.  881  is  what  is  termed  a 
pop  safety-valve ;  the  steam  issu- 
ing as  the  valve  rises,  impinges  on 
a  cup  surface  to  force  the  valve 
farther  open.  The  valve  is  held 
down  by  a  spring,  but  can  be 
raised  by  the  lever  I.  Valves  of 
this  kind  are  often  inclosed  in  a 
locked  box,  that  they  may  not  be 
tampered  with. 

.  To  determine  the  weight  on 
the  spring,  test  it  by  raising  the 
pressure  in  the  boiler,  as  shown  by 
the  gauge,  to  the  height  which  is 
deemed  safe ;  adjust  the  valve  to 
the  lifting  point  by  the  nuts  on 
the  side  bolts.  If  not  in  position 
on  a  boiler,  test  by  a  pump. 

Hydrants. — For  water-service 
in  connection  with  high-pressure 
mains. 

Fig.  882  is  a  section  of  a  post- 
hydrant.  The  valve  v  consists  of 
a  series  of  leather  disks  bolted  together  and  turned  conical,  which  is  brought  in 
contact  with  a  corresponding  seat  by  the  valve-rod  and  its  screw  at  the  top  of 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


383 


the  hydrant.     The  valve  is  opened  by  being  forced  down  into  the  cavity  of  a 
branch  of  the  pipe-main ;  n  is  the-  nozzle  for  the  coupling  of  the  hose ;  outside 

the  main  pipe  of  the  hydrant  there  is  a 
case,  extending  from  near  the  line  of  valve 
to  the  ground  line,  called  the  hydrant 
or  frost  case,  which  prevents  the  hydrant 
from  being  lifted  by  the  frost.  Were 
the  water  left  in  the  hydrant,  it  would 
freeze  in  most  exposures  during  winter; 
the  hydrant,  when  not  in  use,  is  therefore 
kept  empty.  This  is  effected  by  a  small 
hole  at  a,  which,  when  the  valve  is  closed, 
is  opened,  and  the  water  in  the  hydrant,  if 
any,  is  discharged.  This  vent  is  closed  by 
a  slide  attached  to  the  valve-rod,  when  this 
last  is  moved  down  to  open  the  main  valve. 
Instead  of  leather  for  the  valve-face,  many 
valves  are  fitted  with  rubber ;  there  is  also 
a  great  variety  of  valves  for  hydrant  pur- 
poses— slides,  poppets,  disks — but  in  the 
arrangement  of  hydrants  the  illustration  is 
the  common  one,  although  often  without 
the  frost  case. 


FIG.  882. 


FIG.  888. 


Fm.  889. 


Riveted  Joints,  as  used  in  the  Construction  of  Boilers.— Figs.  883-889  are 
forms  of  rivets  with  their  proportions  referred  to  the  diameters  next  the  heads. 
The  thickness  of  the  plate  connected  by  rivets  will  be  given  in  tables  here- 


384 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


FIG.  890. 


after.  Figs.  884  and  885  are  the  usual  finish  of  rivets  in  hand-riveting ;  Figs. 
886  and  887,  when  made  by  machines,  in  which,  as  the  rivet-hole  is  slightly 

counter-sunk,  the  strength  of  the  head  is  increased. 
Fig.  888  is  a  counter-sunk  rivet,  the  head  being 
flush  with  the  outside  of  the  plate.  Fig.  889  is  the 
head  of  a  rivet,  in  which  a  narrow  strip  at  the  edge 
is  burred  down  by  a  chisel,  or  calked,  to  make  the 
joint  between  rivet  and  plate  tight. 

Fig.  890  is  a  plan  and  section  of  a  single-riveted 

lap-joint.  Joints  of  this  kind  fail  from  the  tear  of  the  plate  on  the  line  of 
rivets  if  the  rivets  are  too  close,  or  the  distance  of  the  rivet  to  the  outside  of 
the  plate  too  small,  or  by  the  shear  of  the  rivets  if  they  are  too  few. 

Rivet-holes. — Punching  has  an  injurious  effect  upon  plates  ;  but  this  injury 
(if  the  plates  are  not  cracked  by  the  process)  is  removed  by  afterward  annealing 
them,  or  by  rymering  or  drilling  to  the  extent  of  ^  inch  on  the  diameter. 

It  is  difficult  to  insure  the  correct  spacing  of  the  holes  when  they  are  made 
by  punching.  In  the  best  boiler  work  the  rivet-holes  are  drilled  after  the 
plates  have  been  bent  or  flanged  and  put  together  in  their  proper  places.  This 
insures  that  the  corresponding  holes  in  the  different  plates  shall  be  exactly  op- 
posite to  one  another.  After  drilling,  the  plates  are  taken  asunder  and  any 

burr  that  has  been  formed  at  the  edges  of  the 
holes  is  removed.  Riveting  may  be  performed 
either  by  hand  hammering  or  by  a  machine. 
Hydraulic  riveting  machines  are  the  best. 

For  wrought-iron  plates  a  tenacity  of  47,000 
pounds  is  estimated  per  square  inch  in  the  di- 
rection of  the  fibre,  and  40,000  pounds  per 
square  inch  across  the  fibre ;  steel  plates,  a  te- 
nacity of  65,000  pounds  per  square  inch. 

Shearing  resistance  of  wrought-iron  rivets 
is  about  equal  to  the  tenacity  of  wrought-iron 
plates ;  the  shearing  resistance  of  steel  rivets  is 
about  eight  tenths  the  tenacity  of  steel  plates. 

Fig.  891  shows  the  connection  of  two  plates 
by  means  of  single-riveted  lap-joint.  AVhen 
the  plates  are  arranged  as  shown  in  the  lower 
section,  the  tension  in  the  plates  causes  a  bend- 
ing action  on  them  at  the  lap.  To  avoid  this, 
the  plates  have  sometimes  a  set  at  the  lap,  as  shown  in  the  upper  section. 

DIMENSIONS  OP  SINGLE-RIVETED  LAP-JOINTS  FOR  BOILER  WORK. 


FIG.  891. 


IRON  PLATES  AND  IRON  RIVETS. 

STEEL  PLATES  AND  STEEL  RIVETS. 

THICKNESS  OF  PLATE. 

Diam.  of  rivet. 

Pitch. 

Diam.  of  rivet. 

Pitch. 

A 

1 

li 

1A 

*    ! 

»   ! 

il     :* 

l           f 

•j2 

A 

H     / 

2i        2 

1              1J 

2i        g** 

H       * 

1A 

H 

14 

5 

MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


385 


The  efficiency  of  the  joint  in  the  percentage  of  the  strength  of  the  plate  is 
to  be  taken  at  the  lowest  figure,  wKether  in  tear  or  shear.  In  the  above  table 
it  is  55  per  cent.  The  distance  between  the  edge  of  the  plate  and  the  centre 
of  the  outer  rivet,  as  shown  in  the  figures  by  Z,  is  invariably  one  and  a  half  time 
the  diameter  of  the  rivet. 


FIG.  892. 


FIG.  893. 


The  arrangement  of  the  rivets  in  Fig.  892  is  known  as  zigzag  riveting,  while 
that  of  Fig.  893  is  chain  riveting. 

DIMENSIONS  OP  DOUBLE-RIVETED   LAP-JOINTS. 


t. 

IRON   PLATES  AND   IRON   RIVETS. 

STEEL  PLATES   AND   STEEL  RIVETS. 

d. 

P- 

c. 

cl. 

d. 

p- 

c. 

cl. 

1 

H 

n 

1ft 

11 

f 

2£ 

If 

2 

A 

t 

2f 

If 

2 

it 

2f 

1ft 

2i 

i 

H 

21 

1* 

24 

1 

m 

H 

2i 

ft 

1 

3 

1ft 

8* 

H 

21 

1ft 

2i 

1 

If 

3i 

If 

2f 

i 

3 

l| 

21 

to 

i 

3± 

If 

21 

ift 

3i 

lii 

2| 

i 

ift 

3ft 

m 

2| 

H 

8J 

if 

2f 

n 

H 

3ft 

11 

2f 

1ft 

3| 

m 

21 

i 

1ft 

3f 

2 

21 

i± 

31 

m 

3 

H 

1J 

31 

2rV 

3 

1ft 

8f 

2 

8t 

i 

1ft             4 

2fV 

3i 

if 

8| 

2i 

3J 

The  efficiency  of  joints  in  the  above  table  is  for  iron  plates  68  per  cent, 
and  steel,  64  per  cent. 

In  all  riveted  joints  the  distance  between  adjacent  rivets,  measured  from  cen- 
tre to  centre,  whether  in  the  same  or  different  rows,  should  not  be  less  than  2d. 

On  the  results  of  experiments  on  riveted  joints,  Professor  Kennedy  has  stated 
that  the  net  section  of  metal  in  the  plate,  measured  zigzag,  should  be  from  30 
to  35  per  cent,  in  excess  of  that  measured  straight  across.  This  gives  a  diago- 


nal  pitch  of  . 

o 
26 


386 


MACHINE   DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


Treble-riveted  Lap-joints.— In  Fig.  894  the  riveting  is  zigzag,  and  in  Fig. 
895  chain. 


FIG.  894.  FIG.  895. 

DIMENSIONS  OF  TREBLE-RIVETED   LAP-JOINTS. 


t. 

IRON  PLATES  AND  IRON  RIVETS. 

STEEL  PLATES  AND  STEEL  RIVETS. 

d. 

p- 

c. 

cl. 

d. 

p- 

c. 

cl. 

1 

H 

8J 

If 

24 

i 

34 

If 

8J 

tt 

i 

8J 

If 

2i 

H 

3f 

If 

2| 

1 

H 

3H 

1* 

2| 

i 

3* 

HI 

2* 

If 

i 

8| 

Itt 

2* 

iiV 

8H 

lit 

2f 

i 

1A 

44 

2iV 

H 

H 

31 

2 

24 

it 

1* 

4A 

2A 

21 

1& 

4 

2A 

21 

i 

1A 

4i 

2J 

2i 

ii 

*ft 

2A 

3 

IA 

H 

4tt 

2f 

3 

1A 

4f 

2± 

34 

H 

iA 

*i 

2i 

3i 

if 

4* 

2f 

8J 

The  efficiency  of  joints  for  iron  plates  is  74  per  cent,  and  that  of  steel  70  per 
cent.  The  strength  of  a  treble-riveted  joint  (Figs.  896  and  897)  may  be  increased 
by  making  the  pitch  of  the  inner  row  of  rivets  one  half  that  of  the  outer. 

d  =  1-27 1  for  iron  plates  and  iron  rivets. 

d  =  l-59£  for  steel  plates  and  steel  rivets. 

The  pitch  of  a  quadruple  lap-joint  will  be  the  same  as  in  the  last  example. 

A  butt  joint  with  a  single  cover-strap  (Fig.  898)  is  composed  of  two  lap- 
joints,  and  is  proportioned  by  the  rules  previously  given  for  lap-joints.  With 
this  form  of  joint,  the  tension  on  the  plates  will  tend  to  bend  the  cover-strap. 
For  that  reason  the  cover-strap  is  made  thicker  than  the  plates.  If  ^,  =  thick- 
ness of  cover-strap  and  t  —  thickness  of  plates,  then  #,  =  1#.  For  single- 
riveted  butt-joints  (Fig.  899),  with  double  cover-straps,  the  usual  rule  for  the 
thickness  of  each  butt-strap  is  t1  =  f  t. 

The  diameter  of  the  rivets  for  different  thicknesses  of  plates  may  be  as  fol- 
lows : 

d  =  t  -\-  \  for  iron  plates  and  iron  rivets. 

d  =  t  -j-  ^  for  steel  plates  and  steel  rivets. 


MACHINE   DESIGN  AND   MECHANICAL  CONSTRUCTIONS.  387 


FIG.  901. 


388 


MACHINE   DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


Double-riveted  Suit-joints  with  Double  Cover-straps  (Fig.  900). — The  pitch 
of  the  rivets  are  the  same  in  each  row.  If  alternate  rivets  in  the  outer  rows  be 
removed,  as  in  Fig.  901,  the  arrangement  is  stronger. 

The  diameter  of  the  rivets  (Fig.  900)  for  different  thicknesses  of  plates  may 
be  as  follows : 

d  =  t  -f-  T^-  for  iron  plates  and  iron  rivets. 

d  =  t  -\-  %  for  steel  plates  and  steel  rivets. 

The  diameter  of  the  rivets  (Fig.  901)  for  different  thicknesses  of  plates  may 
be  as  follows : 

d  =  t  +  £  for  iron  plates  and  iron  rivets. 

d  =  t  +  y^-  f  or  steel  plates  and  steel  rivets. 

Fig.  902  is  a  triple-riveted  butt-joint  with  double  cover-plate,  as  butt-joints 
with  double  covers,  one  on  each  side  of  the  plates,  increase  the  shearing  resist- 


FIG.  902. 


FIG.  905. 


ance  of  the  rivets,  so  that  rupture  always  takes  place  in  the  plates ;  and  as  these 
can  not  bend,  and  there  is  considerable  frictional  resistance  between  the  plates, 
the  strength  of  the  joint  has  been  found  to  be  more  than  that  due  to  the  net 
section  of  the  plates  between  the  rivets. 

Fig.  903  is  a  plan  and  section  of  a  combined  lap-  and  butt-joint.  The  pitch 
of  the  exterior  rows  is  double  that  of  the  central  one ;  for  a  f"  plate,  4"  for  the 
former  and  2"  for  the  latter. 

Fig.  904  is  a  section  of  joint,  showing  a  better  arrangement  than  Fig.  903, 
requiring  less  work,  more  easily  calked,  and  of  as  much  strength. 

Fig.  905  is  the  plan  and  section  of  a  butt-joint  when  the  cover  is  of  T-iron— 
a  not  uncommon  form  of  strengthening  flues  to  resist  collapse. 

Junction  of  more  than  Two  Plates,  shown  in  Plans  and  Sections  (Figs.  906, 
907,  and  908).— These  become  necessary  when  cross-joints  intersect  longitudi- 
nal ones.  At  these  joints  one  or  more  of  the  plates  are  thinned  or  drawn  out 
by  forging. 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


389 


Fig.  909  is  the  plan  .and  section  of  an  angular  connection  of  plates  by  the 
means  of  angle-iron ;  this  should  be  a  little  thicker  than  the  plates,  and  its 
width  four  times  the  diameter  of  the  rivets. 


C 


.kj    iv 

ryl       K^ 


IxxXl      [^3 


FIG.  906. 


FIG.  907. 


FIG.  908. 


Figs.  910,  911,  and  912  are  sections  of  angular  connections  by  flanging  the 
plates.  The  iron  should  be  good  and  the  curvature  easy ;  inside  radius  at  least 
four  times  the  thickness  of  the  plates. 


FIG.  909. 


FIG.  910. 


FIG.  911. 


FIG.  912. 


Figs.  913  and  914  are  sections  of  joints  of  cylinders  of  unequal  diameters, 
or  surfaces  not  in  line  with  each  other. 

Figs.  915,  916,  and  917  are  sections  of  fire-box  legs. 


)      ( 


FIG.  913. 


FIG.  914. 


FIG.  915. 


FIG.  916.         FIG.  917. 


In  all  connections  provisions  are  to  be  made  for  the  means  of  holding  the 
head  of  the  rivet,  and  for  riveting  and  for  calking  the  joints. 

Fig.  918  is  the  perspective  view  of  a  horizontal  tubular  boiler,  very  largely 
used  with  anthracite  as  a  fuel,  but  with  bituminous  coal  the  tubes  should  be  of 
the  larger  diameters. 

The  proportions  of  the  boiler  vary  with  the  requirements  of  their  position, 
and  with  the  views  of  the  mechanical  engineer  or  maker  constructing  them. 
Many  use  a  dome,  but  it  is  the  better  practice  to  increase  the  diameter  of  the 
boiler  an  inch  or  two  for  more  steam  space,  if  necessary,  and  insert  a  dry  pipe 
in  the  space.  Those  in  most  extensive  use  are  with  shells  of  4  to  5  feet  inside 
diameter  and  3"  to  3£"  tubes,  14  to  16  feet  long.  The  line  of  the  top  of  the 
upper  tubes  is  usually  about  y1^  of  the  diameter  of  the  boiler  above  its  centre ; 
tubes  arranged  in  vertical  rows,  with  distance  between  tubes  $  of  their  diam- 


390 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


eter.  By  keeping  the  average  distance  the  same,  but  making  them  farther 
apart  at  the  top  row,  say  %  diameter,  and  the  lowest  £  diameter,  so  that  the  line 
of  tubes  is  radial  instead  of  vertical,  the  outside  of  the  tube  will  meet  the  flame 
better,  and  at  the  same  time  be  more  readily  cleaned  with  a  brush. 


FIG.  918. 


The  following  table  is  from  Barr,  showing  the  greatest  number  of  tubes 
which  should  be  put  in  a  given  head,  no  tube  to  come  nearer  to  the  shell  than 
2"  for  boilers  of  small  diameter,  2£"  for  medium,  and  3"  for  the  larger  series : 


Diameters  of 

bodies  inside, 
in  inches. 

3  in. 

3iin. 

3i  in. 

3}  in. 

4  in. 

4}  in. 

5  in. 

36 

26 

23 

20 

19 

16 

12 

10 

40 

34 

34 

25 

23 

20 

14 

14 

44 

48 

36 

32 

25 

25 

20 

16 

48 

50 

38 

36 

30 

26 

21 

18 

52 

57 

50 

48 

38 

32 

26 

21 

56 

72 

57 

55 

48 

41 

32 

23 

60 

80 

68 

62 

55 

46 

36 

30 

A  is  the  man-hole,  to  enable  the  mechanic  to  get  into  the  boiler  to  examine 
it.  It  consists  of  a  cast-iron  frame,  bolted  to  the  shell  of  the  boiler,  with  an 
elliptical  opening  usually  9"  X  15"  in  the  clear ;  the  valve  laps  about  1"  on  each 
side.  In  closing  the  opening  the  valve  is  passed  down  into  the  boiler,  and  is 
brought  up  against  the  valve-seat,  where  it  is  held  by  its  stem  passing  up 
through  a  movable  yoke,  and  brought  up  tight  by  a  nut  and  screw.  The  joint 
is  made  with  a  gasket  or  with  sheet-rubber.  The  man -hole  is  often  placed  in 
one  of  the  boiler  heads,  or  at  one  side,  above  the  tubes,  for  convenience  of 
access.  B  is  the  hand-hole,  of  the  same  general  construction  as  the  man-hole, 
but  smaller,  to  enable  the  fireman  to  clean  the  boiler.  Formerly  this  hand- 
hole  was  quite  small,  but  of  late  the  practice  is  to  place  a  hand-hole  at  the  rear 
end  of  the  boiler  and  a  man-hole  at  the  front  in  the  position  B.  This  is  for  the 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


391 


readier  cleaning  and  repairs  of  the  boiler ;  it  reduces  the  number  of  tubes  by 
four,  but  without  detriment  to  the  ^evaporation  of  the  boiler ;  and  by  taking  off 
both  covers  one  can  look  directly  through  the  boiler.  As  the  hand-hole  is  ex- 
posed to  the  flame  and  products  of  combustion,  it  is  well  to  make  it  small,  say 
3"  X  5" ;  III  are  lugs  by  which  the  boilers  are  supported  on  the  brickwork, 
but  they  are  in  the  way  in  getting  the  boiler  through  a  confined  space,  and 
rest  so  solidly  on  the  brickwork  that  it  often  becomes  cracked  by  the  expansion 
of  the  boiler.  It  is  preferable  that  the  boiler  should  be  hung  as  in  Fig. 
1252.  In  the  head  above  the  tubes  there  are  rivet-heads,  and  also  in  the  sides 
back  of  the  first  seams  at  each  end.  These  are  for  the  attachment  of  diagonal 
stays.  The  tubes  themselves  serve  as  stays  in  the  lower  part  of  the  boiler,  but 
above,  the  flat  surface  needs  something  to  prevent  the  head  from  moving  out 
under  pressure.  The  stays  are  made  of  round  or  flat  iron  (see  Fig.  1249), 
bolted  directly  to  the  shell,  the  round  part  being  flattened,  and  connected  by 
a  yoke  and  pin  to  a  crow-foot  or  piece  of  angle-iron  attached  to  the  head. 
The  stays  are  from  f "  to  1^"  diameter  or  equivalent  sections. 

To  determine  the  diameter  of  stays  in  square  inches  multiply  the  area  sup- 
ported by  the  stays  and  divide  the  product  by  7,000  for  wrought-iron  stays  not 
welded ;  and  for  steel  stays,  under  same  condition,  by  9,000 ;  but  if  welded  or 
otherwise  worked  after  heating,  take  three  fourths  of  above. 

Forms  of  Boiler  Stays. — Fig.  919  is  a  direct  stay  in  which  a  hole  is  drilled 
through  the  head  of  a  boiler ;  the  stay  has  an  outside  nut  of  a  thickness  equal 


tt-J 


FIG.  919. 


FIG.  920. 


FIG.  922. 


to  the  diameter  of  the  screwed  part,  and  the  inside 

or  locked  nut  three  fourths  of  this  thickness.     The 

plates  are  stiffened  by  inside  and  outside  washers. 

If  the  stay  is  diagonal  it  is  usual  to  increase  its  area  in  the  proportion  of  the 

length  of  the  diagonal  to  that  of  the  horizontal. 

The  flat  parallel  surfaces  surrounding  the  fire-boxes  of  locomotive  and 
marine  boilers  are  secured  by  means  of  screwed  stays,  so  called  because  they 
are  screwed  into  the  plates  (Figs.  920,  921,  and  922).  After  being  screwed 
into  the  plates  their  ends  are  riveted.  The  fracture  of  the  stays  is  detected  by 
the  escape  of  steam  through  the  small  holes  which  are  sometimes  drilled  through 
the  screwed  parts.  The  screwed  stays  for  locomotive  boilers  are  usually  placed 
about  4  inches  apart,  centre  to  centre,  and  vary  in  diameter  from  f-  inch  to  1 
inch. 

In  marine  boilers  the  screwed  stays  are  made  of  steel,  and  they  vary  in 
diameter  from  1^-  inch  to  If  inch.  They  are  provided  with  washers  and 
nuts  at  each  end,  as  shown  at  Fig.  919.  The  nuts  have  a  thickness  of  from 
five  eighths  to  three  fourths  the  diameter  of  the  stay. 


392 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


FIG.  923. 


In  the  steel-screwed  stays  the  ends  of  these  stays 
are  drilled  as  shown,  and  after  they  are  screwed  into 
place  a  steel  drift  is  driven  into  the  holes  by  slight 
blows  to  expand  the  ends  tightly  into  the  plates  to 
make  steam-tight  joints. 

Fig.  923  is  a  gusset  stay,  used  in  angles,  consist- 
ing of  a  triangular  plate  with  the  edges  flanged  and 
riveted  to  the  shell. 


BARK'S   PROPORTIONS  FOR  STAY-BOLTS   FOR  FLAT  SURFACES. 


CENTRE  TO  CENTRE  OF  STAY-BOLTS  IN  SQUARE  INCHES. 


JL  1  l^ODlll  V3   jyt'A 

square  inch. 

\"  plate. 

TV'  plate. 

f"  plate. 

Ty  plate. 

i"  plate. 

60 

5f 

61 

7* 

8* 

9 

80 

4f 

5£ 

8* 

7* 

71 

100 

4i 

4f 

5J 

6| 

7 

120 

81 

4i 

5 

H 

6f 

140 

8| 

4* 

4f 

5J 

6 

00 

oooo 

'OOOOOO 

oooooo 

OOOOOO 

oooooo; 
ooo. 


poooo 

oooooo  , 
ooooooo 
ooooooo 
ooooooo 

OOOOOOOj 

oooooo. 


Stationary  boilers  as 
designed  and  built  un- 
der the  direction  of 
John  E.  Codman,  M.  E., 
for  the  Philadelphia 
Water- Works,  of  which 
Fig.  924  is  a  transverse 
section  and  one  half 
cross  -  section  through 
fire-box,  and  one  half 
front  view  without  the 
doors.  Fig.  925  is  a 
longitudinal  section. 
These  boilers  have  inside 
fire-boxes,  and  the  out- 
side is  protected  by  a 
covering  of  brick  or 
some  clothing  of  a  non- 
conducting material  to 
prevent  radiation.  The 
corrugated  furnaces  are 
made  in  this  country 
by  the  Continental  Iron 
Works,  Brooklyn,  of  an 
inside  diameter  of  from 
30"  to  60"  and  up  to  32 
feet  long. 

Kules  for  calculat- 
ing the  pressure  allowa- 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS.  393 


394 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


395 


ble  on  corrugated  furnaces  adopted  by  the  Board  of  United  States  Supervising 
Inspectors  : 

Corrugations  to  be  6  inches  pitch  and  1£  inch  deep. 

14000      _  ,  . 

— y^ —  X  T  =  working  pressure  in  pounds  per  square  inch. 

T  =  thickness  in  inches. 

D  =  mean  diameter  in  inches. 

Example. — Given  a  corrugated 
furnace  40  inches  mean  diameter 
to  carry  175  pounds  working  pres- 
sure, required  the  thickness  of 
metal. 


P.  XD. 


=  thickness. 


175  X  40 


FIG.  927. 


14000  14000 

=  |  inch  thickness  of  metal. 

Figs.  926  to  929  are  drawings 
of  a  locomotive  boiler  as  designed 
and  constructed  by  Mr.  Buchanan 
for  express  passenger  locomotives 
for  the  N.  Y.  C.  and  H.  R.  R.  R, 
Fig.  926  is  a  longitudinal  section 
Fig.  927  a  transverse  section  of 
one  half  the  fire-box  and  an  eleva- 
tion of  one  half  of  that  end.  Fig. 
928  of  the  fire-box  with  cover  off, 
and  showing  one  half  of  the  tubes. 
Fig.  929  are  details  of 'the  riveting. 

Figs.  930  and  931  are  drawings 
of  a  marine  boiler  of  the  United 
States  steamer  Minneapolis,  show- 
ing longitudinal  and  cross-section 
of  fire-box  end.  When  locomo- 
tive or  marine  boilers  are  used  as 
stationary  their  outsides  should  be 
protected  as  the  Codman  boiler 
(page  392). 

Water-tube  boilers  are  now  in 
extensive  use,  economical  in  evap- 
oration, and  popular  from  the 
comparative  safety  from  explosion. 
Some  of  the  numerous  and  varied 
forms  will  be  found  illustrated  in 
the  Appendix. 

Flue  Boilers. — Where  bitumi- 
nous coal  is  used,  small  tubes  be- 
come  clogged   with   soot;    it  was 
therefore  customary  to  construct  boilers  with  large  tubes  or  flues  of  boiler-iron 
riveted  together,  which  sometimes  failed  from  collapse.     It  may  be  considered 


-A.. 


396 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


ample  to  make  the  tubes  subject  to  outside  stress  50  per  cent  thicker  than  for 
bursting,  especially  for  the  large  drawn  tubes  now  made.  Mr.  Fairbairn,  from 
his  experiments,  considered  it  necessary  to  make  the  joints  of  tubes  subject  to 
collapse  as  in  Figs.  932  and  933. 


1  Spaces  in  bottom  Row 
"-•»  ftTPAtcB  Bolts  in  Ring  li'deep 


3  Equal  Spaces  in  bottom  Ro 
j'Patch  bolts  Ij'deep  in  RiJg 


FIG  929. 

Fig.  934  is  a  section  of  the  Shapley  boiler,  as  made  by  the  Knowles  Steam- 
Pump  Works — a  good  form  of  upright  boiler,  with  the  head  of  the  boiler 
stayed  by  rods  directly  to  the  crown-sheet,  beneath  which  short  tubes  or  nip- 
ples connect  the  fire-box  with  a  cast  iron  smoke-box  around  the  boiler  and  the 
draft  is  downward  through  vertical  tubes  to  a  smoke-box  in  the  base.  The 
crown-sheet  and  downward  draft  tubes  are  well  covered  by  water.  It  is  an  ad- 
mirable illustration  for  the  draughtsman  of  how  a  boiler  in  action  may  be 
represented. 

The  usual  form  of  upright  boiler  consists  of  a  fire-box,  extending  a  little 
above  the  door,  and  tubes  extending  from  the  crown-sheet  to  the  top-head, 
over  which  there  is  a  bonnet  to  receive  the  smoke,  which  is  led  off  by  a  smoke- 


MACHINE   DESIGN  AND  'MECHANICAL   CONSTRUCTIONS. 


397 


>H£fl 

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398 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


pipe.  It  is  a  convenient  form  for  furnishing  steam  for  a  small  power,  but  not 
as  economical  in  combustion,  and  apt  to  prime — that  is,  take  up  water  with 
the  steam,  and  leak  at  the  top  of  the  tube  exposed  in  the  smoke-box. 

The  common  vertical  boilers  are 
from  2  feet  6"  to  4  feet  6"  outside 
diameter  of  shell,  with  water  space  in 
legs  of  2£"  to  3" ;  extreme  height  of 
boiler  from  2  to  2|-  times  the  outside 
diameter  of  fire-box  ;  tubes  from  2"  to 
2£"  diameter,  and  spaced  from  1"  to 
1£"  apart  Water-line  from  10"  to  15" 
above  crown-sheet. 

There  is  supposed  to  be  a  propor- 
tion between  the  tube  sectional  area 
and  the  grate-surface,  say  from  ^  in 
the  horizontal  to  £  in  the  verti- 
cal ;  but  this  rule  is  entirely  em- 
pirical. There  is  also  a  propor- 
tion of  grate  to  heating  surface  ; 
but  only  the  same  class  of  boilers 
can  be  compared  with  each  other, 
as  fire-box  surface — and  that  ex- 
posed directly  to  the  flame — is 
much  more  effective  than  that  of 
the  tubes,  and  the  products  of 


FIG.  932. 


FIG.  934. 


FIG. 


combustion  escape  at  much  different  temperatures  in  different  boilers. 

Flange  Connections  for  Steam  and  Water  Pipe. — Fig.  935  is  a  section  of  a 
flanged  connection  of  a  cast-iron  pipe  of  the  most  usual  form,  but  some  thick- 
en or  re-enforce  the  pipe  a  little  for  1"  to  2"  in  length  next  the  flange  ;  but  if 
there  is  a  good  fillet  in  the  angle  of  the  flange  it  is  unnecessary. 

The  flanges  are  almost  invariably  faced,  and  joints  made  with  red  and  white 
lead,  or  a  sheet-rubber  washer,  or  with  corrugated  copper  gaskets  (Fig.  936) 
of  very  thin  sheet  copper,  which  are  used  of  full  diameter  of  flanges  on  rough 
boiler  joints  and  red-lead  putty  ;  but  for  faced  surfaces  thin  paint  will  insure  a 
perfect  joint  inside  the  bolts. 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


399 


FIG.  935. 


FIG.  936. 


DIMENSIONS  OF  PIPE  FLANGES  AND  CAST-IRON   PIPES. 

J.  E.  Codman,  M.  E.,  Pro.  Engrs.  Club,  Philadelphia. 


Diam. 
of 
pipe. 

DIAMETER  OP 
FLANGE. 

Diameter 
of  bolt 
circle. 

Diam. 
of 
bolt. 

No.  of 
bolts. 

Thick- 
ness of 
flange. 

THICKNESS  OF  PIPE. 

Weight  per 
foot  with- 
out flange. 

Weight 
of  flange 
and  bolts. 

Diagr. 

Form. 

Inches. 

Dec. 

2 

«k 

a* 

44 

i 

4 

1 

1 

0-373 

6-96 

4-41 

3 

71 

H 

f 

4 

1 

H 

0-396 

11-16 

5  93 

4 

9 

8| 

7 

i 

6 

h 

1% 

0-420 

15-84 

7-66 

5 

9* 

8 

i 

6 

f 

A 

0-443 

21-00 

9-63 

6 

lOf 

11 

H 

f 

8 

* 

rt 

0-466 

26-64 

11-82 

8 

18} 

.... 

ill 

* 

8 

If 

i 

0-511 

39-36 

16-91 

10 

l«i 

154 

18* 

t 

10 

i 

A 

0-557 

54-00 

23-00 

12 

17| 

15f 

1 

12 

if 

H 

0-603 

70-56 

30-13 

14 

20 

18 

1 

14 

i 

H 

0-649 

89-04 

38-34 

16 

22 

22* 

20 

1 

16 

iA 

H 

0-695 

109-44 

47-70 

18 

24 

24* 

22* 

i 

16 

11 

f 

0-741 

131-76 

58-23 

20 

27 

26f 

24i 

1 

18 

1A 

M 

0-787 

156-00 

70-00 

22 

88f 

29 

26* 

1 

20 

li 

H 

0-833 

182-16 

83-05 

24 

81* 

28| 

1 

22 

1A 

i 

0-879 

210-24 

97-42 

26 

33* 

33J 

31 

1 

24 

if 

II 

0-925 

240-24 

113-18 

28 

35J 

35f 

33i 

1 

24 

i* 

14 

0-971 

272-16 

130-35 

30 

38 

.... 

35i 

1 

26 

1A 

1 

1-017 

306-00 

149-00 

32 

40 

40* 

37| 

H 

28 

if 

1A 

1-063 

341-76 

169-17 

34 

42* 

40 

11 

30 

itt 

11 

1-109 

379-44 

190-90 

36 

45 

44f 

42 

H 

32 

it 

16 

1-155 

419-04 

214-26 

38 

47 

44 

H 

32 

lie 

1A 

1-201 

460-56 

239-27 

40 

49 

49± 

46 

H 

34 

11 

ii 

1-247 

504-00 

266-00 

42 

51* 

5H 

48i 

H 

34 

HI 

1A 

1-293 

549-36 

294-49 

44 

53$ 

.... 

50i 

li 

36 

2 

i« 

1-339 

596-64 

324-78 

46 

55$ 

56 

52f 

11 

38 

»A 

if 

1.385 

645-84 

356-94 

48 

58 

58i 

55 

li 

40 

2i 

1A 

1-431 

696-96 

391-00 

Fig.  937  is  a  section  of  the  joint  used  by  Sir  William  Armstrong  for  the 
pipes  of  his  accumulator.  For  a  working  pressure  of  800  pounds  per  square 
inch,  pipes  of  5"  diameter  are  made  1"  thick  and  tested  to  3,000  pounds  per 
square  inch.  The  flange  is  elliptical,  and  there  are  but  two  bolts ;  one  pipe 
slightly  enters  the  other,  forming  a  dovetailed  recess  in  which  is  placed  a  gutta- 
percha  ring  £"  in  diameter. 

Figs.  938  and  939  are  sections  of  two  other  forms  of  cast-iron  flanged  pipes, 
both  with  projections  fitting  into  grooves.  The  packing  in  Fig.  939  is  a  ring 
of  lead.  In  Siemens's  air  reservoirs,  where  the  pressure  sustained  by  steel  rings 
is  1,000  pounds  per  square  inch,  the  joint  is  made  by  turning  a  V-groove  in 


400 


MACHINE  DBSiaN  AND  MECHANICAL  CONSTRUCTIONS. 


the  face  of  the  rings,  and  placing  in  it  a  ring  of  annealed  copper  15F"  diameter. 
This  form  is  adopted  by  many  mechanics  for  forming  flanged  joints  even  for 
steam  purposes. 


FIG.  937. 


FIG.  938. 


FIG.  939. 


Figs.  940,  941,  and  942  are  steam-pipe  joints,  as  used  at  the  works  of 
Narragansett  Electric  Lighting  Company,  where  it  is  essential  to  maintain 


the 
the 


CALKING  EDGE 


FIG.  940. 


FIG.  941. 


FIG.  942. 


full  boiler  pressure  permanently.    Fig.  940  is  a  joint  between  two  wrought-iron 

pipes;  Fig.  941  that  between  a  wrought-iron  and  cast-iron  pipe.  In  "both  these 
the  joints  are  calked.  In  Fig.  942,  between  two  cast- 
iron  pipes,  the  joint  is  made  by  a  gasket  of  vulcanized 
asbestos  placed  in  a  recess  of  the  female  joint. 

Fig.  943  is  a  connection  between  wrought-iron  plates, 
in  which  the  joint  is  made  by  a  copper  ring  brazed  to- 
gether. 

Wrought-iron  Pipe  Connections. — With  the  present 
cost  of  wrought-iron  pipes,  they  are  almost  invariably 
used  for  the  conveyance  of  steam,  but  are  more  liable 
to  rust  for  water  purposes  than  cast  iron.  Wrought- 
iron  pipes  are  either  butt-welded  or  lap-welded.  It  is  a 

mere  question  of  manufacture.     It  is  difficult  to  make  a  lap-welded  tube  less 

than  1£"  diameter,  and  therefore  below  this  size  they  are  usually  butt-welded ; 

but  this  size  and  above,  lap- welded. 

Wrought-iron  pipes   of   the   smaller 

diameters  are  connected  by  socket-sleeve 

couplings    (Fig.   944),  of  wrought-iron, 

of  large  diameters,  by  cast-iron  flanges 

screwed  to  the  ends  of  the  pipes  to  be 

coupled.     The  screw  in  the  coupling  is 

tapped  parallel  usually,  but  the  ends  of 


FIG.  943. 


MACHINE  DESIGN   AND   MECHANICAL   CONSTRUCTIONS. 


401 


the  tubes  are  cut  with  a  taper  thread,  uniform  with  all  makers,  of  1  in  32  to 
the  axis.     The  length  of  the  screwed  portion  varies  with  the  diameter. 


FIG.  944. 


FIG.  945. 


Fig.  945  is  the  longitudinal  section  of  tapering  tube-end  with  the  screw 
thread  as  actually  formed,  and  considered  standard  by  the  late  Eobert  Briggs, 
C.  E.,  in  his  "  Treatise  on  Warming  Buildings  by  Steam."  It  is  shown  in  the 
figure  double  full  size  for  a  nominal  2£"  tube. 

DIMENSIONS  OF   WROUGHT  TUBES  AND  COUPLINGS. 


DIAMETER  OF  TUBE. 

CIRCUMFERENCE. 

SCREWED  ENDS. 

Weight 
per  foot 
in  length. 

COUPLINGS. 

Nomi- 
nal in- 
side. 

Actual  in- 
side. 

Actual  out- 
side. 

Inside. 

Outside. 

No.  of 
threads 
perend. 

Length  of 
screw. 

Outside 
diameter. 

Length. 

In. 

In. 

In. 

ID. 

In. 

lu. 

In. 

Us. 

In. 

ID. 

i 

0-27 

0-41 

0-85 

1-27 

27 

0-19 

0-24 

0-55 

1 

i 

0-36 

0-54 

1-14 

1-70 

18 

0-29 

0-42 

0-70 

1 

1 

0-49 

0-67 

1-55 

2-12 

18 

0-30 

0-56 

0-83 

1 

4 

0-62 

0-84 

1-96 

2-65 

14 

0-39 

0-84 

1-01 

1A 

1 

0-82 

1-05 

2-59 

3-30 

14 

0-40 

1-13 

1-24 

if 

1 

1-05 

1-31 

3-29 

4-13 

1H 

0-51 

1-67 

1-53 

if 

li 

1-38 

1-66 

4-33 

5-21 

114 

0-54 

2-26 

1-89 

i| 

14 

1-61 

1-90 

5-06 

5-97 

114 

0-55 

2-69 

2-17 

2 

2 

2-07 

2-37 

6  49 

7-46 

llj 

0-58 

3-67 

2-68 

2i 

24 

2-47 

2-87 

7-75 

9-03 

8 

0-89 

5-77 

3-19 

2f 

3 

3-07 

3-50 

9-64 

11-00 

8 

0-95 

7-55 

3-87 

3 

34 

3-55 

4-00 

11-15 

12-57 

8 

1-00 

9-06 

•4-40 

3£ 

4 

4-03 

4-50 

12-65 

14-14 

8 

1-05 

10-73 

4-99 

O  l 
Of 

44 

4-51 

5-00 

14-15 

15-71 

8 

1-10 

12-49 

5-49 

8| 

5 

5-04 

5-56 

15-85 

17-47 

8 

1-16 

14-56 

6-19 

6 

6-06 

6-62 

19-05 

20-81 

8 

1-26 

18-77 

7-24 

3f 

7 

7-02 

7-62 

22-06 

23-95 

8 

1-36 

23-41 

8-36 

4 

8 

7-98 

8-62 

25-08 

27-10 

8 

1-46 

28-35 

9-49 

4£ 

9 

9-00 

9-69 

28-28 

30-43 

8 

1-57 

34-08 

10-54 

4i 

10 

10-02 

10-75 

31-47 

33-77 

8 

1-68 

40-64 

11-72 

5 

Figs.  946,  947,  948,  also  from  Briggs's  treatise,  give  the  dimensions  of  the 
parts  of  elbows,  tees,  crosses,  and  branches.  Fig.  947  shows  the  parts  of  an 
elbow  designated  by  letters  in  Fig.  940,  and  Fig.  948  shows  the  applicability  of 
the  same  to  tees  and  crosses.  The  scale  is  one  quarter  full  size ;  if  much  used, 
it  would  be  better  for  the  draughtsman  to  construct  one  of  full  size.  The 
dimensions  are  obtained  by  measuring  from  the  base  or  zero  to  the  inclined 
lines,  on  ordinates  corresponding  to  the  inside  diameter  of  pipe  required. 

When  pipes  are  thus  put  together  in  lengths,  with  couplings,  it  is  frequently 
impossible  to  take  out  a  length  of  pipe  for  repairs  or  alterations  without  break- 
27 


402 


MACHINE   DESIGN   AND    MECHANICAL  CONSTRUCTIONS. 


ing  a  coupling  or  fitting ;  provision  is  made  for  disconnections  by  the  insertion 
of  a  union  or  unions  in  the  line. 


FIG.  946. 


Fig.  949  is  an  exterior  view,  and  Fig.  950  a  section,  of  the  common  mal- 
leable-iron union ;  p  and  p'  are  the  halves  into  which  the  tube  is  screwed,  and 
the  joint  is  made  by  a  male  and  female  coupling.  The  male,  b,  turning  on  a 
flange  on  the  tube  jo,  is  screwed  to  the  other  half  of  the  coupling,  and  the  joint 
is  made  tight  by  a  rubber  washer,  shown  in  black.  These  unions  are  used  only 


FIG.  949. 


FIG.  951. 


in  the  smaller  sizes  of  pipes.  The  flange  coupling  (Fig.  951)  is  preferred  by 
most  fitters,  and  they  are  made  of  diameters  up  to  14" ;  the  thickness  is  about 
one  half  that  of  the  length  of  a  coupling  of  the  same  diameter.  The  bolts  are 
from  •§-"  to  f ",  and  spaced  somewhat  larger  than  that  given  for  cast-iron  flanges. 
The  width  of  flange  is  such  as  to  admit  of  the  head  and  nut  of  the  bolt  without 
projection  beyond  the  edge  of  the  flange. 

Fig.  952  is  a  common  cast-iron  flange,  and  with  about  the  same  proportions 
as  in  Fig.  951.  When  the  lines  are  long,  and  provision  can  not  be  made  by 
bends  for  the  expansion  and  contraction  of  pipes  under  changes  of  temperature, 
a  fitting  like  a  stuffing-box  is  often  used,  the  end  of  one  of  the  tubes  being 
attached  to  the  box,  and  the  other  sliding  in  and  out  like  a  piston-rod ;  some- 
times expansion  is  permitted  by  two  flexible  flanges,  admitting  of  a  sort  of  bel- 


MACHINE  DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


403 


lows-like  movement;  sometimes  by^a  U-connection  between  pipes,  as  in  Fig. 
933,  or  a  succession  of  corrugations. 

Fig.  953  is  a  soldering  union  ;  the  ring,  &,  is  like  that  of  the  male  coupling 
(Fig.  950),  which  is  screwed  directly  to  the  wrought-iron  pipe,  while  a  is  a 
brass  tube,  with  a  shoulder  on  the  bottom  on  which  the  coupling,  a,  turns,  and 
a  lead  pipe  is  soldered  to  the  tube.  If  it  is  not  necessary  to  break  the  joints,  a 
soldering  nipple  (Fig.  954)  only  is  necessary,  one  end  of  which  is  screwed  into 
the  wrought-iron  pipe,  and  the  other  soldered  to  the  lead  pipe. 


FIG.  952. 


FIG.  953. 


FIG.  954. 


FIG.  955. 


Fig.  955  is  a  close  nipple  ;  Fig.  956  is  a  shoulder  nipple. 

If  the  uncut  part  of  the  tube  is  longer  than  in  the  figure,  it  is  called  a  long 
nipple ;  they  serve  the  purpose  of  short  pipes. 

Fig.  957  is  a  bushing.  There  is  a  thread  cut  inside.  It  is  screwed  into  a 
coupling,  and  the  pipe  that  is  screwed  into  the  bushing  must  be  smaller  in 
diameter  than  that  connected  with  the  coupling.  The  service  of  the  bushing 


FIG.  956. 


FIG.  957. 


FIG.  958. 


FIG.  959. 


is  to  connect  pipes  of  different  diameters,  but  the  reduction  of  one  side  or  arm 
of  a  coupling  tee,  or  cross  is  better. 

Fig.  958  is  a  plug  to  close  up  the  end  of  a  pipe  by  screwing  it  into  the 
coupling ;  caps  are  used  for  the  same  purpose  ;  half-couplings  with  one  end 
closed,  or  blank  flanges — that  is,  flanges  covering  the  aperture  in  the  pipe — 
bolted  to  a  flange  on  the  end  of  a  pipe. 

It  will  be  seen  by  Fig.  947  that  the  cast-iron  elbow  makes  a  very  short  turn, 
with  considerable  obstruction  to  the  flow  of  the  fluid  through  it.  Fig.  959  is 
an  elbow  in  which  the  obstruction  is  very  much  reduced.  It  consists  of  a 
piece  of  wrought-iron  pipe  curved  to  an  easy  radius  ;  and,  as  a  general  rule,  it 
may  be  said  that  for  the  connection  of  pipes  not  in  a  line  with  each  other,  it  is 
better  to  bend  the  pipe,  if  possible,  than  make  angles  by  cast-iron  elbows. 

Figs.  960,  961,  and  962  are  oblong,  spiral,  and  flat  coils,  showing  the  extent 
to  which  pipe  can  be  bent  by  machinery,  and  are  used  largely  for  heaters  and 
in  refrigerating  plants. 


404 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


FIG.  960. 


Figs.  963  and  964  are  a  tee  and  a  cross,  as  used  in  connections  of  hydraulic 
presses,  made  of  composition.  The  tubes  are  of  wrought-iron,  extra  thick. 
The  usual  dimensions  for  such  are  as  follows : 


Outside  diameter. 
Inside  diameter . 


de  diameter f "  .*-"  J 

n  Da 

The  joints  are  made  by  leather  washers,  square  ends  on  square  seats. 

^-.----^ 


FIG.  965. 


FIG.  966. 


FKI. 


In  Leland's  lead-pipe  coupling  (Figs.  965  and  966)  a  double-cone  ring  is 
inserted  between  the  ends  of  the  pipes  to  be  coupled,  and  they  are  brought  to- 


FIG.  967. 


FIG.  970. 


gether  by  the  common  wrought-iron  pipe-union,  the  inner  surfaces  of  which 
are  adapted  to  the  surfaces  of  the  lead  pipe,  compressing  it  between  the  pipe 
and  the  cone. 

Figs.  967  and  968  are  a  section  and  plan  for  a  similar  joint  of  steel  water 
pipe. 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


405 


Figs.  969  and  970  are  Petit's  pipe  joint  used  in  the  water  system  of  the  camp 
at  Chalons.  A  rubber  ring  is  inserted  in  the  short  bell,  one  clamp  being  con- 
nected ;  the  other  is  brought  over  and  secured,  compressing  the  rubber,  making 
a  tight  and  a  slightly  flexible  joint,  easily  taken  apart  and  put  together. 

Fig.  971  is  a  flexible  steam  joint  consisting  of  a  ball  and  socket  carefully 
turned  and  then  ground  to  a  close  fit,  to  be  connected  with  wrought-iron  pipe. 

The  earlier  flexible  joints  for  water  mains  were  turned  and  fitted,  but  about 


FIG.  971. 


1870  John  T.  Ward,  C.  E.,  introduced  a  ball-and-socket  pipe  in  which  the 
socket  was  turned  but  the  ball  was  fitted  by  a  lead  packing  run  in.  There  was 
some  danger  to  the  socket  by  the  stress  of  the  ball  if  the  movement  was  in  ex- 
cess of  that  contemplated.  Mr.  Ward  in  his  late  designs  made  stops  o  o  (Fig. 
972)  to  prevent  this.  Other  engineers  have  re-enforced  the  ball  by  a  hoop,  of 
which  Fig.  973  is  an  example,  from  the  "  Transactions  "  A.  S.  C.  E.,  designed 
by  James  C.  Duane,  C.  E.,  and  laid  beneath  the  East  River  from  New  York 
city  to  Ward's  Island. 

Fig.  974  is  a  section  and  elevation  of  a  flexible  joint  for  a  submerged  steel 
water  main  used  at  Toronto,  Ontario.     This  joint  is  5  feet  in  diameter,  con- 


NOTE: 

A  BAND  SEAT  TO  BE  TURNED 
TRULY  CYLINDRICAL  AND 
BAND  SECURELY  SHRUNK  ON 

B  CORNERS  TO  BE  ROUNDED 
OFF  AS  SHOWN 


FIG.  973. 


sisting  of  two  parts,  one  part  having  a  turned  spherical  section  riveted  to  the 
straight  pipe ;  the  other  part  is  a  socket,  on  the  inside  of  which  are  two  U- 
shaped  sections,  one  riveted  to  the  sheet-iron  of  the  socket  and  the  other  to  a 
flange  fastened  to  another  flange  on  the  end  of  the  socket ;  these  U-shaped 


406 


MACHINE   DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


rims  are  filled  with  soft  pig  lead  projecting  -J-  of  an  inch  beyond  the  rim  ;  the 
lead  joint  bears  against  the  spherical  section  and  makes  a  close  yet  flexible 


Wood  feck/ntf 

£*•,         /     rt         >•  *5 


C&sf  Iron  f/an$e 


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FIG.  974. 


joint.     The  space  between  the  two  flanges  on  the  socket  end  is  made  tight 
by  a  wood  packing. 

Fig.  975  is  the  section  of  a  ball-joint  used  as  a  connection  for  the  12"  steel 
pipe  for  a  temporary  supply  of  water  to  Liverpool  and  sunk  beneath  the  Mer- 
sey, which  was  connected  for  a  length  of 
800  feet  on  the  shore  and  drawn  across 
the  river  by  the  united  forces  of  horses 
and  a  steam  winch  in  twenty-eight  min- 
utes. The  ball  is  of  cast-iron,  turned,  and 
has  a  socket  of  the  same  material,  with  a 
joint  of  cast  lead,  for  which  two  holes  are 
shown — one  for  running  the  metal  and 
the  other  for  the  vent. 

Governors. — In  the  running  of  all  ma- 
chinery there  are  variations  of  speed,  due  to  varying  powers  and  resistances 
caused  by  increase  or  decrease  in  the  pressure  producing  the  power,  as  of 
steam  or  water,  or  in  the  resistances  of  the  machinery,  from  more  or  less  being 
brought  into  action,  or  through  inequalities  of  work  done.  To  maintain  the 
speeds  at  as  much  uniformity  as  possible,  governors  are  used,  which,  applied 
to  steam  engines  or  water-wheels,  open  or  close  valves  or  gates,  and  increase  or 
reduce  the  supply  of  steam  or  water  to  the  cylinders  or  wheels,  according  to 
the  varying  necessities.  The  ordinary  governor  (Fig.  976)  consists  of  two 
heavy  balls,  suspended  by  links  from  a  spindle,  and  caused  to  revolve  by  some 
connection  with  the  shaft  of  the  motor.  In  the  figure  the  governor  is  driven 
by  a  belt-connection  to  the  pulley,  jo,  bevel-geared  to  the  governor.  When  at 
rest,  the  balls  hang  close  to  the  spindle,  but  when  in  motion  the  balls  rise  by 


FIG.  975. 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


407 


the  centrifugal  force.  When  the  motor  is  running  at  its  established  speed,  for 
which  the  pulley  is  to  be  adjusted,  the  links  assume  a  position  nearly  at  45° 
with  the  spindle.  If  the  speed  falls  off,  the  balls  fall,  and,  acting  on  the  lever, 
as  shown  in  side  view,  open  the  valve  or  gate  controlling  the  passage  of  steam 
to  the  cylinder  or  water  to  the  wheel ;  if  the  speed  rises,  the  balls  rise  and  close 
the  valve  or  gate.  The  lever  does  not  always  connect  directly  with  the  gate, 
nor  is  there  always  a  lever,  but  the  rise  or  fall  of  the  balls  acts  on  some  mech- 
anism which  performs  the  function  of  reducing  or  increasing  the  supply  of 
steam  or  water.  /  • 

The  size  of  the  balls  depends  somewhat  on  the  work  to  be  done,  the  resist- 
ance to  be  overcome  in  the  movement  of  the  gate  and  connections,  and  may  be 
much  reduced  if  this  work  is  thrown  on  some  other  mechanism,  which  is  usu- 
ally the  case  in  the  regulation  of  water-wheels ;  while  for  steam  engines  the 


FIG.  976. 


FIG.  977. 


work  to  be  done  by  the  governor  is  reduced  by  balancing  the  steam-valve,  or 
to  the  merely  releasing  of  a  trip,  cuts  off  the  movement  of  the  valve  at  any 
point  of  stroke. 

The  common  governor  (Fig.  976)  is  sufficient  for  the  regulation  of  drop 
cut-off  engines  like  the  Corliss  (Figs.  422,  423),  but  for  slide-valve  engines  with 
throttle  regulation  the  Porter  governor  (Fig.  977)  is  better  adapted;  the  balls 
of  this  governor  are  comparatively  light,  but  they  are  connected  to  a  heavy  cen- 
tral weight  by  levers,  the  same  as  those  connecting  the  balls  with  the  spindle. 

Of  late  it  has  become  very  common  to  run  engines  at  very  high  speeds,  be- 
yond that  possible  to  be  obtained  by  drop  cut-offs;  and  light  slide-valves  are 
used  in  which  the  governors  act  by  shifting  the  cams  (actuating  the  valves) 
placed  within  the  pulley  or  fly-wheel.  Fig.  978  is  an  elevation  of  one  of  this 
class  of  governors — the  Westinghouse.  The  disk  A  is  cast  solid  and  keyed  to 
one  of  the  cranks.  The  loose  eccentric  C  is  suspended  by  the  arm  c  from  the 
pin  (7,  around  which  it  has  a  motion  of  adjustment ;  B  B  are  the  governor 
weights,  pivoted  on  the  pins  b  b ;  one  of  the  weights  is  connected  to  the  ec- 


408 


MACHINE   DESIGN  AND   MECHANICAL   CONSTRUCTIONS. 


centric  by  the  link  /",  and  both  weights  are  connected  to  operate  in  unison  by 
the  link  e.  Coil  springs,  D  D,  furnish  the  centripetal  or  returning  force.  The 
eccentric  encircles  the  shaft  S,  the  opening  being  elongated  to  admit  of  the 


FIG.  978. 


FIG.  979. 


proper  motion.  The  stops  ss  limit  the  motion  of  the  weights.  Fig.  979  shows 
the  governor  in  the  position  of  latest  cut-off.  The  governor  weights  are  shown 
in  the  position  of  rest,  whereby  the  eccentric  is  thrown  over  to  its  position  of 
greatest  eccentricity,  giving  a  maximum  travel  to  the  valve  corresponding  to  a 
cut-off  of  about  f  stroke.  The  parts  of  the  governor  remain  in  this  position 
till  the  engine  is  within  a  few  revolutions  of  its  full  speed.  The  centrifugal 
force  of  the  weights  then  overbalances  the  tension  of  the  springs,  and  the 
weights  move  outward,  reducing  the  travel  of  the  eccentric  and  valve,  conse- 
quently shortening  the  cut-off  and  closing  the  exhaust  earlier,  thus  increasing 
the  compression  curve  and  preserving  greater  economy  in  running  the  engine. 

Fly-  Wheels. — In  most  machinery  there  are  great  inequalities  of  movements, 
from  the  great  difference  in  power  exerted  or  resistances  overcome,  and  in  the 
application  of  the  force,  as  through  cranks.  To  obviate  this,  fly-wheels  are 
used,  which  absorb  energy  in  one  part  of  their  revolution  and  give  it  out  at 
another,  or  by  their  mass  in  movement  overcome  resistances,  as  in  the  punch- 
ing, shearing,  and  rolling  of  metal,  which  comes  only  periodically,  and  is  much 
in  excess  of  that  usually  required.  In  addition,  fly-wheels  give  governors  time 
to  act,  and  consequently  the  motion  is  more  uniform  and  constant. 

All  shafting,  pulleys,  and  machines  in  movement  act  as  regulators,  and 
where  the  resistances  vary  largely  on  machines  they  require  independent  fly- 
wheels. In  addition,  friction,  hygrometric,  and  other  conditions  vary  so  much 
at  different  times,  even  with  the  same  engines,  that  it  is  impossible  to  get  data 
for  an  estimate  by  any  mathematical  formula  embracing  the  conditions.  From 
the  experience  of  the  best  mechanical  engineers,  and  from  published  examples 
of  constructions,  are  deduced  the  following  rules,  applicable  to  common  prac- 
tice for  the  fly-wheels  of  steam  engines :  The  diameter  of  fly-wheel  to  be  4 
times  that  of  the  stroke  of  the  engine,  and  the  entire  weight  of  the  wheel  40 
times  the  square  root  of  the  diameter,  its  exterior  velocity  being  about  5,000 
feet  per  minute ;  if  less  or  more,  increase  or  reduce  the  weight  inversely  as  the 


MACHINE   DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


409 


velocity.  The  rim  is  generally  a  little  less  than  £  of  the  whole  weight,  but  the 
arms  should  be  made  strong  in  view  of  the  fact  that  a  great  strain  may  be 
produced  in  them  by  any  suddenly  interposed  obstacle.  For  rolling-mill  en- 
gines, Prof.  C.  B.  Richards  takes  the  weight  of  the  fly-wheel  at  60  times  the 
square  of  the  diameter  of  the  cylinder,  and  the  diameter  of  the  wheel  5  times 
that  of  the  stroke,  and  rim  velocity  not  to  exceed  125  feet  per  second. 


FIG.  980. 


In  most  stationary  engines  the  fly-wheel  is  a  pulley  or  band-wheel  or  gear 
driving  the  machinery,  but  often  the  fly-wheel  is  independent.  Fig.  980  is  the 
elevation  and  section  of  a  fly-wheel  built  by  the  Southwark  Foundry.  The 
construction  will  be  understood  from  the  drawings,  but  the  wrought-iron  links 


410 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


MACHINE  DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


411 


connecting  the  segments,  shown  pn  a  larger  scale  (Fig.  981),  do  not  project, 
but  are  countersunk  in  the  sides  of  the  rim. 

The  cast-iron  fly-wheel  of  a  steam  engine  36"  X  72",  built  for  the  Amos- 
keag  Manufacturing  Company  in  1883,  30  feet  diameter,  110"  face,  with  one 
set  of  12  arms,  and  total  weight  116,000  pounds,  making  61  revolutions  per 
minute ;  exploded  in  1891,  and  was  replaced  by  a  wooden-rimmed  pulley  with 
two  sets  of  arms  (Figs.  982  and  983).  The  counterbalance  of  the  cranks  and 
connecting-rods  was  obtained  by  placing  heavy  cast-iron  plugs  in  the  outer  ends 
of  the  three  arms  directly  opposite  each  crank.  Though  the  total  weight  of 
the  wheel  is  not  much  less  than  that  of  the  old  one,  the  weight  of  the  rim 
(31,855  pounds)  is  only  about  one  half,  but  has  shown  itself  ample  for  a  very 
steady  speed  at  much  less  cost  and  greater  security. 

Fly-wheels,  and  in  fact  all  wheels  that  have  a  rapid  motion,  should  be  bal- 
anced, and  if  driven  by  cranks  their  connections  should  be  balanced  dynamic- 
ally to  make  the  motion  as  uniform  as  possible. 

Air- Chambers. —The  action  of  the  air-chamber  is  very  similar  to  that  of  a 
fly-wheel ;  it  tends  to  make  the  outflowing  or  inflowing  pressure  of  the  fluid 
uniform,  and  cushions  or  prevents  the  reaction  that  takes 
place  from  the  fluid  in    reciprocating   pumps,   especially 
crank-pumps ;   but  pumps  in  which  the  pistons  or  plung- 
ers start  very  slowly  and  stop  equally  so  require  but  little 
air-chamber.     Cornish  engines  are  usually  provided  with 
a  stand-pipe  instead  of  an  air-chamber — that  is,  a  vertical 
pipe   of   considerably  larger   diameter   than   that  of   the 
pump,  and  high  enough  to  contain  the  water-column. 

Fig.  984  is  the  section  of  a  copper  air-chamber  for  the 
smaller  size  of  steam  or  hand-pumps.  It  is  screwed  into 
the  top  of  the  pump-chamber.  Fig.  985  is  the  elevation  of 
an  air-chamber  for  power  pumps  of  larger  size  of  cast-iron 
or  a  cast-iron  base  with  a  copper  chamber.  A  flange  is 
cast  on  the  top  of  the  pump-chest,  and  the  chamber  is 
bolted  to  it. 

Fig.  986  is  the  elevation  of  an  air-chamber  of  one  of 
the  older  Brooklyn  pumping-engines. 

The  lower  end  of  the  small  air-chamber  (Fig.  984)  is 
necked,  or  of  smaller  diameter  than  the  main  part  of  the 
chamber.  This  prevents  a  too  sensitive  reaction  of  the  air 
and  retards  its  escape ;  for  the  same  purpose  a  diaphragm 
perforated  with  holes  is  put  across  the  inside  of  the  cham- 
ber. When  the  inlet  column  is  long,  whether  suction  or 
under  pressure,  put  an  air-chamber  on  it. 

Air-chambers  should  be  from  ten  to  fifteen  times  the 
capacity  of  the  pump-cylinder,  with  glass  gauges  to  show 
the  quantity  of  air  in  them  for  large  pumps,  and  some  pro- 
vision to  supply  and  maintain  the  air  at  such  levels  as  will  be  found  by  experi- 
ment suited  to  the  easiest  working  of  the  pump.  A  large  air-chamber  can  in 
this  way  be  reduced  in  capacity,  while  that  of  a  too  small  chamber  can  not  be 
increased.  Air-chambers  are  made  of  wrought-iron  or  steel  and  the  heads 


FIG.  985. 


412 


MACHINE   DESIGN  AND  MECHANICAL  CONSTRUCTIONS. 


are  bumped  up  or  dished.     The  thickness  of  the  cylindrical  part  is  to  be  deter- 
mined by  the  rules  on  riveting  (page  383).     The  dished  head,  struck  up  on  a 

spherical  radius  (Fig.  987)  equal 
to  the  diameter  of  the  cylinder 
and  of  the  same  thickness  of 
plate,  is  of  equal  strength. 

In  the  earlier  application  of 
water  to  the  distribution  of  power 
the  air-chamber  held  the  reserve 
of  force,  but  since  the  use  of 
power  in  this  form  has  become  of 
general  application,  the  accumu- 
lator (Fig.  988)  is  the  form 
adopted,  in  which  the  pressure  of 
the  water  in  the  pipe  A  raises  the 
piston  B  from  which  is  suspended 
the  dead  weight  C  sufficient  to 
maintain  the  pressure  required. 
For  the  distribution  of  power 
throughout  the  city  of  London 
the  pressure  is  about  700  pounds 
to  the  inch.  At  the  Forth  "Bridge 
Works  there  are  two  forms  of 
accumulators  in  use  through 
which  the  high-pressure  water  is 
pumped ;  in  one  form  a  16"  cylin- 
der is  loaded  with  dead  weights,  in 
the  other  an  8"  cylinder  is  loaded 
with  steam. 


rfi  ffi  ffi  fft  rfi  ftiffifflffli 


FIG 


FIG.  987. 


To  make  a  hydraulic  riveting  machine  that  could  be  introduced  into  some 
of  the  more  complex  parts  of  the  structure,  it  was  necessary  to  increase  the 
pressure  of  the  riveter  and  reduce  its  dimensions.  This  was  effected  by  the 
multiplier  (Fig.  989),  in  which  the  usual  high  pressure  is  introduced  into  a  large 


MACHINE  DESIGN  AND   MECHANICAL  CONSTRUCTIONS.  413 


FIG.  991. 


u 


414 


MACHINE   DESIGN  AND   MECHANICAL  CONSTRUCTIONS. 


cylinder  with  its  piston  connected  with  a  plunger  of  smaller  diameter,  and  the 
pressure  from  the  smaller  cylinder  is  connected  with  the  riveter. 

For  hydraulic  cylinders  the  common  rules  are  for  cast-iron  to  a  pressure  up 
to  2,000  pounds  per  square  inch  and  cast-steel  to  6,000  pounds  per  square  inch, 
rarely  exceeding  8,000  pounds.  For  the  resistance  of  thick  shells  Rankine  gives 
the  bursting  strain  — 


--> 


in  which  /is  the  tenacity  of  the  metal,  E  and  r  exterior  and  interior  diameter 
respectively. 

Figs.  990  and  991  are  the  elevation  and  plan  of  a  common  form  of  hydraulic 
press  for  the  baling  of  goods.  The  dimensions  of  the  bolts  at  the  four  corners 
should  be  estimated  from  the  hydraulic  pressure^  with  a  factor  of  safety  of  5. 

As  tools  the  hydraulic  punch,  riveter,  and  jack  are  in  general  use. 


Yin.  992. 


FIG.  993. 


FIG.  994. 


FIG. 


Fig.  992  is  the  section  of  a  common  jack-screw  in  which  the  screw  is  turned 
by  a  lever  of  which  the  hole  beneath  shows  where  its  end  is  inserted.  The  whole 
weight  is  taken  by  the  extended  base. 

Figs.  993  and  994  are  side  and  end  views  of  a  cast-iron  housing ;  the  screw 
exerts  a  pressure  on  the  roll  box  journals  to  be  resisted  by  the  frame. 

Fig.  995  is  the  side  elevation  of  a  cam  punch  and  shear,  the  action  being  to 
spring  the  jaws,  which  are  reinforced. 

The  above  drawings  of  machines,  not  shown  elsewhere  in  the  work,  are  given 
as  illustrations  of  forms  adapted  to  the  stresses  for  which  they  are  designed, 


ENGINEERING  DRAWING. 


THERE  is  no  part  of  engineering  more  important  than  that  of  securing  a 
good  foundation  for  the  structure.  Where  likely  to  be  disturbed  by  frost,  the 
structure  should  start  below  it,  unless,  as  in  the  extreme  northern  regions  where 
frost  is  permanent  at  certain  depths,  the  support  should  be  in  it.  In  preparing 
the  foundation  for  any  structure,  there  are  two  sources  of  failure  which  must 
be  carefully  guarded  against :  viz.,  inequality  of  settlement,  and  lateral  escape 
of  the  supporting  material ;  and  if  these  radical  defects  can  be  guarded  against, 
there  is  scarcely  any  situation  in  which  a  good  foundation  may  not  be  obtained. 
It  is  therefore  important  that,  previous  to  the  commencement  of  the  work, 
soundings  should  be  taken  to  ascertain  the  nature  of  the  soil  and  the  lay  of  the 
strata,  to  determine  the  kind  of  foundation  ;  and  the  more  important  and 
weighty  the  superstructure,  the  more  careful  and  deeper  the  examination.  But 
it  must  be  understood  that  in  general  it  is  not  an  unyielding  but  a  uniformly 
yielding  stratum  that  is  required,  and  that  a  moderate  settlement  is  not  objec- 
tionable, but  an  inequality  of  settlement. 

In  good  sand  or  gravel,  the  load  on  foundations  per  square  foot  is  usually 
from  three  to  five  tons.  Many  soils  are  very  compressible,  not  supporting  one 
ton  per  square  foot ;  if  the  structure  is  important,  the  bearing  resistance  of  the 
strata  should  be  tested  by  experiment.  The  base  of  the  wall  is  extended  to 
secure  the  requisite  area  of  bearing-surface,  either  by  a  base-stone  (Fig.  996), 
by  a  bed  of  concrete  (Fig.  997),  or  by  extending  the  wall  by  steps  (Fig.  998), 


FIG.  996. 


FIG.  997. 


FIG. 


with  or  without  concrete  base,  or  the  weight  may  be  distributed  by  inverted 
arches  between  walls  and  piers. 

Wooden  platforms  are  often  used  for  foundations,  but  must  be  laid  beneath 
the  water  line  where  they  are  kept  wet,  otherwise  rot  will  take  place.  These 
platforms  may  be  of  a  single  course  of  plank  or  plank  and  timber,  as  in  Fig.  999, 
or  may  be  very  much  extended,  forming  rafts  or  grillages  of  many  courses.  A 
similar  foundation  has  been  introduced  in  Chicago,  where  the  great  depth  of 
clay  requires  extended  areas  of  foundation,  but  instead  of  timber  it  consists 

415 


4:16 


ENGINEERING   DRAWING. 


of  a  combination  of  masonry  with  common  rails  or  I-beams,  affording  greater 
length  of  offsets  and  less  depth  than  by  timber  or  masonry.     The  length  of 

offsets  may  be  calculated  from  the  insistent  weight, 
by  the  formula  of  beams  fixed  at  one  end  and  uni- 
formly loaded  or  one  quarter  that  given  in  the  tables 
(pages  243  and  244). 

Fig.  1000  is  a  section  of  one  of  these  foundations 
beneath  a  pier,  but  equally  applicable  to  the  support 
of  walls.  The  space  between  the  beams  is  filled 
with  cement,  mortar,  or  concrete,  which  adds  to  the 
stiffness  of  the  structure  and  is  a  preservative  of  the 
metal.  The  iron  grillages  for  piers  are  distinct,  and 
each  proportioned  in  bearing-surface  toVits  proposed  load.  In  astronomical 
observatories  it  is  especially  necessary  that  the  foundations  for  the  large  and 


FIG.  999. 


STEEL  I   BEAMS 

. STEEL  RAILS' 

'TTTTTTTTTTTTT^  f 


JXXXXJ.XXX  J.XX  JTT  T  T  T  ,T  T  T.XXS 


FIG.  1000. 


delicate  instruments  should  be  detached  from  those  of  the  building,  and  also 
where  the  noise  and  jar  of  the  machinery  might  interfere  with  the  occupancy  of 
the  building  for  other  purposes. 


Walls  on  party  lines  and  confined  to  these  lines  are  often  partially  supported 
by  cantilever  beams  reaching  over  interior  posts.  Such  a  construction  is  shown 
in  Figs.  1001  and  1002. 

It  is  the  safer  construction  to  lay  walls  in  air  and  open  to  inspection,  and 


ENGINEERING   DRAWING. 


therefore  important  that  their  foundations  should  be  freed  from  water,  which 
can  be  done  by  inclosing  them  with  a  bank  of  earth  or  by  a  curb  of  sheet-piling 
(Figs.   1003    and    1004).      Sheet- 
piling  is  usually  of  plank  two  to 
three  inches  thick,  set  or  driven.     -^g~ 
For   driving,  the  bottom  of   the 
plank  should  be  sharpened   to  a 
chisel-edge,  a  little  out  of  centre 
toward  the  ranging  timber  side, 
and  cornered  slightly  at  the  outer 
edge,  that  it  may  hug  the  timber     -^ 
and  the  plank  while  being  driven- 
Fig.  1005  is  the  section  of  a 
timber   sheet-piling,  in  which   a 
tongue    and    groove    forms    the 
guide,   the   grooves   being  either 


FIG.  1003. 


FIG.  100-1. 


FIG.  1005. 


made  in  the  timber,  as  shown  at 

a  a,  or  planted  on,  b  b.  The  pile  should  be  of  uniform  thickness,  but  the 
widths  may  be  random  ;  six  inches  thick  is  a  good  practical  thickness,  driving 
well  under  short  and  frequent  blows  of  a  ram  ;  the  tongue  should  be  of  hard, 
straight-grained  wood,  2  inches  by  2  inches,  and  well  spiked  to  the  pile. 

Frequently,  to  secure  the  foundation  from  water,  a  wall  is  constructed  of 
two  rows  of  sheet-piling,  driven  one  within  the  other,  and  the  space  between  the 

two  filled  with  clay  or  some  compact  earth. 
This  is  called  a  coffer-dam  ;  the  two  rows 
of  piling  are  stayed  to  each  other  by  bolts, 
and  if  the  wall  is  wide  enough  no  other 
stays  or  braces  will  be  necessary. 

Pile-drivers  are  now  constructed  to  drive 
sheet-piling  in  panels  of  6  to  8  feet  wide,  which  serves  to  preserve  the  line  and 
make  tight  joints. 

In  quicksands  it  is  very  common  to  secure  a  foundation  by  consolidation 
with  small  stones  or  rubble  worked  down  by  iron  bars  or  driven  by  rams  of  a 
pile-driver,  till  sufficient  resistance  is  secured  for  the  structure.  Some  success- 
ful experiments  have  been  made  in  compacting  such  sands  by  forcing  down 
cement  mortar  through  pipes.  *  In  soft  earths  piles  are  generally  used  for  this 
purpose,  and  if  a  firm  bottom  can  be  secured  at  a  reasonable  depth  they  are  the 
most  economical  expedient. 

Piles  are  used  either  as  posts  or  columns  driven  through  soft  earth  to  a  hard 
bottom,  or  depending  on  their  skin  resistance  to  give  the  necessary  support, 
either  in  earth  naturally  compact  or  made  so  by  the  driving  of  the  piles.  In, 
the  first  case  care  must  be  taken  that  the  piles  be  driven  sufficiently  deep  into 
the  lower  strata  to  secure  their  ends  from  slipping  laterally,  and  soundings 
should  be  made  carefully  to  ascertain  the  dip  and  character  of  these  strata.  In 
many  places,  from  the  hardness  and  the  inclined  position  of  the  lower  strata, 
this  kind  of  foundation  is  inapplicable  and  unsafe. 

For  a  foundation  where  no  firm  bottom  can  be  found  within  an  available  depth, 
piles  are  driven,  to  consolidate  the  mass,  a  few  feet  apart  over  the  whole  area  of 
28 


418 


ENGINEERING  DRAWING. 


the  foundation,  which  is  surrounded  by  a  row  of  sheet-piling  to  prevent  the  escape 
of  the  soil  ;  the  space  between  the  pile-heads  is  then  filled  to  the  depth  of  several 
feet  with  stones  or  concrete,  and  the  whole  is  covered  with  a  timber  platform. 

It  is  very  difficult  to  establish  a  rule  of  general  application  for  the  load  which 
a  pile  will  sustain.  It  is  well  in  untried  soil  to  drive  a  few  piles,  noting  the  set- 
tlement under  blows,  and  then  load  the  piles  in  excess  of  what  they  will  be  re- 
quired to  bear,  noting  the  results  from  time  to  time  ;  and  if  settlement  con- 
tinues, drive  deeper,  or  more  piles  with  less  spaces. 

Major  Saunders,  in  the  "  Journal  of  the  Franklin  Institute,"  gave  a  rule  for 
the  safe  load  of  piles  depending  on  the  skin  resistance,  which  has  been  of  general 
application,  but  of  which  the  factor  of  safety  is  unnecessarily  large,  and  is  given 
below  modified  to  4  instead  of  8. 

Multiply  the  weight  of  the  ram  in  pounds  by  the  distance  in  which  it  falls 
in  inches  at  the  last  blow,  and  divide  the  product  by  four  times  the  depth 
driven  in  inches  at  this  blow. 

Weight  of  ram  2,000  pounds,  fall  15'  or  180",  set  If. 

2000  X  180 

=  60,000  pounds. 


Safe  load  = 


X    4: 


In  driving  piles  the  effect  of  the  ram  should  be  carefully  noted,  the  rate  of 
fall  under  successive  blows,  the  brooming  or  splitting  of  the  head  of  the  pile, 
and  the  rebound  of  the  ram  after  the  blow.  Especial  note  should  be  taken 
toward  the  close  of  the  driving  to  determine  the  last  set  when  the  .formula 
above  given  is  used. 

The  usual  weight  of  the  ram  or  hammer  employed  on  our  public  works  va- 
ries from  1,400  to  2,400  pounds,  and  the  height  of  leaders  or  fall  from  20  to  35 
feet ;  but  there  is  a  great  advantage  in  reducing  the  fall,  increasing  the  weight 
of  the  hammer,  and  the  frequency  of  the  blows.  As  generally  driven,  and  of 
average  size,  when  the  whole  weight  is  to  be  supported  by  the  pile,  ten  tons 

may  be  considered  a  usual  load,  but  when 
additional  support  is  received  from  com- 
pacted earth,  broken  stone,  or  concrete  be- 
tween piles  and  caps,  this  bearing  surface 
should  also  be  taken  into  consideration. 


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FIG.  1006. 


FIG.  1007. 


Figs.  1006  and  1007  represent  plan  and  elevation  of  a  pile  foundation  ;  the 
piles  are  usually  from  10"  to  14"  top  diameter,  and  driven  at  about  3  feet  be- 
tween centres.  The  tops  are  cut  off  square  and  capped  with  timber  the  caps 


ENGINEERING  DRAWING. 


419 


treenailed  or  ragbolted.  to  the  piles,  and  plank  spiked  to  the  timber.  In  the 
figure  a  sheet-piling,  s  s,  is  shown,  inclosing  the  piles  ;  the  spaces  between  piles 
and  timbers  are  often  filled  with  concrete,  small  stone,  or  closely  packed  earth. 

In  compacting  some  soils  it  has  been  found  that  good  results  may  be  ob- 
tained by  drawing  the  pile  and  filling  the  hole  with  sand.  It  would  seem  that 
the  best  result  would  be  obtained  by  forming  these  piles  of  a  uniform  taper 
downward,  as  the  consolidation  would  be  more  uniform,  the  withdrawal  easier, 
and  less  disturbance  of  the  sides  of  the  hole.  The  consolidation  might  be  still 
further  increased  by  ramming  the  sand  in  thin  layers,  owing  to  the  ability  of 
the  latter  to  transmit  pressure  laterally.  The  sand  should  be  fine,  sharp,  clean, 
and  the  grains  of  uniform  size. 

It  is  often  difficult  to  obtain  or  drive  piles  of  sufficient  length,  and  they 
must  be  spliced.  After  the  first  pile  is  driven,  its  head  is  cut  level ;  a  wooden 
dowel  or  iron  pin,  penetrating  each  pile  about  a  foot,  is  inserted  in  the  centre ; 
the  upper  pile  is  then  fitted  to  the  lower  one,  or  a  cast-iron  collar  or  ring  of 
plate  iron  6"  to  12"  wide  may  be  used  to  strengthen  the  joint  and  protect  the 
pins  from  splitting  either  head  of  the  piles. 

Spliced  in  this  way,  the  pile  is  deficient  in  lateral  stiffness.  In  most  posi- 
tions it  is  safer  to  re-enforce  the  splice  by  flatting  the  sides  of  the  piles  and 
nailing  on  with,  say,  8-inch  spikes,  four  pieces  2  or  3  inches  thick,  4  or  5  inches 
wide,  and  4  to  6  feet  long.  In  the  erection  of  the  bridge  over  the  Hudson 
River  at  Poughkeepsie,  N.  Y.,  two  piles  were  thus  spliced  together  to  form  a 
single  one  130  feet  long. 

Piles  may  be  made  of  any  required  length  or  cross-section  by  bolting  and 
fishing  together,  sidewise  and  lengthwise,  a  number  of  squared  timbers.  Hol- 
low-built piles  40  inches  in  diameter  and  80  feet  long  were  used  as  guide- 
piles  in  constructing  the  St.  Louis  bridge.  To  protect  the  head  of  the  pile 
against  brooming  or  splitting  it  is  usual  to  drive  on  a  tight-fitting  wrought- 
iron  ring  or  cap  (Fig.  1008)  by  a  blow  of 
the  hammer.  In  driving  into  compact 
gravel  or  shingle  the  point  of  the  pile 
should  be  protected  with  iron  straps,  as 
shown  in  Fig.  1009. 

Fig.  1010  is  a  section  of  a  bulkhead 
wall  on  the  North  Eiver  front,  in  positions 
where  the  mud  is  deep,  as  designed  and 
constructed  by  George  S.  Greene,  Jr.,  Chief 
Engineer  for  the  Department  of  Docks, 
New  York  city. 


FIG.  1008. 


FIG.  1009. 


The  site  of  the  wall  is  first  dredged  to  hard  mud  compacted  with  sand.  The  vertical- 
piles  are  then  driven,  and  small  cobble-stones  mixed  with  coarse  gravel  put  around  and 
among  the  piles  to  the  height  of  the  under  side  of  the  binding  frames,  and  rip-rap  stone 
placed  outside  the  piles,  in  front  and  rear. 

The  binding  frames,  then  slid  down  to  their  places,  were  made  of  two  pieces  of  spruce 
plank  5  x  10  inches,  placed  edgewise  one  over  the  other,  and  running  from  front  to 
rear  of  the  piles  between  the  rows.  An  oak  beam  8x8  inches  is  let  through  these 
planks  in  front  of  the  front  row  and  in  rear  of  the  rear  row  of  piles,  and  an  oak  wedge 
block  fitted  and  placed  by  the  divers  between  the  oak  beam  and  each  pile  nearest  it. 


420 


ENGINEERING  DRAWING. 


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rt  ^ 


© 


ENGINEERING   DRAWING. 


421 


These  frames  hold  the  front  rows  of  piles  firmly,  in  case  there  should  be  any  tendency  in 
them  to  tilt  outward.  More  cobble-stone  is  then  put  in  to  the  height  of  the  bottom  of 
the  base  blocks  of  the  wall,  weighting  the  binding  frames  and  preventing  any  tendency 
to  floating. 

The  bracing  piles  are  then  driven  on  a  slope  of  6  inches  horizontal  to  12  inches  ver- 
tical, between  the  rows  of  vertical  piles,  and  spaced  3  feet  from  centre  to  centre  longi- 
tudinally and  transversely.  All  the  piles  are  staylathed  and  adjusted  in  position  as  soon 
as  they  are  driven. 

The  bracing  piles  are  cut  off  at  right  angles  to  their  axis,  about  1  foot  below  mean 
low  water,  and  capped  with  12-inch  square  timber,  running  longitudinally.  The  sides 
of  the  caps  are  kept  horizontal  and  vertical,  and  a  sloping  recess  or  notch  made  to  re- 
ceive the  head  of  each  bracing  pile,  and  give  it  a  good  bearing. 

The  six  rear  rows  of  vertical  piles  are  cut  off  at  2  inches  above  mean  low  water,  and 
notched  front  and  rear  to  give  an  8-inch -wide  bearing  across  their  tops  for  the  trans- 
verse caps. 

The  three  front  rows  of  vertical  piles  are  cut  off  by  a  circular  saw,  suspended  in  the 
ways  of  a  pile-driver,  at  15 -3  feet  below  mean  low- water  mark,  to  receive  the  concrete 
base  blocks  of  the  wall.  It  being  impossible  to  cut  off  piles  at  this  distance  below  the 
surface  of  the  water  to  exactly  the  same  height,  and  as  the  bottom  of  the  concrete  base- 
blocks  would  rest  only  upon  the  highest  piles  of  those  under  them,  a  mattress  of  burlap, 
containing  freshly  mixed  soft  mortar,  in  a  layer  about  2  inches  thick,  placed  on  a  net- 
work of  marline  stuff,  supported  by  a  plank  frame  about  its  edges,  is  lowered  upon  the 
tops  of  these  piles  immediately  before  setting  the  base-blocks  upon  them.  The  diver 
then  cuts  the  netting  between  the  edge  of  the  mattress  and  the  plank  frame,  and  the 
frame  floats  to  the  surface  of  the  water. 

The  base-block  is  then  immediately  placed  in  position  upon  the  mattress  of  mortar 
resting  on  the  piles,  and  the  excess  of  mortar  is  pressed  out  from  between  the  head  of  the 
pile  and  the  bottom  of  the  base-block,  until  each  pile  has  a  well  and  evenly  distributed 
portion  of  the  load  to  carry. 

The  concrete  base-blocks  for  this  section  are  7  feet  wide  at  the  bottom  and  5  feet 
wide  at  the  top;  on  the  front  the  vertical  height  is  13  feet,  and  on  the  rear  14  feet.  The 
top  has  a  step  on  the  rear  of  1  foot  height  and  1£  foot  wide,  extending  the  entire  length 
of  the  block,  for  the  purpose  of  giving  the  mass  concrete  backing  of  the  granite  super- 
structure a  good  hold  upon  the  block.  For  handling,  grooves  for  chains  are  moulded  in 
the  end,  and  a  longitudinal  hole,  2  feet  in  the  clear  above  the 
bottom,  connects  them,  with  the  corners  rounded,  to  enable  the 
chain  to  render  easily.  The  face  is  curved  inward,  to  save  ma- 
terial while  giving  a  broad  base;  their  length  is  12  feet. 

After  the  blocks  are  set,  the  vertical  chain-grooves  in  each 
block,  coming  opposite  to  each  other,  are  filled  in  with  concrete 
in  bags,  well  rammed  into  place.  This  closes  the  joints  between 
the  blocks,  and  also  acts  as  a  tongue  set  into  the  grooves  in  the 
blocks. 

Fig.  1011  shows  a  block  in  section  with  the  central- 
and  side-groove  spaces,  which  are  deep  enough  to  admit 
of  the  easy  slipping  in  and  withdrawal  of  the  chain. 


T 


FIG.  1011. 


As  soon  as  the  base-blocks  are  set,  and  the  groove  filled  in, 
the  cross-caps  resting  on  the  tops  of  the  vertical  piles,  and  on 
the  longitudinal  caps  of  the  bracing  piles,  reaching  about  half 
way  across  the  base-blocks,  are  placed  and  fastened.  Oak  treenails  are  used  in  all  fast- 
enings. The  small  cobbles  are  then  filled  in  around  and  among  the  piles  to  the  top  of 
the  caps,  and  the  rip-rap  placed  in  the  rear  of  them. 


422 


ENGINEERING  DRAWING. 


Figs.  1012  and  1013  are  the  elevation  and  plan  of  a  crib  with  dock  or  pier. 
Below  the  level  of  the  water,  as  here  shown,  the  logs  are  round  and  locked 


I 

2 

V. 
5 
EE 

1 

% 
I 

1 

pS                       tra                       ei 

P3    I                  p|                       p™    ^ 

1 

^  ^  ^  $fo  ffli  -%fc—', 

FIG.  1013. 


to  the  cross-timbers ;  above  the  water  the  timber  is  squared,  the  exterior  walls 
presenting  a  tight,  smooth  surface  into  which  the  cross-timbers  are  dovetailed. 

A  quarantine  station,  built  for  the  port  of  New  York,  on  the  west  bank  con- 
sists of  an  exterior  wall  of  cribwork,  of  which  Fig.  1014  is  a  section ;  the  in- 
closed space  is  filled  with  sand,  comprising  an  extent  of  about  228'  X  448'.  The 
base  to  low  water  consists  of  cribs  about  80'  in  length,  sunk,  and  loaded  with 
stone;  above  it  £he  construction  is  continuous.  The  base  timbers  14"  X  14", 
upper  12"  X  12",  interties  12"  X  12",  at  intervals  of  7  feet  centres  ;  the 
ranging  timbers  to  be  secured  at  every  joint  to  these  below,  and  at  every  cross- 
ing by  1"  square  bolts  21"  long.  The  exterior  is  close-fendered  with  oak  plank, 
iron  bolted,  with  three  iron  bands  at  the  corners. 

Fig.  1015  is  a  transverse  section  of  the  river-wall  Thames  embankment, 
Middlesex  side  ;  a  wall  of  concrete,  etc.,  faced  with  granite,  with  a  sewer  and 
subway  within  the  same,  lined  with  brickwork.  The  different  material  is  rep- 
resented by  different  shadings  and  letters :  g,  granite ;  b  b,  brickwork ;  c  c, 
concrete. 


ENGINEERING  DRAWING. 


423 


Extracts  from  specifications : 

"The  embankment- wall  is  to  be  formed  within  iron  caissons  or  coffer-dams.  As 
soon  as  the  excavations  shall  have  been  made  to  the  requisite  depths,  and  the  works 
cleared  of  water,  the  trenches  shall  be  filled  up  with  concrete  to  a  level  of  12J  feet  be- 
low datum,  and  a  bed  dressed  to  the  proper  slope  and  level  for  the  footings  of  the  brick 
wall.  This  wall  to  be  formed  thereon,  generally  in  courses  at  right  angles  to  the  face 
of  the  wall.  The  subway  shall  be  formed  7  feet  6  inches  high  by  9  feet  wide  in  the 
clear,  generally ;  the  side-walls  to  be  18  inches,  the  arch  1  foot  1£  inch  thick.  The  sub- 
way sewer  and  river- wall  shall  be  tied  into  each  other,  at  intervals  of  6  feet,  by  cross  or 


FIG.  1014. 


counterfort  walls  18  inches  thick,  extending  from  the  brickwork  of  the  wall  to  a  vertical 
line  9  inches  beyond  the  side  of  the  sewer  farthest  from  the  said  wall,  and  from  footings 
9  feet  below  datum,  which  are  to  be  bedded  on  a  concrete  foundation  12  inches  thick, 
up  to  the  under  side  of  the  subway.  The  upper  arch  of  the  subway,  and  all  other  simi- 
lar arches,  shall  be  coated  on  their  outside  circumference  with  a  1"  layer  of  Claridge's 
patent  Seyssel  asphalt.  The  whole  of  the  stones  above  11 V  datum  to  be  dowelled  to- 
gether in  bed  and  joints  with  slate-dowels,  not  less  than  5  for  every  foot  run  of  wall ; 
each  2J  inches  square  at  least,  let  fully  2£  inches  into  each  stone,  very  accurately  fitted, 
and  run  in  with  neat  cement;  the  stones  to  be  bedded  and  jointed  in  cement,  and  the 
joints  struck  with  neat  cement." 

Fig.  1016  is  an  isometrical  view  of  the  overflow  and  outlet  of  the  Victoria 
and  Regent  Street  sewers  in  the  Thames  embankment.  S  is  the  main  sewer, 
and  W  the  subway  shown  in  Fig.  1015  ;  s  s  s  the  street-sewers,  discharging  into 
the  overflow  basin  0  ;  w  w  the  weirs  over  which  the  water  is  discharged  into 
the  weir-chamber  c  c ;  p  is  the  penstock-chamber,  which  is  but  a  continuation 
of  the  weir-chamber.  Whenever,  from  storms,  the  discharge  from  the  street- 
sewers  (s  s  s)  is  greater  than  can  be  carried  off  by  the  main  sewer  (S),  the  water 
rises  in  the  overflow-chamber  (0),  passes  over  the  weirs  (w  ^v)  down  into  the 
weir-chamber  (c),  then  into  the  penstock-chamber,  and  through  the  flap-gates 
(</)  into  the  river. 


424 


ENGINEERING   DRAWING. 


Extracts  from  the  specifications  : 

"The  foundation  to  be  of  concrete,  not 
less  than  2  feet  in  thickness  ;  upon  this 
brick-work  shall  be  built  for  the  flooring  of 


the  chambers,  and  for  the  side- 
end  and  weir- walls.  The  weir- 
chamber  shall  be  divided  in  the 
direction  of  its  length,  by  a  brick 
wall,  into  two  rectangular  over- 
flow-channels, covered  with  cast- 
iron  plates,  6  feet  8J  inches  long, 
3  feet  wide  by  |  inch  general 
thickness,  with  strong  ribs  and 
flanges  on  the  under  side,  prop- 
erly bolted  together  and  jointed 
with  iron  cement,  and  bolted 


FIG.  1015. 

down  to  stones  which  are  to  be  built  into  the  under  side  of  the  brickwork  of  the  base- 
ment chamber.  Arches  on  either  side,  running  parallel  thereto,  and  communicating  with 
this  chamber  and  with  the  weirs  which  are  to  be  formed,  upon  which  weir-walls,  divided 
so  as  to  correspond  with  these  arches,  are  to  be  built  in  brickwork,  capped  with  granite 


ENGINEERING  DRAWING. 


425 


426 


ENGINEERING   DRAWING. 


blocks,  4  feet  long,  2  feet  deep,  and  2  feet  3  inches  in  the  bed.  The  floor  of  the  pen- 
stock-chamber to  be  formed  with  York  landings,  6  inches  thick,  having  a  fall  of  3  inches 
to  the  river.  The  outlets  for  the  penstock-chamber  through  the  river-wall  shall  be 
formed  by  an  arch-recess  in  granite,  and  fixed  with  two  tidal  flaps,  well  hung,  and  firm- 
ly secured  to  the  masonry  by  strong  bolts  and  screws. 

"The  subway  is  to  be  continued  over  the  low-level  sewer,  and  across  the  overflow- 
chamber,  by  cast-iron  plates,  curved  to  the  form  of  the  arch,  J  inch  general  thickness, 
with  strong  ribs  and  flanges  on  the  upper  side,  properly  bolted  together,  and  strongly 
bolted  down  to  the  brickwork ;  jointed  with  iron  cement,  and  covered  with  brickwork, 
to  form  the  floor  of  the  subway.  From  a  point  of  10  feet  3  inches  on  either  side  of  the 
central  longitudinal  line  of  the  chamber,  where  the  sewer  and  subway  are  farthest  from 
the  river-wall,  these  are  again  to  be  brought  into  their  general  position  by  two  curves, 
each  not  less  than  80  feet  in  length. 

"The  whole  of  the  cast-iron  shall  receive  one  coat  priming  of  red  lead  and  linseed 
oil,  and  three  coats  best  coal-tar,  before  fixing;  and  the  accessible  surfaces  one  further 
coat  best  coal-tar,  when  fixed." 

Fig.  1017  is  the  section  of  the  dike  or  jetty  forming  a  breakwater  for  the 
harbour  of  Boulogne,  France.  It  may  be  considered  in  two  distinct  parts,  cor- 


responding  to  the  substructure  and  the  superstructure.  The  substructure  is 
formed  by  a  mass  of  natural  and  artificial  rip-rap,  with  a  central  core  of  stones 
weighing  about  two  hundred  and  fifty  pounds  each,  resting  on  the  bottom,  and 
rising  to  a  level  of  one  metre  above  low  tide.  The  shore  side  is  protected  by  a 
pitching  of  stone,  each  about  twelve  hundred  pounds  weight ;  the  sea-side 
slope,  by  one  of  heavy  rubble  of  about  seven  tons  each,  and  covered  by  beton- 
blocks  weighing  uniformly  thirty-three  tons  each ;  on  the  above  is  built  the 
masonry  superstructure.  On  each  £ide  of  the  wall,  on  a  level  with  the  lower 
platform,  the  slopes  are  consolidated  by  masonry  bermes  formed  of  isolated 
blocks,  which  protect  the  foot  of  the  wall  and  afford  a  path  for  the  workmen 
and  materials  at  low  tide. 

The  water-jet  is  extensively  employed  on  sandy  shores  for  the  sinking  of 
piles  for  foundations  of  lighthouses,  wharves,  etc.,  and  in  the  Southern  States 
it  renders  the  palmetto  available,  which  resists  the  ravages  of  the  teredo,  but  is 
too  soft  to  withstand  the  blows  of  the  pile-driver.  In  a  simple  and  effective 
application  it  consists  of  a  pile  to  which  a  small  iron  pipe  is  attached,  extend- 
ing below  the  bottom  of  the  pile.  A  flexible  hose  is  attached  to  the  top  of  the 


ENGINEERING  DRAWING. 


427 


FIG.  1018. 


pipe  and,  water  being  forced  through,  the  earth  is  washed  away  from  the  bot- 
tom and  side  of  the  pile,  which  falls  by  its  own  or  superadded  weight  or  light 
blows  of  a  maul  or  hammer. 

The  jet  has  also  been  employed  in  a  great  variety  of  ways  to  facilitate  the 
passage  of  screw  and  disk  piles,  cylin- 
ders, etc.,  through  earthy  material,  and 
as  an  ejector  to  remove  earth  from  the 
inside  of  caissons,  and  relieving  stranded 
vessels  by  removing  the  sand  from  their 
bottoms  and  sides. 

Cast-iron  or  wrought-iron  is  used  for 
piles,  and,  at  the  present  prices  of  iron, 
with  economy.  They  can  be  driven  by 
the  pile-driver,  the  interior  earth  removed 
by  an  augur,  by  sand-pump,  or  water-jet. 
The  blows  of  the  ram  should  be  cush- 
ioned by  a  wooden  block.  For  the  con- 
struction of  the  iron  pier  at  Coney 
Island,  N.  Y.,  to  the  bottom  of  the 
wrought-iron  pipes  8f"  in  diameter,  in 
lengths  of  from  12  to  20  feet,  cast-iron 
disks  were  fastened  by  set  screws  and 
sunk  by  an  inside  water-jet  to  a  depth  of 
17  feet  in  the  sand. 

In  Chili  iron  piles  were  sunk  14f" 
diameter  with  bottom  flange  of  42";  the 
pump  discharged  12,000  gallons  per  hour 
through  two  2"  pipes  extending  8"  below 
the  base,  and  would  sink  two  piles  28  feet 
on  an  average  in  18  hours.  The  bottom 
was  of  coarse  compact  sand  and  the  pile 
was  worked  down  by  an  endless  cable 
passing  around  a  pulley  on  the  pile  and 
giving  it  a  motion  of  rotation. 

The  screw  pile  usually  consists  of  a 
wrought  shaft  from  3"  to  8"  diameter  to 
which  is  keyed  a  cast-iron  screw  from  2 
to  5  feet  in  diameter  sunk  by  turning 
the  shaft  by  hand  or  power,  mostly  used 
for  marine  purposes,  for  the  foundations 
of  lighthouses,  or  anchors  for  buoys 

where  they  resist  the  upward  motion  of  the  waves.  As  they  are  sunk  without 
jar  or  disturbance  of  the  soil,  they  are  adapted  to  positions  where  the  neigh- 
bouring structure  might  be  injured  by  other  methods  of  sinking  foundations. 

Figs.  1018,  1019,  and  1020  are  sections  of  masonry  curbs  sunk  by  water-jets 
for  a  quay  at  Calais,  France. 

The  base  is  of  concrete  made  in  a  mould,  the  rest  of  the  masonry  laid  in 
cement  mortar. 


FIG.  1019. 


FIG.  1020. 


428 


ENGINEERING  DRAWING. 


The  sand  surface  beneath  the  blocks  was  exposed  to  the  action  of  strong 
jets,  and  the  mixture  of  sand  and  water  was  pumped  up  by  centrifugal  pumps ; 
the  suction-pipe  nozzle  was  just  below  the  level  of  the  bottom  of  the  block  ; 
care  was  taken  that  the  quantity  of  water  forced  in  should  be  the  same  as  that 
pumped  out,  and  the  level  of  the  water  in  the  curb  should  be  just  below  that 
in  the  surrounding  sand.  When  the  curb  had  reached  the  bottom  after  a  de- 
scent of  about  15  feet,  the  sand  was  allowed  to  settle  and  the  opening  was  filled 
with  concrete  up  to  a  level  where  it  could  be  filled  with  masonry. 

The  blocks  1,  3,  5  are  sunk  alternately, 
and  then  2,  4,  6,  the  blocks  being  cemented 
together  as  shown  in  Fig.  1021. 

It  has  long  been  common  in  India  to 
sink  brick  wells  in  clusters  by  hand  labour, 


24  WALL 


FIG.  1021. 


FIG.  1023. 


excavating  and  pumping  for  the  foundations  of  bridges,  but  by  substitution  of 
bucket-dredges  to  remove  the  inner  cores  of  earth  greater  .facility  in  work  and 
depth  of  sinking  has  been  secured.  This  system  has  been  successfully  applied 
to  the  sinking  of  iron  caissons. 

In  the  sinking  of  small  curbs  for  wells  it  is  common  to  make  circular  plank 
curbs  supported  by  segmental  ribs  inside,  and  load  them  so  that  they  will  sink 
as  the  earth  is  removed  from  the  inside  and  then  lining  with  masonry. 

Fig.  1022  is  a  partial  section  of  a  shoe  of  the  50-foot  diameter  well  sunk  at 
Long  Island  City,  N.  Y.  It  consists  of  timber  segments  bolted  together  on 
the  top  of  which  a  brick  wall  was  laid ;  on  the  outside  is  a  board  sheathing. 
As  the  earth  is  removed  from  the  inside  the  curb  settles  from  the  weight  of  the 
brick  masonry,  which  is  built  up  and  settles  again  and  again  till  the  required 
depth  is  reached.  As  the  boards  are  set  at  a  batter  of  2"  to  1  foot,  the  struc- 
ture settles  readily  as  the  earth  is  removed.  Were  it  not  for  the  batter  the 
earth  would  press  against  the  sheathing  and  masonry,  and  vertical  bolts  would 
be  necessary  in  the  latter  to  anchor  the  courses  together  and  prevent  rupture. 
The  sheathing  of  boards  is  planed  on  the  outside  and  firmly  attached  to  the 
shoe  with  bound  wooden  segments  above  to  preserve  the  form,  which  are  re- 
moved as  the  brickwork  reaches  them. 

Fig.  1023  is  a  partial  section  of  a  steel  caisson,  exhibiting  the  cutting  edge 
re-enforced  by  steel  plates  and  supported  by  beams  to  the  bottom  girder. 

Foundations  for  the  abutments  of  piers  and  bridges  may  be  constructed  on 


ENGINEERING  DRAWING. 


429 


FIG.  1023. 


any  of  the  systems  illustrated,  but  as  it  is  generally  necessary  that  they  should 

not  extend  in  width  so  as  to  obstruct  the  current  of  the  stream  and  increase  its 

velocity,  it  is  usual  to  inclose  the  site  of 

the    foundations    within    a   coffer-dam, 

freeing  it  from  water  and  preparing  the 

foundation  ;  but  this  is  expensive  in  deep 

water,  and  other  means  are  adopted. 

Figs.  1024,  1025,  and  1026  are  plans 
and  sections  of  the  foundations  of  one 
of  the  Poughkeepsie  bridge  piers,  which 
may  be  designated  as  a  crib,  although  its 
walls  are  tighter  than  usual  in  such  con- 
structions. 

It  is  built  of  12"  X  12"  white  hemlock 
timber,  except  the  bottom  or  cutting 
course  of  the  shoe,  which  is  white  oak. 
The  shoe  is  carried  up  in  a  triangular 
section  of  solid  lumber  around  the  sides 
and  a  central  longitudinal  division  to 
the  height  of  20  feet.  Top  surface  at 
sides  10  feet  wide,  at  ends  9  feet,  central 
16  feet ;  above  the  shoe  there  are  hollow 
spaces.  Cross-timber  walls  2  feet  thick 
divide  the  spaces  into  pockets,  of  which  those  above  the  shoe  are  weighting 
pockets  and  those  open  at  the  bottom  are  dredging  pockets  D.  The  earth  is 
dredged  from  the  pockets  D  and  discharged  into  the  pockets  W,  and  acts  as  a 
weight  to  sink  the  crib,  care  being  taken  to  distribute  the  load  to  equalize 
the  sinking.  As  the  earth  is  dredged  from  the  pockets  D  the  crib  sinks,  and 
when  it  reaches  the" bottom  they  are  cleared  out  and  the  space  filled  with  con- 
crete lowered  into  place  in  boxes  of  one  cubic  yard  capacity  and  unloaded  by  a 
trip. 

The  top  of  the  crib  was  sunk  to  a  level  of  7  feet  below  water  mark  and  the 
concrete  brought  to  within  2  feet  of  this  level ;  this  space  was*lled  with  broken 
stone  and  levelled  by  divers;  a  floating  caisson,  or  tight  box  with  timber  bottom 
and  sides,  was  floated  over  the  crib  and  sunk  and  the  masonry  begun.  When 
complete  above  water  the  sides  of  the  caisson  was  removed. 

The  Chinese  anchors  used  in  mooring  the  cribs  of  the  Poughkeepsie  bridge 
as  shown  in  Fig.  1027  is  composed  of  3"  X  8"  hemlock  planks  10  feet  ]ong 
piled  to  make  the  interior  dimensions  6'  X  6'  X  6',  which  is  filled  with  broken 
stone,,  each  anchor  holding  8  cubic  yards  ;  the  eye-bolts  shown  at  the  corners 
serve  the  double  purpose  of  holding  the  framework  together  and  carrying  the 
slings  to  which  the  cable  is  fastened. 

Open  caissons,  as  shown  in  the  description  of  the  Poughkeepsie  bridge,  are 
useful  when  a  suitable  foundation  can  be  secured  either  in  a  uniformly  yield- 
ing material  or  by  preparing  one  by  means  of  piles  or  divers. 

Figs.  1028  and  1029  are  illustrations  of  the  means  adopted  by  G.  A.  Parker, 
C.  E.,  in  lowering  the  caissons  for  the  erection  of  some  of  the  piers  of  the  Sus- 
quehanna  bridge. 


430 


ENGINEERING   DRAWING. 


He  commenced  by  dredging  away  as  much  as  possible  of  the  material  in  the  bed  of 
the  river  at  the  pier  site.  A  f-inch-thick  boiler-iron  curb  was  then  sunk  and  secured  in 
place.  The  curb  was  about  30  feet  wide  and  50  to  60  feet  long,  and  of  sufficient 
height  to  reach  above  the  bed  of  the  river.  The  material  was  then  pumped  by  sand- 
pumps  out  of  the  curb,  which  gradually  undermined,  and  settled  down  to  the  estab- 
lished depth,  or  to  the  bed-rock.  When  stumps,  logs,  or  boulders  were  met  with  they 
were  removed  by  divers  working  in  a  bell.  After  the  rock  had  been  thoroughly 
cleaned  off,  it  was  brought  to  a  uniform  level  by  a  solid  bed  of  concrete  extending  over 
a  greater  space  than  the  size  of  the  bottom  of  the  pier  by  the  use  of  the  diving  bell. 

Three  guide-piles  on  each  side,  and  one  at  each  end,  were  fixed  firmly  in  position.  A 
strong  platform  of  solid  timber,  the  size  of  the  bottom  of  the  pier,  was  then  placed  in 
position  over  the  curb  and  at  the  surface  of  the  water.  On  this  was  placed  a  caisson  of 
iron  large  enough  to  contain  the  pier,  and  with  sides  and  ends  high  enough  to  reach  to 


the  level  of  high  water  after  the  caisson 
was  landed  on  the  bottom.  The  caisson 
was  then  made  water-tight.  The  bottom 
was  then  floored  over  with  masonry  and 
stone,  and  laid  in  mortar  up  the  sides  of 
the  caisson  to  the  top,  thus  constituting  a 
stone  caisson  inside  of  an  iron  one.  This 
was  secured  to  the  guide  piles,  and  the 
masonry  of  the  pier  proper  was  laid  up,  the  caisson  sinking  as  the  weight  of  masonry 
inside  increased,  until  it  finally  settled  upon  the  bottom  which  had  been  prepared  for 
it.  At  some  of  the  piers  (Figs.  1028  and  1029)  screw-rods  were  used  to  suspend  the 
pier  and  gearing  attached,  governed  by  one  man,  who  could  raise  or  lower  without  assist- 
ance the  whole  pier.  Wooden  piles  were  driven  for  some  piers  and  cut  off  by  machinery 
just  above  the  ground,  and  the  platform,  with  its  masonry,  lowered  upon  them. 


Fm.  1026. 


ENGINEERING  DRAWING. 


431 


Piers  are  sometimes  made  by  sinking  a  wrought-iron  curb,  extending  from 
the  bottom  to  above  the  level  of  the-  water,  driving  within  it  the  usual  propor- 
tion of  piles,  and  then  filling  the 
spaces     entirely     with     concrete. 
This  process  was  adopted  in  form- 
ing some  of  the  piers  of  the  bridge 
of  the  Shore  Line  Eailroad  across 
the    Connecticut    River    at    Say- 
brook,  under  Oushing's  patent. 

Pneumatic  Piles.  —  The  vac- 
uum process  in  which  the  hollow 
pile  of  cast-  or  wrought-iron  was 
sunk,  by  capping  it  and  exhaust- 
ing the  air  within,  and  thus  load- 
ing it  with  the  pressure  of  the  ex- 
terior atmosphere,  gave  place  to 
the  plenum  process,  which  was 
adopted  for  the  old  piers  of  the 
Third  Avenue  bridge  across  the 
Harlem  River,  of  which  Fig.  1030 
is  a  section.  It  conists  of  a  pipe 

in  two  sections  ;  the  upper  one  is  called  the  air-lock,  which  can  be  connected 
with  either  the  lower  chamber  or  the  atmosphere.  The  lower  chamber  being 
under  pressure  and  shut  off  from  the  air-lock,  the  workman  passes  from  the 
outer  air  into  the  lock,  closes  the  door,  opens  the  pipe  connection  between  the 
two  compartments,  and,  when  the  pressure  becomes  equal,  opens  the  lower  door 
and  passes  down. 


1027_ 


y 


i  M  i  i  i  i  rr 


FIG.  1028. 


FIG.  1029. 


Mr.  McAlpine  enlarged  the  bottom  of  the  cylinder  to  a  conical  form,  and 
also  added  largely  to  the  bearing  surface  by  poling-boards  driven  obliquely  out- 
ward. After  the  excavation  was  completed,  a  strong  course  of  concrete  was 
laid,  and,  when  set,  the  air-lock  was  taken  off  and  the  balance  of  the  concrete 
filling  was  done  in  open  air. 


432 


ENGINEERING   DRAWING. 


ENGINEERING   DRAWING. 


433 


The  pneumatic  caisson  has  superseded  the  pneumatic  pile.  The  system  of 
air-lock  is  the  same,  but,  instead  of  sinking  several  piles  and  then  combining 
them  with  a  structure,  the  caisson  em- 
braces the  whole  pier  and  starts  from 
the  bottom.  The  pneumatic  caisson 
is  an  inverted  boat  or  diving  bell  of 
timber,  which  forms  the  working  or 
air  chamber,  connected  with  the  upper 
air  by  pipes  and  air-locked  shafts  for 
the  ascent  and  descent  of  the  work- 
men and  for  the  removal  of  waste 
from,  and  the  delivery  of  material 
into,  the  working  chamber. 

Figs.  1031,  1032,  and  1033  are  the 
plan  and  partial  sections  of  a  late  form 
of  the  framing  of  a  caisson.  The  ceil- 
ing of  the  working  chamber  is  of 
plank,  and  between  the  first  and  sec- 
ond courses  of  beams  there  is  a  double- 
plank  floor,  which  are  calked  and  then 
coated  with  pitch,  and  the  spaces  be- 
tween the  timbers  filled  with  concrete. 

Fig.  1240  is  a  section  of  the  pier 
of  the  Bismarck  bridge.  The  sand 
was  removed  from  the  air  chambers 
by  water  electors.  As  it  is  removed 

,  , ,  ,  .    .  FIG.  1030. 

from  the  chamber,  the  masonry  sinks 

the  caisson,  and  when  it  reaches  the  bottom  the  space  is  filled  with  concrete 
or  with  sand.  If  the  top  of  the  caisson,  when  first  sunk,  does  not  reach  the 
surface  of  the  water,  a  curb  is  formed  on  the  top  to  a  height  sufficient  to  per- 


w 

I 

1 

\ 

\ 

X 

1 

1 

<4/'r  Si//7/y/v 

FIG.  1034. 


FIG.  1035. 


mit  the  construction  of  the  masonry  in  the  open  air.     To  preserve  the  position 
of  the  air-lock  during  the  whole  construction  there  is  an  offset  in  the  pipe  at 
29 


434 


ENGINEERING  DRAWING. 


FIG.  1036. 


FIG.  1037. 


ENGINEERING  DRAWING. 


435 


this  point,  and  necessarily  an  inconvenience  in  the  change  of  movement  of  ma- 
terial and  workmen,  but  in  later  constructions  this  is  avoided. 

Fig.  1034  is  a  recent  plan  and  section  of  a  main  shaft,  through  which  access 
to  the  caisson  is  obtained  by  the  workmen  ;  each  length  consists  of  a  cylindrical 
shell  4  feet  in  diameter  and  8  feet  long,  flanged  at  the  bottom,  with  a  head  hav- 
ing an  opening  in  it;  these  lengths  are  added  as  fast  as  the  caisson  sinks  8  feet. 
The  head  of  the  top  and  second  section  are  provided  with  doors  (Fig.  1035), 
thus  making  the  air-lock.  When  a  length  has  been  added  the  top  door  is  re- 
moved and  placed  on  the  top  of  the  new  length ;  the  lower  door  may  then  be 
taken  off  and  placed  where  the  other  has  been  removed. 

Figs.  1036  and  1037  are  plan  and  section  of  the  Barr-Moran  air-lock  on  the 
excavating  shaft.  The  top  doors  are  double  slides,  tight-fitting  and  working 
on  cast-iron  guides,  operated  by  pistons  driven  by  steam  or  by  compressed  air 
from  the  caisson.  The  lower  door  is  a  flap-valve,  balanced  by  a  counterweight 
and  operated  through  a  rocker-shaft  extending  through  the  air-lock,  and  a 
quadrant  and  chain  attached  to  the  piston-rod  of  a  steam  or  of  a  pneumatic 
cylinder  in  connection  with  the  caisson.  In  the  figures  both  doors  are  shut. 
Under  atmospheric  pressure  the  upper  doors  can  be  opened  for  the  clear  move- 
ment of  the  bucket  by  a  rope  attached  to  the  bail,  the  rope  passes  through  a 
stuffing-box,  around  which  the  doors  close  when  shut.  With  the  upper  doors 
shut,  and  the  air  in  the  lock  brought  to  caisson  pressure,  the  flap-door  can  be 
opened  and  the  bucket  lowered  to  the  bottom.  At  the  bottom  of  the  shaft 
there  is  a  flap-door  which  can  be  raised  when  it  is  necessary  to  repair  the  air- 
lock or  to  raise  it  by  adding  another  length  of  pipe. 

The  air-lock  at  the  top  of  the  shaft  adds  to  the  security  of  the  workmen 
and  to  the  easier  supervision  of  the  machinery,  while  the  single  straight  pipe 
gives  greater  facility  to  the  movement  of  men  and  materials. 

In  the  freezing  process,  invented  by  F.  H.  Poetsch,  of  Austria,  the  site  of 
the  foundation  is  inclosed  with  large  vertical  pipes  sunk  by  a  water  jet ;  within 
these  pipes,  which  are  closed  at  the  lower  end  and  sunk  to  the  proper  depth,  a 
small  pipe  open  at  the  bottom  is  inserted,  through  which  is  forced  a  freezing 
mixture  (as  chloride  of  calcium),  returning  through  the  outer  pipe.  In  this 
way  a  curb  of  ice  is  formed,  inside  which  the  earth  is  removed  for  the  foundation. 
In  Fiusterwalde,  Austria,  12 
tubes  of  8£"  diameter  were 
sunk  through  115  feet  of 
quicksand,  in  a  circle  of 
about. 14  feet  diameter,  for  a 
shaft  8£  feet  diameter.  After 
the  brick  lining  was  laid  the 
tubes  were  withdrawn,  a  hot 
circulation  freeing  them  from 
the  ice. 

•  This  process  has  been  used 
successfully  in  this  country. 

Retaining -\\a\\s  are  such 
as  sustain  a  lateral  pressure 
from  an  embankment  or  head  of  water  (Figs.  1038  and  1039).  The  width  of 


FIG.  1038. 


FIG.  1039. 


436  ENGINEERING  DRAWING. 

a  retaining- wall  depends  upon  the  height  of  the  embankment  which  it  may 
have  to  sustain,  the  kind  of  earth  of  which  it  is  composed  (the  steeper  the  nat- 
ural slope  at  which  the  earth  would  stand,  the  less  the  thrust  against  the  wall), . 
and  the  comparative  weight  of  the  earth  and  of  the  masonry.  The  formula 
given  by  Morin  for  ordinary  earths  and  masonry  is  b  =  0-285  Ti  -\-li'  \  that  is,  to 
find  the  breadth  of  a  wall  laid  in  mortar,  multiply  the  whole  height  of  the  em- 

285 
bankment  above  the  footing  by  —  — ;  for  dry  walls  make  the  thickness  one 

fourth  more. 

Most  retaining-walls  have  an  inclination  or  batter  to  the  face,  sometimes 
also  the  same  in  the  back,  but  offsets  (Fig.  1038)  are  more  common.  The 
usual  batter  is  from  one  to  three  inches  horizontal  for  each  foot  vertical.  To 
determine  the  thickness  of  a  wall  having  a  batter,  "  determine  the  width  by 
the  rule  above,  and  make  this  width  at  one  ninth  of  the  height  above  the  base." 

The  formulas  for  the  thickness  of  retaining-walls  are  very  complicated.  En- 
gineers make  use  of  some  general  rules  as  above,  and  depend  on  their  experi- 
ence for  any  modification.  The  top  of  the  wall  should  not  be  less  than  2  feet, 
and  in  climates  subject  to  frost  it  will  be  impossible  to  secure  permanently  the 
upper  part.  Where  the  soil  is  saturated  with  water,  it  is  usual  to  put  weep- 
holes  at  or  near  the  bottom  to  relieve  the  pressure  against  the  back  of  walls  laid 
in  mortar. 

Buttresses  and  counterforts  in  the  rear  of  a  wall  of  which  the  construction 
requires  a  uniformity  of  thickness  are  only  considered  equivalent  to  increasing 
the  strength  by  the  mean  amount  added  to  the  horizontal  section  of  the  wall ; 
but  when  the  buttresses  are  on  the  line  of  the  bridge  trusses,  they  add  to  the 
strength  by  the  better  distribution  of  the  weight  of  the  truss  and  by  the  secu- 
rity which  the  weight  of  the  truss  gives  at  this  point  to  the  wall.  The  but- 
tresses should  be  well  bonded  to  the  wall. 

Dams  are  constructed  to  pond  water  for  the  supply  of  cities  and  towns ;  for 
inland  navigation,  by  deepening  the  water  over  shoals,  and  the  feeding  of  ca- 
nals ;  for  power  in  its  application  to  mills  and  workshops ;  and  for  irrigation. 
To  whatever  purpose  the  water  is  to  be  applied,  there  are  two  questions  to  be 
settled :  Whether  the  level  will  be  raised  high  enough  by  the  construction,  and 
whether  the  flow  of  the  stream  is  sufficient  for  the  purpose  required  ;  and,  fur- 
ther, it  may  often  be  important  to  know  how  large  a  pond  will  be  thus  formed, 
how  ample  a  reservoir  to  balance  unequal  flows  or  intermittent  use.  If  the 
pond  be  small,  so  that  the  water  can  not  be  retained,  and  the  supply  is  only 
the  natural  run  of  the  stream,  then  the  minimum  flow  of  the  stream  ds  the 
measure  of  its  capacity. 

The  rule  that  obtains  on  the  Merrimac  Eiver,  at  Lowell  and  Lawrence, 
where  the  pondage  is  more  than  the  average,  is  that  1  cubic  foot  per  second 
per  day  of  12  hours  per  square  mile  of  water-shed  can  be  depended  on  for  per- 
manent mill-power.  On  small  streams  it  happens  that  comparatively  large 
pondage  may  be  secured,  and  the  supply  be  equal  to  one  half  the  rainfall. 

Blodgett,  in  his  "  Climatology  of  the  United  States,"  says  that  "  in  this 
sense  of  permanence  as  a  physical  fact  we  may  consider  the  quantity  of  rain 
for  a  year  as  a  surface-stratum,  on  the  Alantic  slope  and  in  the  Central  States 
of  3£  feet,  which  may  be  diminished  to  half  this  quantity,  or  increased  to  twice 


ENGINEERING  DRAWING. 


437 


as  great  a  depth  in  the  extreme  years.  The  evaporation  from  a  water  surface 
is  now  usually  considered  equal  to  that  of  a  rainfall ;  therefore  in  the  estimate 
of  the  water-shed  available  for  pondage  the  area  of  the  reservoir  is  not  taken 
into  account;  the  quantity  of  rain  falling  upon  it  is  offset  by  the  evaporation. 

The  usual  form  of  dams  for  small  streams  and  but  little  fall  is  to  build  a  rub- 
ble wall  across  the  stream  and  secure  the  up-stream  side  with  an  earth  of  loamy 
gravel  puddled  with  water  to  the  consistence  of  mortar  or  rammed  in,  the  top 
where  the  water  is  to  flow  over  or  through  being  protected  by  tight  planking, 
around  or  beneath  which  the  water  can  not  leak. 

Lake  McMillan  dam,  built  across  Pecos  River,  Colorado,  intercepting  its 
entire  flow  for  the  purpose  of  irrigation,  is  1,686  feet  long,  54  feet  high,  with 
an  estimated  water  capacity  of  1,000,000,000  cubic  feet.  Fig.  1040  is  a  section 


FIG.  1040. 


showing  its  construction,  a  heavy  rock  fill  with  a  puddle  slope  in  reservoir 
front.  There  is  an  ample  spillway  or  waste  channel  by  which  all  surplus  water 
will  be  discharged,  with  no  flow  over  the  dike.  The  South  Fork,  Pa.,  dam, 
similar  in  construction  to  the  above,  gave  way  from  a  flow  over  the  top  of  the 
dam,  due  to  an  insufficient  waste  and  an  extreme  freshet. 

In  the  "  Transactions  "  of  the  A.  S.  C.  E.,  December,  1892,  James  D.  Schuy- 
ler,  a  member,  gives  a  description  of  the  asphalt  lining  of  reservoirs  for  the  city 
of  Denver.  The  excavation  consisted  of  2'  to  3'  sandy  loam,  12'  to  15'  hard  clay 
impregnated  with  alkali,  and  8'  to  12'  of  shale.  On  the  completion  of  the  em- 
bankment the  slopes  were  sprinkled  and  rolled  with  a  roller  of  5  tons,  drawn  up 
and  lowered  by  an  engine.  Beginning  at  the  bottom,  the  slopes  were  laid  in 
horizontal  strips  of  asphalt  10'  wide  and  about  If"  thick  spread  with  hot  rakes, 
tamped  with  hot  tampers,  and  smoothed  with  hot  smoothing-irons.  While  the 
sheet  was  still  warm  anchor  spikes  of  strap  iron  1"  X  £",  7"  to  8"  long,  were 
driven  through  it  into  the  bank,  in  rows  about  12"  centres,  alternately  flush 
with  the  surface  and  projecting  1£"  ;  lumber  strips  of  2"  X  4"  were  placed  loosely 
above  them  on  the  slope  for  the  workmen.  After  the  finishing  coat  was  applied, 
the  projecting  spikes  were  driven  flush  and  painted  over.  The  bottom  thick- 
ness was  1",  spread,  tamped,  and  rolled  with  a  cold  roller  of  5  tons.  The  finish- 
ing coat  of  refined  Trinidad  asphalt,  fluxed  with  residuum  oil,  was  poured  on 
from  hot  buckets,  and  ironed  over  with  smoothing-irons  heated  to  a  cherry-red. 

Dikes  or  dams  over  which  there  is  no  flow  of  water  can  be  made  entirely  of 
earth.  It  is  sufficient  that  the  material  be  made  more  compact  than  the  natu- 
ral earth  in  which  the  dam  is  built,  that  it  be  of  sufficient  section  to  resist  the 
pressure,  and  width  to  obstruct  the  flow  of  water  through  it,  and  reduce  the 
percolation  to  a  safe  and  economical  limit,  the  passage  of  water  between  the 
particles  of  earth  being  like  that  through  very  small  broken  and  crooked  pipes. 


438 


ENGINEERING 
"5 


DRAWING. 

Dikes  across  salt  marshes  are 
made  of  material  taken  from  the 
marsh  at  some  distance  from  the 
site  of  the  dike,  well  packed  in  thin 
layers  on  a  base  prepared  on  the 
soil  without  excavation.  Sand  and 
gravel,  being  heavier  than  the  moist 
material,  break  through  it  and  set- 
tle to  the  bottom,  involving  often 
the  construction  of  a  large  em- 
bankment, while  by  the  use  of  a 
homogeneous  material  the  founda- 
tion is  not  displaced  but  compressed. 

Fig.  1041  is  a  section  of  the 
dike  or  embankment  for  the  Ashti 
Tank  or  Keservoir,  constructed  for 
retaining  water  for  irrigation  pur- 
poses in  India.  The  following  is 
an  abstract  of  the  description  of 
the  work  given  in  the  "  Minutes 
of  the  Proceedings  of  the  Insti- 
tute of  Civil  Engineers,"  vol.  Ixxvi : 

"The  net  supply  available  for  irri- 
gation may  be  calculated  thus : 
Available  capacity 

of  tank 1,348,192,450  cub. ft. 

Deduct     loss    by 

evaporation,  etc.      233,220,240     " 

Net  supply  availa- 
ble for  irrigation  1,114,972,210     " 

"  Area  of  catchment  basin  nearly  92 
square  miles." 

The  total  length  of  the  dam  is 
12,709  feet ;  the  breadth  at  the  top, 
which  is  uniform  throughout,  6 
feet ;  breadth  at  full  supply-level, 
42  feet;  height  of  the  top  of  the 
dam  above  full  supply-level,  12  feet; 
greatest  height  of  dam,  58  feet. 
The  seat  of  the  dike  throughout 
was  cleared  of  vegetable  mould, 
stones,  and  loose  material,  all  trees 
and  shrubs  with  their  roots  being 
completely  grubbed  or  dug  out. 
The  puddle-trench  laid  in  the  nat- 
ural ground  is  rectangular  in  cross- 
section,  10  feet  in  width,  excavated 


ENGINEERING  DRAWING. 


439 


through  various  materials  to  a  compact  water-tight  bed,  and  then  filled  in  with 
puddle  material,  consisting  of  two  parts  of  sand  and  three  parts  of  black  soil, 
carefully  mixed  and  worked  by  treading  with  the  feet,  and  then  kneaded  into 
balls  and  thrown  or  dashed  into  the  trench  in  layers  up  to  12  inches  in  thick- 
ness. The  puddle  was  brought  to  a  level  of  1  foot  above  the  ground.  Across 
the  river  the  trench  was  cut  down  to  the  rock  and  filled  with  concrete. 

The  general  distribution  of  the  material  of  the  dam  is  shown  in  the  figure. 
The  central  core  is  formed  of  the  best  black  soil  attainable  ;  on  each  side,  ex- 
tending to  the  surface  of  the  mixed  material,  brown,  reddish,  or  white  earth  is 
used.  The  outer  part  of  the  dike  is  formed  of  a  mixture  of  equal  parts  of 
black  soil  and  sand.  The  black  soil  may  be  described  as  a  clayey  earth,  tena- 
cious and  adhesive  when  wet — a  product  of  the  decomposition  of  volcanic  rock. 
The  brown  and  reddish  soils  are  of  a  clayey  nature,  but  contain  admixtures  of 
fine  sand,  nodules,  and  thin  layers  of  fine  grains  of  lime.  The  white  soil  con- 
sists of  finely  powdered  particles  of 
a  grayish  color,  similar  to  wood 
ashes,  which  when  dry  possesses  lit- 
tle adhesion,  but  when  wet  is  ad- 
hesive. 

The  various  soils  were  laid  in  the 
work  in  layers  8  inches  in  thickness, 
every  layer  being  thoroughly  watered 
and  rolled  with  iron  rollers.  The 
outer  slope  was  protected  by  a  mix- 
ture of  equal  parts  of  soil  and  sand, 

and  with  sods  of  grass,  laid  about  3  feet  apart,  which  in  time  extended  over  the 
whole  slope. 

The  inner  slope  is  protected  from  the  action  of  the  waves  by  being  pitched 
or  faced  with  dry  stone,  set  by  hand,  and  laid  on  a  layer  of  coarse  sand.  The 
stones  of  the  pitching  were  bedded  on  the  slope,  and  were  laid  with  their 
broadest  end  downward  (Fig.  1042),  each  stone  being  roughly  squared  with  the 
hammer,  and  touching  for  at  least  3  or  4  inches.  The  interstices  were  then 
packed  with  small  stone-chippings,  and  finished  off  with  sand. 

P 


FIG.  1042. 


FIG.  1043. 


Fig.  1043  is  the  section  of  a  crib-dam  in  northeastern  Colorado  for  the 
pondage  of  water  for  the  purposes  of  irrigation.  The  crib-work  is  of  round 
logs,  10"  at  least  in  diameter,  joined  at  the  end  as  in  ordinary  log  huts,  with 


440  ENGINEERING  DRAWING. 

dovetail  or  tongue.  Each  crib  is  18  feet  long  on  the  face,  and  the  fastenings 
are  2"  X  18"  treenails.  The  cribs  are  set  radially,  forming  a  curve  up-stream 
of  200  to  238  feet  radius.  The  crib  gives  the  stability,  but  the  water-tightness 
depends  on  a  shutter,  p,  or  vertical  panel  of  timber,  and  the  filling  of  earth  on 
the  up-stream  side. 

For  dikes  where  water  does  not  flow  over  the  top  a  construction  similar  to 
Fig.  1043  is  very  strong  and  in  many  places  the  most  economical,  but  without 
any  wood,  which  is  likely  to  decay  or  rot  when  exposed  to  the  air.  In  con- 
struction it  consists  of  a  mass  of  masonry  laid  dry,  with  a  nearly  vertical  up- 
stream face  pinned  and  pointed  with  cement  mortar  and  again  faced  with  a 
concrete  or  cement  wall  in  close  connection  with  the  wall  face  and  mortar 
bonded  with  it.  The  face  of  the  concrete  or  cement  wall  is  plastered  with  a 
light  coat  of  cement  and  protected  against  the  wash  of  the  water  or  thrust  of 
the  ice  by  an  earth  embankment.  This  embankment  adds  to  the  security  of 


FIG.  1044. 

the  dam  by  cutting  off  seams  in  the  rock  foundations  and  to  the  stanchness 
of  the  cement  wall. 

Fig.  1044  is  a  section  of  the  dam  across  the  Connecticut  River,  at  Holyoke, 
Mass.  This  dam  is  1,017  feet  long  between  abutments,  averages  30  feet  high 
by  a  base  of  80  feet  and  is  constructed  of  timber  crib-work,  loaded  with  stone 
for  about  one  third  its  height.  The  foot  of  each  rafter  is  bolted  to  the  ledge, 
and  all  their  intersections  are  treenailed  together  with  2"  white-oak  treenails. 
The  inclined  plank  face  is  loaded  with  gravel,  and  the  joint  at  the  ledge  cov- 
ered with  concrete.  The  lower  or  base  tier  of  ranging  timbers  are  15"  X  15", 
the  other  timbers  12"  X  12".  The  rafters  are  placed  vertically  over  each  othe,r, 
in  bents  of  6  feet  between  centres.  The  planking  is  of  hemlock  6"  thick,  with 
oak  cross  planking  at  crest  of  dam  4"  thick  at  bottom  and  8"  at  top.  The  crest 
is  plated  with  iron  £"  thick,  5  feet  wide.  During  the  construction  the  dam 
was  planked  first  about  30  feet  on  the  incline ;  a  space  was  then  left  of  about 
16  feet  width  by  sufficient  length,  through  which  the  water  flowed  ;  and  the 
balance  of  the  dam  was  then  completed.  A  plank  flap  was  then  made  for  the 
opening,  and  when  everything  was  ready  it  was  shut  down  and  the  pond  filled. 
The  objection  to  the  flap  construction  is  that  the  space  left  for  the  waterway 
through  the  dam,  after  its  completion,  serves  as  a  duct  for  air  from  below 
which  softens  and  rots  the  timber-work. 


ENGINEERING  DRAWING. 


441 


When  the  dam  was  first  contemplated  the  longer  time  and  extra  cost  re- 
quirud  for  a  masonry  construction  turned  the  scale  in  favour  of  crib-work. 
Some  twenty-five  years  after  its  completion  it  was  found  that  the  water  over- 
fall from  the  crest  was  cutting  out  the  ledge  beneath  the  dam,  and  a  crib-apron 
was  constructed  entirely  across  the  river,  sheathed  with  plank  on  a  slope  of 
about  2|  to  1  from  the  crest  downward.  From  the  decay  and  weakening  of  the 
timbers  of  the  old  darn,  continual  repairs  have  been  required,  and  it  is  now  de- 
cided to  put  in  a  masonry  dam,  the  wooden  dam  having  served  its  purpose  for 
some  fifty  years. 

Fig.  1045  is  a  section  of  the  dam  across  the  Croton  Eiver,  constructed  under 
the  direction  of  Mr.  John  B.  Jervis,  for  the  supply  of  the  aqueduct  for  the  city 
of  New  York.  This  dam  was  built  on  an  earth  foundation,  with  curved  roll  in 


FIG.  1045. 

cut  stone,  extending  by  a  timber-apron  some  50  feet,  supported  by  strong  crib- 
work.  Originally  there  was  a  small  supplementary  dam  farther  down  to  set  the 
water  back  on  to  the  crib-apron,  but  this  was  washed  out,  and  the  crib- work  is 
replaced  by  heavy  rock  pave.  In  the  erection  of  this  dam  all  loose  material  was 
removed,  and  then  the  cribs  C  and  D  were  built  up  and  the  tops  were  planked ; 
on  this  planking  were  carried  up  the  cribs  F  and  G.  Between  these  piers  the 
space  E,  as  well  as  e  below  and  on  the  cribs,  was  filled  in  with  concrete  ;  on  this 
the  body  of  the  dam  was  erected  in  stone-masonry,  laid  in  cement.  The  face- 
work  of  granite  is  cut  to  admit  of  a  joint,  not  exceeding  T3^  of  an  inch.  The 
radius  of  the  granite  face  is  55  feet,  and  the  dam  38  feet  high  from  level  of 
apron  to  crest  of  dam.  This  dam  has  been  in  use  fifty  years  and  is  in  very  good 
condition  and  tight. 

Fig.  1046  is  a  section  of  a  part  of  the  dam  across  the  Merrimac  River,  at 
Lowell,  built  under  the  direction  of  Mr.  James  B.  Francis.  It  was  laid  dry,  with 
the  exception  of  the  upper  face  and  coping,  which  was  laid  full  in  cement. 
The  horizontal  joints  at  the  crest  were  run  in  with  sulphur.  The  coping- 
stones  were  dowelled  to  the  face  and  together,  and  clamped  to  an  inclined  stone 


442 


ENGINEERING  DRAWING. 


on  the  lower  slope  ;  the  end-joint  between  these  stones  was  broken  by  making 
every  alternate  lower  stone  longer,  and  the  upper  shorter,  than  shown  in  the 
drawings. 

The  Cohoes  dam  (Fig.  1047)  was  built  by  W.  E.  Worthen,  C.  E.,  directly 
below  an  old  dam  of  somewhat  similar  construction  to  that  of  Holyoke.     The 


SCALE  :  }  inch  =  1  foot. 


old  dam  had  become  very  leaky  and  worn,  and  the  overfall  had  in  many  places 
cut  deep  into  the  rock,  and  in  some  places  within  the  line  of  the  dam.  It  was 
therefore  proposed  to  make  the  new  dam,  as  a  roll  to  the  old  one,  to  discharge 
the  water  as  far  from  the  foot  of  the  dam  as  possible,  and  to  keep  the  old  dam 
for  the  protection  of  the  new.  The  exterior  of  the  dam  was  of  rock-faced  ash- 
lar ;  the  caps  were  in  single  lengths  of  10  feet,  and  none  less  than  15"  thick  and 
2  feet  wide ;  they  were  dowelled  together  with  two  galvanized  wrought-iron 
dowels  each.  The  whole  work  was  laid  full  in  cement ;  the  20"  face  was  laid 
first  to  divert  the  leak  of  the  old  dam  from  the  new  work.  The  whole  was 
brought  up  to  the  outline,  to  receive  the  cap-stones,  which  were  bedded  in  ce- 
ment ;  the  top-joints  were  then  run  or  grouted  in  neat  cement,  to  within  about 
6"  of  the  top  of  the  stone,  which  was  afterward  run  in  with  sulphur.  Entire 
length  of  overfall,  1,443  feet ;  average  depth  below  crest  of  dam,  12  feet. 

Where  the  body  of  water  which  may  at  any  time  discharge  over  the  dam  is 
largo  and  the  fall  high,  it  is  especially  desirable  to  secure  a  location  where  the 
overfall  can  be  upon  solid  rock.  If  there  be  a  ledge  at  the  side  of  the  river,  and 
none  can  be  found  in  the  channel,  it  is  often  better  to  make  a  solid  dike  across 
the  river  and  above  the  level  of  freshets,  and  cut  the  overfall  out  of  the  bank. 


ENGINEERING  DRAWING. 


443 


FIG.  1047. 

When  the  dam  can  have  only  an  earth  foundation,  an  artificial  apron,  or  plat- 
form of  timber  or  rock,  is  to  be  made,  on  which  the  water  may  fall,  or  the  high 
fall  may  be  broken  up  by  a  succes- 
sion of  steps.  In  some  cases  a  roll 
or  incline,  like  that  given  in  the 
Croton  dam,  is  extended  to  the  bed 
of  the  stream,  and  continued  by  an 
apron.  The  water  thus  rolls  or 
slides  down,  and  takes  a  direction, 
as  it  leaves  the  apron,  parallel  with 
that  of  the  bed  of  the  stream.  But  FIG.  1043. 

care  must  be  taken  to  protect  the  outer  extremity  of  the  apron  by  sheet-piling 
and  heavy  paving,  as  the  current,  by  its  velocity,  takes  with  it  gravel  and  all 
small  rocks,  and  undermines  the  apron. 


FIG.  1049. 


444 


ENGINEERING  DRAWING. 


FIG.  1051. 


To  retain  the  flow  of  rivers  in  dry  seasons  when  the  ponding  will  have  little 
or  no  effect  on  works  farther  up  the  stream,  flash-boards  are  used,  which  usually 

consist  of  an  iron  bolt  driven 
into  the  crest  of  the  dam, 
against  which  common  boards 
are  raised  to  be  swept  off  when 
the  river  rises  unexpectedly. 
To  control  the  levels  of  the  ca- 
nal, hand  flash-boards  are  used, 
as  in  Fig.  1048,  sliding  in  per- 
manent grooves. 

Figs.  1049,  1050,  and  1051 
are  plan,  elevation,  and  section 
of  the  Beetaloo  dam,  South 
Australia.  The  dam  is  built  of 
concrete,  580  feet  long,  110  feet 


high,  110  feet  thick  on  a  level 
with  the  bed  of  the  creek,  and 
14  feet  thick  at  the  top.  The 
cross-section  is  in  accordance  with  Prof.  Kankine's  formula,  the  horizontal 
curvature  having  a  radius  of  1,414  feet.  The  structure  is  founded  on  rock 
and  has  a  spillway  200  feet  long  by  5  feet  deep,  its  channel  below  being  di- 
vided by  walls  into  three  sections,  as  shown  by  the  drawings. 

Head-gates  are  constructions  necessary  to  control  the  flow  from  the  river- 
pond  or  reservoir  into  the  canal  or  conduit  by  which  the  water  is  to  be  con- 
veyed and  distributed  for  the  purposes  to  which  it  is  to  be  applied.  The  top 
of  the  works  should  therefore  be  entirely  above  the  level  of  the  highest  freshets, 
that  no  water  may  pass,  except  through  the  gates  ;  and  it  is  better  that  the 
opening  of  the  gates  should  be  entirely  below  the  level  of  the  top  of  the  dam, 
to  prevent  as  much  as  possible  the  passage  of  drift  and  ice,  which  are  often  ex- 
cluded by  booms  and  racks  placed  outside  the  gates. 

Figs.  1052,  1053,  and  1054  are  drawings,  in  plan  and  detail,  of  the  head- 
gates,  and  the  machinery  for  hoisting  them,  at  the  Cohoes  Company's  dam. 
There  are  ten  gates,  four  8'  x  6'  6"  and  six  8'  x  9'  in  the  clear ;  all  can  be 
hoisted  by  machinery  connected  with  a  turbine- wheel  at  a,  or  separately  by  hand. 
At  b  there  is  an  overfall,  at  the  same  height  as  the  dam,  over  which  any  drift 
that  is  brought  against  the  gate-house  is  carried.  At  c  there  is  a  similar  over- 
fall within  the  gates,  and  another  at  d,  by  which  any  sudden  rise  of  the  level 
of  the  canal  is  prevented.  At  e  there  is  a  gate  for  drawing  down  the  pond,  and 
another  at  /,  for  drawing  off  by  the  canal,  both  raised  and  lowered  like  the 
head-gates.  The  head-gates  are  of  solid  timber  bolted  together,  moving  in 
cast-iron  guides  set  in  grooves  in  the  stone  ;  in  front  of  these  grooves  there  is 
another  set  of  grooves  (g  g},  which  are  intended  for  slip-planks  or  gates,  to  be 
put  in  whenever  it  is  necessary  to  shut  off  the  water  from  the  gates  themselves 
in  case  of  repairs. 

Hoisting  Apparatus. — To  each  gate  there  are  strongly  bolted  two  cast-iron 
racks,  geared  into  two  pinions  on  a  shaft  extending  across  the  gate-space,  and 
supported  on  cast-iron  standards  on  the  piers.  At  one  extremity  of  this  shaft 


ENGINEERING  DRAWING. 


445 


a? 


H 
^ 
fei 
"1 


Cl 


446 


ENGINEERING  DRAWING. 


ENGINEERING  DRAWING. 


447 


there  is  a  worm-wheel,  driven  by  a  worm  or  screw  on  a  shaft  perpendicular  to 
the  pinion-shaft.  The  worm-shaft  can  be  driven  either  by  a  hand-wheel  at  one 
end,  or  by  ihe  friction-bevel  at  the  other.  The  friction-bevel  can  be  driven  in 
either  direction  by  being  brought  in  contact  with  one  or  other  of  the  friction- 
bevels  on  a  shaft  extending  the  whole  length  of  the  gate-house,  and  in  gear 
directly  with  the  small  turbine  at  a.  The  small  turbine  draws  its  supply  through 
a  pipe,  built  in  the  walls,  and  opening  into  the  space  between  the  gates  and  the 
slip-plank  groove. 

In  the  guard  gates  at  Lowell,  instead  of  racks  attached  to  the  gates  they  are 
supported  by  strong  rods  with  screws  cut  at  the  upper  ends  and  are  raised  by 


FIG.  1055. 

nuts  in  the  hubs  of  a  pair  of  horizontal  gears  driven  by  a  pinion  between  the 
two  on  an  upright  shaft,  connected  with  the  gearing  of  a  turbine  water-wheel. 
In  late  constructions  the  gates  are  raised  by  hydraulic  jacks  in  connection 
with  the  city  water  mains. 

Small  gates  in  canals  are  usually  made  of  wood,  with  wooden  starts  on  which 
a  rack  or  racks  are  planted  and  hoisted  by  hand  through  a  crank  and  pinion 
shaft.  Fig.  1055  is  a  perspective  of  the  hoisting  apparatus  of  such  a  gate  with 
a  single  stem  or  start.  The  pinion  is  driven  through  a  horn  wheel  and  lever. 
The  lever  is  pressed  down  and  the  gate  raised ;  when  this  movement  is  stopped 
a  dog  catches  a  ratchet  on  the  back  of  the  wheel  and  the  gate  is  held.  The 
lever  is  slipped  outward,  and  is  brought  in  contact  with  another  horn,  with 
another  depression  and  raise  of  gate.  The  fulcrum  of  the  lever  is  the  centre 
pin  of  the  wheel.  In  dropping  the  gate  the  lever  holds  it  in  position,  the  dog 
is  thrown  out,  the  lever  thrown  out  from  the  horn,  and  the  gate  drops  from  its 
own  weight ;  if  it  sticks,  it  can  be  forced  down  by  the  reverse  movement  of  the 
lever. 

Gates  seldom  used  are  raised  by  chains  over  a  barrel  by  handspikes,  and 
held  by  ratchet  and  dog  and  dropped  as  above ;  but  for  gates  at  the  head  of 


448 


ENGINEERING  DRAWING. 


ENGINEERING   DRAWING. 


449 


flumes  leading  to  wheels  the  provision  for  their  movement  must  be  positive  in 
both  directions,  as  they  are  of  frequent  use. 

Figs.  1056  and  1057  are  the  elevation  and  section  of  flume  head-gates •  as 
manufactured  and  used  at  Holyoke,  Mass.,  for  such  positions.  G  Gr  are  plank 
gates  sliding  laterally,  moved  by  two  pinions  working  into  racks  at  the  top  and 
bottom  of  the  gates,  turned  by  a  capstan  bar  on  a  horn  wheel  head.  F  is  the 
flume,  circular,  of  wooden  staves  or  wrought-iron  plates.  P  is  a  paddle  gate  by 
which  the  flume  must  be  filled  slowly,  and  A  the  pipe  for  escape  of  air  from 
the  flume  during  filling. 

The  Cheney  head-gates  (Figs.  1058  and  1059),  as  applied  to  several  of  the 
water  gates  of  the  canals  at  Lowell,  are  gates  supported  by  wheels,  which  run 


FIG.  1058. 


FIG.  1059. 


on  upright  cam  shafts  on  each  side  of  the  gate ;  when  the  gate  is  moved  either 
up  or  down,  the  cam  shafts  are  turned  to  raise  the  gate  from  the  flat-closing 
surface,  and  take  the  whole  water  pressure,  which  is,  in  a  measure,  relieved  by 
the  opening  of  this  joint,  and  the  whole  friction  is  transferred  to  the  wheels 
and  the  gate  readily  raised. 

Fig.  1060  is  the  elevation  of  a  circular  tube  of  plate-iron,  as  used  for  a 
waste  gate  in  the  canal  of  the  Connecticut  River  Company  at  Windsor  Locks. 
It  is  of  the  form  of  a  hollow  plug,  largely  used  for  bath  tubs,  and  now  called  a 
standard  waste.  The  tube  is  8  feet  diameter  and  9  feet  high.  The  joint  be- 
tween the  plug  and  the  pipe  extending  to  the  river,  is  made  by  angle  irons  A  A. 
The  movement  of  the  plug  vertically  is  controlled  by  radius  bars  working  in 
30 


450 


ENGINEERING  DRAWING. 


FIG.  1060. 


ENGINEERING  DRAWING. 


451 


centres  on  the  back  wall ;  they  are  made  of  channel  bars,  each  set  braced  hori- 
zontally. The  plug  is  raised  by  a  differential  pulley-block  suspended  at  C  from 
a  wooden  beam  across  the  water.  The  hoist  chain  is  carried  by  a  yoke  to  the 
two  radii  bars  at  B ;  when  eased,  the  plug  drops  readily  to  its  seat.  The  level 
of  the  canal  is  about  35  feet  above  that  of  the  river,  and  the  discharge  is  so 
large  that  it  produces  a  scour  in  the  canal.  When  the  level  of  the  canal  rises 
above  the  crest  of  the  tube  it  forms  an  overfall ;  a  depth  of  a  little  over  2  feet 
will  take  the  whole  capacity  of  the  tube. 

Figs.  1061  and  1062  are  the  front  elevation  and  section  of  the  gates  of  Farm 
Pond,  Sudbury  River  Conduit,  Boston  Water- Works.     The  main  web  or  plate 


FIG.  1061. 


Flo.  1062. 


of  the  gate  is  1£"  thick,  the  ribs  6"  deep,  the  gate-stems  2£"  diameter.  The 
nuts  by  which  the  gates  are  raised  are  geared  together,  and  actuated  by  a 
double  crank.  The  gates  and  guides  are  faced  with  brass,  about  -fo"  thick. 

Similar  gates  are  very  common,  plates  of  cast-iron  strengthened  by  ribs ; 
the  guides  are  also  of  cast-iron,  bolted  to  the  masonry,  with  faces  of  the  gates 
and  guides  usually  of  brass  plates,  as  iron  faces  become  rusty  and  stick. 

Canals. — The  sections  of  canals  depend  upon  the  purposes  to  which  they 
are  to  be  applied,  whether  for  navigation  or  for  power ;  if  for  navigation,  ref- 


452 


ENGINEERING  DRAWING. 


erence  must  be  had  to  the  class  of  boa£s  for  which  they  are  intended ;  if  for 
power,  to  the  quantity  of  water  to  be  supplied,  and  sundry  precautions  of  con- 
struction. 

Fig.  1063  is  a  section  of  the  Erie  Canal:  width  at  water-line,  70  feet;  at 
bottom,  28  feet;  depth  of  water,  7  feet;  width  of  tow-path,  14  feet.     The 


FIG.  1063. 


slopes  are  gravelled  and  paved,  the  edge  of  the  tow-path  is  paved  with  cobble- 
paving,  and  the  path  gravelled.  The  smaller  canals  of  this  State  and  of  Penn- 
sylvania are  generally  40  feet  wide  at  water-line,  and  4  feet  deep  ;  the  Delaware 
and  Earitan,  75'  x  7' ;  the  Chesapeake  and  Delaware,  66'  x  10' ;  the  ship-canals 
of  Canada,  10  feet  deep  and  from  70  to  190  feet  wide. 

The  dimensions  for  canals  for  the  supply  of  mills  depend — first,  on  the 
quantity  of  water  to  be  delivered.  Their  area  of  cross-section  should  be  such 
that  the  average  velocity  of  flow  should  not  exceed  two  to  three  feet  per  second, 
and  in  northern  climates  less  velocity  than  this  would  be  still  better ;  it  should 
always  be  such  that  during  the  winter  the  canals  may  be  frozen  over;  and  re- 


FJG.  1064. 

main  so,  to  prevent  the  obstruction  from  drift  and  anchor-ice  in  the  water- 
wheels.  The  usual  depths  of  the  larger  canals  are  from  10  to  15  feet ;  with 
such  depths  the  cover  of  ice  which  reduces  the  section  by  the  amount  of  its 
thickness  does  not  materially  decrease  the  velocity  of  flow,  nor  diminish  very 
perceptibly  the  available  head. 

Fig.  1064  is  a  section  of  the  Northern  Canal,  at  Lowell,  Mass.,  which  may 
be  considered  a  model  for  large  works.  The  width  at  water-line  is  103  feet 
and  the  depth  16',  and  is  intended  for  an  average  flow  of  2,700  cubic  feet  per 
second.  The  fall  in  the  whole  length  of  4,300  feet  is  between  2"  and  3" ;  when 
covered  by  ice,  about  4".  The  sides  are  walled  in  dry  rubble,  and  coped  by 
split  granite.  The  portion  above,  and  about  three  feet  below,  the  water-line,  or 
between  the  limits  of  extreme  fluctuations  of  level,  is  laid  plumb,  that  the  ice 
may  have  as  free  a  movement  as  possible  vertically. 

Fig.  1065  is  a  section,  on  a  scale  of  -J"  =  1  foot,  of  the  river-wall  of  this 
same  canal,  where  the  canal  passes  out  into  and  occupies  a  portion  of  the  river 
channel.  The  main  wall  is  in  dry  masonry,  faced  on  river-side  with  rough- 
faced  ashlar,  pointed  beds  and  end-joints.  The  inside  lining  is  of  two  courses 
of  cement-wall,  to  the  dry  rubble  wall  pointed  with  cement,  against  which  is 


ENGINEERING  DRAWING. 


453 


laid  the  first  cement  lining,  plastered  on  the  inside,  and  the  interior  wall  is 
then  laid ;  the  granite  inside  wall,  above  lining,  is  laid  in  cement. 


FIG.  1065. 


Locks  of  CanaU, — Figs.  1066  and  1067  are  portions  of  plan  and  vertical 
section  of  locks,  taken  from  the  general  plans  for  timber  locks  on  the  Chemung 
Canal.  They  represent  the  half  of  upper  gates.  Fig.  1068  is  a  section  of  one 
side  of  the  lock  of  the  same.  Fig.  1069  is  the  plan  of  a  portion  of  one  of  the 


FIG.  1066. 


enlarged  locks  of  the  Erie  Canal,  showing  one  of  the  upper  gates  and  the  side- 
walls.     Fig.  1070  is  a  cross-section  of  one  of  the  same  locks,  showing  the  cul- 


454: 


ENGINEERING  DRAWING. 


vert  in  the  centre  between  the  locks,  used  for  the  supply  of  the  waste  of  the 
lower  level.  The  proper  height  of  water  in  this  level  is  controlled  by  gates  in 
the  upper  level. 


FIG.  1067. 


FIG.  1068. 


SCALE  :  -f,"  -  1  foot. 


FIG.  1069. 


ENGINEERING  DRAWING. 


455 


Fig.  1071  is  a  drawing,  in  outline,  of  the  hollow  quoin  of  the  lock-gate,  on 
a  scale  of  ^  full  size  (Chemung  Canal). 


FIQ.  loro. 


SCALE  :  TV  =  1  foot. 


Fig.  1072  is  a  plan  and  elevation  of  pintal  for  heel-post  of  lock,  with  a  sec- 
tion of  the  bottom  of  the  post.  The  pintal  is  imbedded  in  bottom  timber  or 
stone,  as  the  case  may  be. 


FIG.  1071. 


A  full  size. 


FIQ.  1072. 


Fig.  1073  is  a  plan  and  elevation  of  the  strap  for  the  upper  part  of  heel-post. 
Extracts  from  lock  specifications  ("  New  York  State  Canals,"  1854)  : 

"  Locks  to  be  composed  of  hydraulic  stone  masonry,  placed  on  a  foundation  of  tim- 
ber and  plank.  The  chamber  to  be  18'  wide  at  the  surface  of  the  water  in  the  lower 
level,  and  110' long  between  the  upper 
and  lower  gate-quoins.  The  side-walls 
to  extend  21'  above  the  upper  gate- 
quoins,  and  14'  below  lower  gate- 
quoins.  If  the  bottom  is  of  earth, 
and  not  sufficient  to  support  the  foun- 
dation, then  bearing-piles  of  hard 
wood,  not  less  than  10"  diameter  at 
small  end,  shall  be  driven.  The  foun- 
dation timbers  to  be  12"  x  12",  and  of 
such  lengths  as  will  extend  from  and 
cover  the  outside  piles,  and  to  be  tree- 
nailed  with  a  2"  white-oak  or  white- 
elm  treenail,  24"  long,  to  each  pile.  FIG.  1073. 


456  ENGINEERING  DRAWING. 

"If  without  bearing-piles,  the  foundation  to  be  composed  of  timber,  12"  thick  and 
not  less  than  10"  wide,  counterhewed  on  upper  side,  placed  at  uniform  distance,  accord- 
ing to  their  width,  to  occupy  or  cover  at  least  £  of  the  area  of  the  foundation,  and 
under  the  lower  mitre-sill  to  be  placed  side  by  side  :  in  all  cases  to  be  of  sufficient 
length  to  extend  across  the  lock  to  the  back  line  of  the  centre  buttresses,  and  at  the 
head  and  foot  to  the  rear  or  back  line  of  wing-walls.  The  timber  under  the  lower 
mitre-sill  to  be  of  white  oak,  white  elm,  or  red  beech,  the  other  foundation  and  apron 
timber  to  be  of  hemlock.  The  foundation  to  be  extended  3'  above  the  face  of  the  main 
wall  at  the  head  of  the  lock,  and  at  the  foot  from  25'  to  30'  below  the  exterior  wing — 
that  portion  of  the  spaces  between  the  timbers  in  all  cases  to  be  filled  with  clean  coarse 
gravel,  well  rammed  in,  or  concrete.  Where  rock  composes  the  bottom  of  the  lock,  and 
is  of  such  a  character  that  timber  is  not  required  for  the  foundation,  the  same  shall  be 
excavated  smooth  and  level,  and  the  first  course  of  stone  well  fitted  to  the  rock. 

"  Sheet-Piling. — In  all  cases  where  rock  does  not  occur,  there  shall  be  a  course  at  the 
head  of  the  foundation,  under  each  mitre-sill,  and  at  the  lower  end  of  the  wings,  and  at 
the  lower  end  of  the  apron,  to  be  from  4'  to  6'  deep  as  may  be  required — in  each  to  ex- 
tend across  the  whole  foundation. 

"Flooring. — A  course  of  2^"  pine  or  hemlock  plank  to  be  laid  over  the  whole  of  the 
foundation  timbers,  except  a  space,  3'  wide,  under  the  face-line  of  each  wall  to  be  2£" 
white  oak;  the  whole  to  be  well  jointed,  and  every  plank  to  be  treenailed  with  two 
white-oak  treenails  at  each  end,  and  at  every  3'  in  length,  to  enter  the  timber  at  least  5", 
or  with  wrought-iron  spikes,  treenails  to  fill  1£"  bore.  Platform  for  the  upper  mitre-sill 
to  be  5'  10"  wide,  and  6'  high  above  foundation,  and  to  extend  across  from  side-wall  to 
side-wall,  to  be  composed  of  masonry,  coped  with  white-oak  timbers,  extending  6"  into 
each  side-wall.  Mitre-sills  to  be  of  best  white-oak  timber,  9"  thick,  to  be  well  jointed, 
and  bolted  to  the  foundation  or  platform  timbers  with  bolts  20"  long,  1"  x  1",  well 
ragged  and  headed. 

"Masonry. — The  main  walls,  for  21'  6"  in  length,  from  wing-buttresses  at  the  head, 
and  32'  at  lower  end,  to  be  9'  8£"  thick,  including  recesses,  and  for  the  intermediate 
space,  7'  8J"  thick,  with  three  buttresses  projecting  back  2£',  and  9'  long  at  equal  dis- 
tances apart.  The  quoin-stones,  in  which  the  heel-post  is  to  turn,  shall  not  be  less  than 
5'  6"  in  length  in  line  of  the  chamber,  to  be  alternately  header  and  stretcher.  The 
recesses  for  the  gates  to  be  20"  wide  at  top  of  wall,  12'  long,  with  sub-recesses,  9"  wide, 
6'  high,  10'  long,  for  the  valve-gates. 

"  Culvert  between  Locks. — The  sluice-way  shall  be  made  in  the  head- wall  with  cut- 
stone  jambs,  grooves  to  be  cut  in  the  jambs  for  the  sluice-gates,  the  bottom  of  the  aper- 
ture to  be  of  cut  stone,  with  lower  corner  beveled  off,  over  which  the  water  will  fall  into 
the  well,  the  bottom  of  which  shall  be  covered  with  a  sheeting  of  cut  stone,  6"  thick. 

"  Second  flooring  of  seasoned  2"  first-quality  white-pine  plank,  to  be  well  jointed,  and 
laid  on  the  foundation  between  the  walls,  from  the  breast-wall  to  lower  end  of  main  wall, 
and  also  on  the  floor  of  the  wall. 

"  Gates. — The  framing  to  be  made  of  best  quality  white-oak  timber;  the  cross-bar  to 
be  framed  into  heel  and  toe  posts  with  double  tenons,  each  tenon  to  be  7"  long,  and  se- 
cured with  wrought-iron  Ts,  well  bolted.  The  heel  and  toe  posts  to  be  framed  to  the 
balance-beam  by  double  tenons,  and  secured  by  a  wrought-iron  strap  and  balance-rod, 
from  the  top  of  the  beam  to  the  under  side  of  the  upper  bar.  The  lower  end  of  the 
heel-posts  to  be  banded  with  wrought-iron  bars ;  the  collar  and  other  hangings  to  be  of 
wrought-iron,  secured  together  with  a  double  nut  and  screw,  and  to  the  coping  by  bed- 
ding the  depth  of  the  iron  in,  and  by  screw-bolts  fastened  with  sulphur  and  sand-cement. 
The  pivots  and  sockets  which  support  the  heel -posts  to  be  of  best  cast-iron;  a  chilled 
cast-iron  elliptical  ball,  2i"  horizontal,  and  1"  vertical  diameter,  to  be  placed  on  the 
pivot  and  in  the  socket  of  each  heel-post,  gates  planked  with  seasoned  2"  white-pine 
plank,  jointed,  grooved,  and  tongued — tongues  of  white  oak." 


ENGINEERING  DRAWING. 


457 


Water,  ponded  by  dams,  and  conveyed  by  canals  for  use  as  mill-power,  is 
carried  within  the  workshops  or  manufactories,  to  be  applied  on  water-wheels, 
by  some  form  of  covered  channels  usually  designated  as  flumes.  The  common 
form  of  a  flume  for  the  conveyance  of  water  to  breast,  overshot,  or  undershot 
wheels,  is  of  a  rectangular  section,  framed  with  sills,  side-posts,  and  cap,  and, 
if  a  large  section  is  required,  with  intermediate  posts.  The  sills  are  set,  and 
earth  well  rammed  in  the  spaces  between  them  ;  the  bottom  plank  is  then  laid, 
posts  and  cap  framed  with  tenon  and  mortice,  set  and  pinned,  and  the  plank  is 
then  firmly  spiked  on  the  outside  of  posts  and  caps.  The  planks  are  usual- 
ly partially  seasoned  and 
brought  to  close  joints; 
the  size  of  timbers  will 
depend  on  the  depth  be- 
neath the  soil,  or  the  in- 
sistent load.  Within  the 
mill,  and  just  above  the 
wheel,  the  flume  is  framed 
without  a  cover,  and  the 
posts  and  side-planks  are 


brought  above  the  level  of 


FIG.  1074. 


the     water.       This     open 

flume  is  termed  the  penstock,  especially  necessary,  in  the  class  of  wheel  above 

referred  to,  to  secure  the  full  head  of  water. 

For  the  conveyance  of  water  to  turbine-wheels,  wrought-iron  pipes  are 
almost  invariably  used.  Cast-iron  is  also  sometimes  used,  with  flange,  or  hub 
and  spigot-joints.  Plank-pipes  (Fig.  1074)  are  also  used,  made  with  continu- 
ous staves,  and  hooped  with  wrought-iron;  these  constructions  are  much 
cheaper,  and  serve  a  very  good  purpose.  The  head-gates  of  flumes  are  placed 
at  the  head  of  the  flumes,  in  a  recess  back  from  the  face  of  the  canal,  with 
racks  in  front  to  prevent  the  passage  of  any  drift  that  might  obstruct  or  injure 
the  wheel.  The  total  area  of  passages  through  the  racks  should  liberally  exceed 

the  area  of  cross-section  of  the  flume,  not 
only  on  account  of  the  extra  lateral  fric- 
tion of  the  rack-bars,  but  also  on  account 
of  their  liability  to  become  obstructed. 
Sometimes  two  sets  of  racks  are  placed 
in  front  of  the  flumes,  especially  for 
turbines  and  reacting  wheels :  a  coarse 
rack  outside,  with  wide  spaces,  say  2" 
and  a  finer  one  inside,  say  of  f"  to  f" 
spaces. 

Conduits  for  the  supply  of  water  to 
cities  and  towns  are  of  masonry,  or  cast- 
or wrought-iron  pipes.  Their  capacity  to 
deliver  the  required  quantity  depends  upon 
the  area  and  form  of  cross-section,  and 

the  velocity  of  flow  due  to  the  loss  of  head  or  of  pressure  permissible ;  this 
velocity  being  due  primarily  to  gravity,  but  largely  modified  by  conditions  of 


FIG.  1075. 


458 


ENGINEERING  DRAWING. 


structure,  as  the  kind  and  amount  of  wetted  surface,  and  length  and  directness 
of  line. 

Fig.  1075  is  a  cross-section  of  the  main  conduit  of  the  Nassau  Water-Works 
for  the  supply  of  the  city  of  Brooklyn,  Long  Island.  The  width  is  10'  at  the 
springing  of  the  arch;  the  side- walls  3  feet  in  height;  versed  sine. of  invert, 
8"  ;  height  of  conduit  in  centre,  8'  8" ;  fall  or  inclination  of  bottom,  1  in 
10,000. 

The  foundations  to  be  of  concrete,  15'  wide,  on  earth,  or,  if  the  water  was  trouble- 
some, on  a  platform  of  plank.  The  side-walls  of  stone,  with  an  interior  lining  of  4'' 
brick;  arch  brick,  12",  and  the  invert  4"  thick.  The  outside  of  arch,  and  each  wall, 
were  plastered  over  on  the  outside  with  a  thick  coat  of  cement  mortar.  In  both  cuttings 
and  embankments  the  arch  was  covered  with  4'  of  earth,  with  a  width  of  8'  at  top, 
and  slopes  on  each  side  of  1£  to  1,  covered  with  soil  and  seeded  with  grass. 

Fig.  1076  is  a  section  of  the  conduit  of  the  Boston  Water- Works.  The 
inside  section  is  equal  to  a  circle  8£  feet  diameter,  and  is  uniform  throughout 
except  in  tunnels.  The  section  given  is  the  general  one,  resting  on  concrete, 
brick  lining  at  sides  and  invert  at  bottom,  with  an  8"  arch  at  top  for  a  4'  cover, 
and  12"  for  exceptional  depths  or  under  railway-tracks.  The  lower  corners 
were  of  special  brick. 

The  inclination  of  the  conduit  is  1  foot  per  mile,  and  the  flow  80,000,000 
gallons  per  24  hours  when  full,  or  5  feet  above  centre  of  invert.    The  maximum 
flow  takes  place  when   the  depth  of 
water  is  7'  2",  the  delivery  then  being 
109,000,000  gallons. 

Fig.  1077  represents  a  section  of 


FIQ.  1076. 


FIG.  1077. 


the  old  Croton  Aqueduct,  in  an  open  rock-cut.  The  width  at  spring  of  arch, 
7' ;  versed  sine  of  invert,  6" ;  height  of  conduit,  8'  6" ;  fall  or  inclination  of 
bottom,  about  1  in  5,000. 

Fig.  1078  is  a  two  half  section  of  the  new  Croton  Aqueduct,  of  which  one 
is  in  earth  and  rock,  and  the  other  entirely  in  rock.  The  foundation  is  in  con- 
crete, the  lining  and  arches  in  brick.  At  the  junction  of  the  invert  and  side 
linings  there  is  a  special  angle  block  in  brick ;  exterior  of  brickwork  is  plastered. 

Before  the  construction  of  High  Bridge  water  was  conveyed  for  the  supply 
of  the  city  through  siphon  pipes  beneath  the  Harlem  Kiver,  afterward  through 
two  3'  cast-iron  pipes  in  the  masonry  of  the  bridge.  As  the  demand  for  water 
increased  in  the  city,  the  obstruction  caused  by  lack  of  capacity  in  these  pipes 
made  the  introduction  of  a  larger  pipe  necessary  (Fig.  1079),  which  has  been 


ENGINEERING   DRAWING. 


459 


made  of  wrought-iron,  fa"  thick  and  7'  Qfa"  in  diameter,  supported  by  cast- 
iron  columns  which  admit  of  a  rocking  movement,  and  slip-joints  in  the 
pipe  to  compensate  for  any  ex- 
pansion or  contraction.  The 
pipes  are  inclosed  in  a  long  cham- 
ber, extending  the  whole  length 
of  the  bridge,  covered  by  a  brick 
arch,  laid  in  cement  with  a  cover 
of  asphalt,  and  a  brick  pavement 
over  all.  A  A  are  the  arch-stones 
of  the  bridge. 

In  large  works,  where  there 
is  considerable  length  of  conduit, 
receiving  reservoirs,  within  or 
near  the  limits  of  the  city,  are 
necessary  as  a  precaution  to  guard 
against  accidents  which  might 

happen  to  conduit  or  dam,  and  cut  off  the  supply,  and  also  as  a  sort  of  balance 
against  unequal  or  intermittent  draught  among  the  consumers.  The  size  of 
these  reservoirs  must  depend  on  the  necessities  of  the  case,  and  on  the  facilities 


Fia.  1079. 

for  construction.  At  Eidgewood,  Brooklyn,  there  are  three  reservoirs  in  con- 
nection, of  total  capacity  of  about  325,000,000  gallons.  The  capacity  of  the 
upper  Croton  reservoir  in  Central  Park,  New  York,  in  two  compartments,  is 
about  1,000,000,000  gallons. 

Fig.  1080  is  a  section  of  the  division-bank  of  the  Croton  reservoir,  made  of 
earth,  with  a  puddled  ditch  in  the  centre. 


460 


ENGINEERING  DRAWING. 


Extracts  from  the  specification  : 

"All  the  banks  will  have  the  inner  and  outer  slopes  of  1£  base  to  1  perpendicular. 
All  the  inner  or  water-slopes  will  be  covered  with  8"  of  broken  stone,  on  which  will  be 
placed  the  stone  pavement,  1J  foot  thick.  The  outer  slopes  will  be  covered  with  soil  1" 


FIG.  1080. 

foot  thick.  The  banks,  when  finished,  to  be  15  feet  on  top,  exclusive  of  the  soil  on  the 
outer  slope.  The  top  of  the  outer  bank  to  be  4  feet  above  water-line ;  the  top  of  the 
division-bank  to  be  3  feet  below  water-line.  In  the  centre  of  all  the  banks  a  puddle- 
bank  will  be  built,  extending  from  the  rock  to  within  2  feet  of  the  top  of  the  outer  bank. 
It  will  be  6'  2"  wide  at  top  in  division-bank,  and  14'  wide  at  top  in  exterior  bank,  and 
16'  wide  at  a  plane  38'  feet  below  top  of  exterior  bank.  In  the  middle  of  the  division- 
bank  there  will  be  built  a  concrete  wall  4'  high,  20"  wide ;  8"  thickness  of  concrete  to  be 
laid  on  the  top  of  the  bank,  on  each  side  of,  and  connected  with,  this  wall.  On  the 
pavement  18"  thick  will  be  laid  in  concrete.  The  slope-wall  on  each  side  of  the  division- 
bank,  10'  in  width,  to  be  laid  in  cement. 

"Puddle-ditches  are  to  be  excavated  to  the  rock  under  the  centre  of  all  embank- 
ments. The  earth  within  the  working-lines  of  interior  slopes  to  be  excavated  to  the 
depth  of  40'  below  top  of  exterior  bank,  rock  36'.  The  puddle-ditch  to  be  formed  of 
clay,  gravel,  sand,  or  earth,  or  such  admixture  of  these  materials,  or  any  of  them,  as  the 
engineer  may  direct,  to  be  laid  in  layers  of  not  more  than  6",  well  mixed  with  water, 
and  worked  with  spades  by  cutting  through  vertically,  in  two  courses  at  right  angles 
with  each  other;  the  courses  to  be  1"  apart,  and  each  spading  to  extend  2"  into  the 
lower  course  or  bed.  The  puddle  to  extend  to  all  the  masonry  and  pipes,  as  the  engineer 
may  direct. 

"The  embankments  to  be  formed  in  layers  of  not  more  than  6",  well  packed  by  cart- 
ing and  rolling,  and,  where  rollers  can  not  be  effectually  used,  by  ramming.  The  em 
bankments  to  be  worked  to  their  full  width  as  they  rise  in  height,  and  not  more  than  2' 
in  advance  of  the  puddle.  The  interior  slopes  of  all  the  banks  to  be  covered  with  8" 
thickness  of  stone,  broken  to  pass  through  a  2"  ring.  On  this  to  be  laid  the  paving,  18" 
in  thickness,  of  a  single  course  of  stones  set  on  edge  at  right  angles  with  the  slope,  laid 
dry,  and  well  wedged  with  pinners." 

Fig.  1081  is  a  drawing  of  a  sheet-iron  water  pipe  as  used  in  the  States  of  the 
Pacific  slope.  The  bottom  joint  is  a  slip-joint  of  the  stove-pipe  iron  order, 
which  Mr.  Hamilton  Smith  considers  good  for  pressures  not  exceeding  380 
feet.  For  pressures  greater  than  this,  the  lead  joint,  as  shown  in  Fig.  1082 
in  section,  should  be  used ;  it  consists  of  an  inner  sleeve  riveted  to  the  inside 


ENGINEERING  DRAWING. 


461 


of  one  pipe  and  an  outer  sleeve  covering  the  joint  with  a  f "  space,  into  which 
lead  is  run  and  calked  as  for  cast-iron  pipes  (see  page  463). 


FIG.  1081. 


The  pipe  as  drawn  is  on  an  incline  and  is  anchored  by  a  wire  cable.  Un- 
der heavy  heads  and  on  inclines  the  pipes  should  be  wired  together,  and  at 
angles  lead  joints  should  be  used. 

The  pipes  are  invariably  coated  with  asphalt,  inside  and  out,  by  immersing 
them  for  some  minutes  in  the  hot  liquid.  The  pipes  are  double  riveted,  and 
the  thickness  of  the  iron  very  much  less  than  used  here ;  the  Cherokee  pipe,  30 
inches  diameter  up  to  203  feet  head,  is  No.  14,  or  -083"  thick ;  head  900  feet, 
|"  thick. 

At  first  slip-joints  were  made  for  expansion,  but  were  found  unnecessary. 
Time  has  shown  no  practical  depreciation  in  the  pipes. 

For  conduits  of  large  size,  and  under  extreme  pressure,  wrought-iron  or 
steel  may  be  considered  the  rule  in  the  United  States ;  they  are  more  econom- 
ical in  cost  and  safer  than  masonry,  less  disturbance  from  settlement,  practi- 
cally without  leak,  and  admitting  of  prompt  and  easy  connections  and  repairs. 

In  construction  pipes  are  made  up  at  shops  and  riveted  like  boilers,  and  are 
put  together  in  such  lengths  as  can  be  readily  transported  and  laid.  Welded 
longitudinal  joints  on  the  separate  lengths  can  be  obtained  without  much  in- 
crease in  cost,  and  flanges  may  be  turned  on  them  for  bolting  or  riveting. 

For  water  supplies  to  locomotives  on  our  railroads,  the  usual  tanks  are 
wooden  cisterns  strongly  hooped  and  resting  on  timber  frames.  Fig.  1083  is  a 
tank  of  wrought-iron  on  the  Orleans  Railway,  containing  22,000  gallons,  and 
applicable  to  small  services  of  towns  and  villages.  The  inverted-dome  bottom 
has  no  supports  except  at  the  circumference,  where  there  is  a  strong  iron  plate 
with  extra  angle  irons,  as  shown  in  detail.  The  pipes  pass  through  the  bottom, 
but  give  it  no  support.  This  form  has  been  applied  at  the  Liverpool  water- 
works in  the  Norton  Tower,  where  the  tank  is  82  feet  in  diameter  and  contains 
651,000  gallons. 


4:62 


ENGINEERING  DRAWING. 


Water-works  for  small  towns  often  draw  their  supply  from  driven  wells, 
and  for  this  service  stand-pipes  or  tanks  of  iron  are  preferable  to  reservoirs  in 
earth  ;  but  waters  from  these  sources  are  usually  deficient  in  oxygen,  and  con- 
fervae  develop  rapidly  in  open  reservoirs  exposed  to  the  light  and  air.  They 
must  therefore  be  of  small  dimensions,  so  that  there  be  no  stagnation ;  the 
water  must  circulate  and  be  changed  often.  These  inconveniences,  together 


Fie.  1083. 

with  warmth  in  such  metallic  tanks  in  summer  weather,  has  led  to  the  making 
of  tight  tanks  as  in  the  elevator  service,  under  a  pressure  of  about  100  pounds 
to  the  square  inch  and  earth  covered. 

Distribution. — Figs.  1084  to  1088  are  sections  of  the  spigot  and  faucet  ends 
of  cast-iron  water-mains  as  used  in  Brooklyn  and  Philadelphia. 

Below  is  given  a  table  of  dimensions,  thickness,  etc.,  of  pipes,  which  may 
be  considered  fair  averages  for  water-mains  ;  4"  pipe  is  the  smallest  diameter 
to  be  used  in  distribution,  and  if  a  hydrant  is  placed  at  the  extremity  of  500 
feet  of  such  pipe,  the  head  will  be  very  much  reduced  in  case  of  fire  service. 


ENGINEERING  DRAWING. 


463 


In  cities  the  minimum  diameter  is  usually  6",  except  in  the  4"  connection  of 
dead  ends  for  circulation.     The  thicknesses  given  in  the  table  are  as  low  as  ad- 


FIG.  1084. 


FIG.  1085. 


FIG.  1086. 


FIG.  1087. 


missible  for  tapping,  and  if  the  pipe  is  not  of  uniform  thickness,  is  to  be  put 
the  thickest  side  up  for  this  purpose. 

The  diameters  given  in  the  table  are  such  as  can 
be  found  in  stock,  but  other  sizes  will  be  made  to 


FIG.  1088. 


Diameter. 

Thick- 
ness. 

Weight  per 
foot  laid. 

Lead-joint 
weight. 

Safe,  feet 
head. 

4 

0-42 

19-7 

4 

1,609 

6 

0-47 

32-6 

7 

1,200 

8 

0-47 

42-4 

10 

900 

12 

0-61 

82-2 

16 

800 

16 

0-67 

119-7 

23 

680 

20 

0-75 

164-7 

31 

600 

24 

0-80 

210-3 

40 

520 

30 

0-98 

320-0 

57 

520 

36 

1-15 

450-0 

75 

500 

48 

1-44 

757-0 

120 

480 

order ;  if  ordered  of  extra  thickness  the  bore  is  preserved  uniformly,  and  the 
extra  metal  is  put  on  the  outside. 

After  laying,  a  hemp  gasket  is  forced  down  to  the  lower  end  of  the  bell  to 
prevent  the  molten  lead  from  escaping  into  the  pipe  ;  the  end  of  the  pipe  is 
then  stopped  by  a  clay  roll,  or  a  rope  covered  with  clay,  or  clay  alone,  or  with 
a  metal  clamp  containing  clay,  and  the  molten  lead  is  then  poured  in  through 
an  aperture  or  gate  at  the  top  ;  after  cooling,  the  joint  is  made  secure  and  tight 
by  compacting  the  lead  with  calking  tools  made  for  this  purpose. 

Wrought-iron  pipes  have  also  been  used  for  distribution,  generally  with 
cast-iron  bells,  riveted  at  one  end  and  a  small  ring  on  the  other  (Fig.  1089)  or 
by  flanges  secured  on  both  ends  and  bolted  together  when  laid. 

Specials. — All  parts  of  a  main  except  the  straight  pipes  are  called  special 
castings. 

Fig.  1090  is  a  12"  X  8"  4- way  branch,  shown  full  and  in  section,  diagonally. 


464 


ENGINEERING  DRAWING. 


The  horns  on  the  branch  are  for  straps  to  hold  in  a  plug,  cap,  or  a  connected 
short  or  curved  pipe.     The  4- way  branches  are  often  called  crosses,  and  the 


FIG.  1091. 


FTG.  1090. 


FIG.  1092. 


3-way  T's,  or  single  branches.  The  branches  may  be 
of  any  appropriate  size.  In  ordering,  designate'diam- 
eter  of  main  pipe  first,  and  then  that  of  the  branches. 
It  is  very  common  in  these  pipes  to  make  all  of  the 
ends  bell  ends — it  saves  sleeves  when  pipes  are  cut,  as 
they  usually  are  at  street  intersections. 

Fig.  1091  is  a  section  of  a  sleeve  for  uniting  cut 
pipes  or  uncut  spigot-ends ;  a  kind  of  double  hub  is 
often  used  for  the  former.  Sometimes  sleeves  are 
made  in  halves,  and  bolted  together. 

Fig.  1092  is  the  section  of  a  reducer  for  the  con- 
nection of  pipes  of  unequal  diameters. 

Fig.  1093  is  the  section  of  a  bend ;  the  horns  on 
the  outer  circle  are  for  straps  between  the  pipes,  as 
the  pressure  is  unbalanced. 


FIG.  1093. 


ENGINEERING  DRAWING. 


465 


House-services  are  mostly  lead  pipes ;  the  taps  on  the  mains  for  house-con- 
nections in  New  York  city  are  usually  1". 

Fig.  1094  is  a  clamp  sleeve. 
Figs.  1095  and  1096  are  globe  specials 
of  the  Builders'  Iron  Foundry,  Providence, 


FIG.  1094. 


FIG.  1095. 


FIG.  1096. 


a  T  and  a  cross  branch,  which  serve  the  purpose  of  Fig.  1090  and  are  much 
lighter,  and  Figs.  1097  to  1102  are  specials  of  the  same  makers. 


FIG.  1098. 


FIG.  1097. 


FIG.  1099. 


FIG.  1100. 


FIG.  1101. 


FIG.  1102. 


According  to  the  specifications  of  "  Cast-Iron  Distribution- Pipes  and  Pipe- 
Mains,  with  their  Branches,"  etc.,  Brooklyn,  L.  I.  : 

Every  pipe-branch  and  casting  to  pass  a  careful  hammer-inspection,  to  be  subject 
thereafter  to  a  proof  by  water-pressure,  and  while  under  the  required  pressure  to  be 
rapped  with  a  hand-hammer  from  end  to  end,  to  discover  whether  any  defects  have  been 
overlooked.  The  pipes  were  to  be  carefully  coated  inside  and  outside  with  coal-pitch 
and  oil,  according  to  Dr.  R.  A.  Smith's  process,  as  follows : 
31 


466  ENGINEERING  DRAWING. 

"Every  pipe  must  be  thoroughly  dressed  and  made  clean  from  sand  and  free  from 
rust.  If  the  pipe  can  not  be  dipped  promptly,  the  surface  must  be  oiled  with  linseed-oil 
to  preserve  it  until  it  is  ready  to  be  dipped ;  no  pipe  to  be  dipped  after  rust  has  set  in. 
The  coal-tar  pitch  is  made  from  coal-tar,  distilled  until  the  naphtha  is  entirely  removed 
and  the  material  deodorized.  The  mixture  of  5  or  6  per  cent  of  linseed-oil  is  recom- 
mended by  Dr.  Smith.  Pitch,  which  becomes  hard  and  brittle  when  cold,  will  not  an- 
swer. The  pitch  must  be  heated  to  300°  Fahr.,  and  maintained  at  this  temperature 
during  the  time  of  dipping.  Every  pipe  to  attain  this  temperature  before  being  removed 
from  the  vessel  of  hot  pitch.  It  may  then  be  slowly  removed  and  laid  upon  skids  to 
drip." 

Seivers. — For  the  removal  of  waste  water  from  houses  and  rainfall,  sewers 
are  very  convenient  in  towns  and  cities,  even  before  the  construction  of  water- 
works ;  but,  after  the  introduction  of  a  liberal  and  regular  supply  of  water, 
sewers  are  indispensable.  The  ruling  principle  in  the  establishment  of  sewer- 
age-works is,  that  each  day's  sewage  of  each  street  and  of  each  dwelling  should 
be  removed  from  the  limits  of  city  and  town  promptly  before  decomposition 
begins,  and  that  it  should  not  be  allowed  to  stagnate  in  the  sewers,  producing 
noxious  gases  prejudicial  to  health.  To  attain  this  end,  the  refuse  fluids  must 
be  sufficient  in  quantity  to  float  and  carry  off  the  heavier  matters  of  sewage. 

There  has  been  considerable  discussion  of  late  whether  sewage  and  rainfall 
should  be  carried  off  by  a  single  system  of  pipes.  This  must  depend  largely  on 
the  location,  economy  of  construction,  and  the  financial  ability  to  carry  out 
the  design.  If  the  rainfall  can  be  provided  for  by  street  gutters,  the  sewers  may 
be  for  the  conveyance  of  house- waste  only  and  very  small.  If  the  sewage  is  to 
be  discharged  into  a  river  of  so  large  a  flow  that  practically  it  will  not  pollute 
it,  or  into  large  bodies  of  water  not  used  for  domestic  purposes,  it  is  cheaper 
and  better  to  discharge  rainfall  and  sewage  by  one  channel.  The  dimensions 
of  the  sewer  will  depend  on  the  quantity  to  be  discharged  and  the  grade  for 
which  graphic  sheets  will  be  found  in  the  Appendix.  The  rainfall  is  here 
estimated  at  1"  in  depth  per  hour  for  the  whole  area  drained,  but  this  is  in 
many  places  exceeded  for  excessive  rainfalls,  and  it  is  well  at  such  times  to 
have  a  partial  relief  by  the  street  gutters.  For  the  sewage  flow  it  is  usual  to 
calculate  it  from  the  water  that  is  or  may  be  furnished  on  any  length,  and 
that  the  maximum  that  may  be  delivered  at  any  one  time  is  50  per  cent  greater 
than  the  average  flow,  and  further  that  at  that  time  the  sewer  should  be  one 
half  full. 

The  value  of  sewers  depends  on  the  correctness  of  their  lines,  uniformity  of 
descent,  and  smoothness  of  interior  surface. 

For  Washington,  Brooklyn,  and  New  York,  and  many  other  large  cities 
discharging  into  large  rivers,  there  is  but  one  system  of  sewers  for  rainfall  and 
sewage,  and  for  the  great  areas  drained  very  large  sewers  are  necessarily  con- 
structed. Fig.  1103  is  a  section  of  a  Washington  sewer,  the  largest  in  the 
United  States.  The  bottom  course  of  the  sewer,  which  is  exposed  to  a  strong 
current,  is  of  stone ;  the  ring  courses  are  of  brick — three  for  the  13-foot  sewers 
and  two  for  the  7-foot. 

Fig.  1104  is  a  section  of  the  largest  Brooklyn  sewer.  In  general  there  is  no 
base  or  side  supports  of  concrete  or  wall,  except  where  the  bottom  is  of  quick- 
sand. The  sewer  at  the  upper  end  is  of  circular  section  10'  diameter,  brick- 


ENGINEERING   DRAWING. 


467 


work  12" ;  next  size  12',  then  14',  und  15'— all  brickwork  16".  At  the  dis- 
charge into  Gowamis  Creek  the  section  is  nearly  rectangular  with  top  of  iron 
beams  and  brick  arches,  brick  side-walls,  and  inverts. 

The  smaller  sewers  in  all  cities  and  towns  are  of  vitri- 
fied ware  or  cement  of  circular  section,  or  of  cement  of 


FIG.  1103. 


egg-shaped  form,  but  beyond  the  diameter  of  24  inches  or  its  equivalent  section 
brick  is  generally  used.      The  vitrified  pipe  is  laid  either  with  (Fig.  1105)  or 

without  concrete  base  and  side  sup- 
ports, depending  somewhat  on  the 
kind  of  earth  through  which  it  is 


FIG.  1104. 


FIG.  1105. 


468 


ENGINEERING  DRAWING. 


laid  and  the  desirability  of  uniformity  or  security  of  construction,  but  the 
joints  are  laid  full  in  cement  with  a  re-enforce  outside  and  wiped  clean  on  the 
inside.  Up  to  15"  the  pipes  are  usually  bell  and  spigot,  larger  they  are  laid 
with  collars.  The  egg-shaped  cement  pipe  is  usually  constructed  with  a  sole 
plate,  which  rests  on  a  base  of  plank  double  thickness  at  the  joints.  The  joints 
of  the  pipe  are  struck  with  cement  mortar  inside  and  out,  made  very  strong 


FIG.  1106. 


FIG.  1107. 


outside  and.  very  smooth  inside,  but  usually  without  concrete  backing,  but 
packed  solidly  in  earth.  Fig.  1106  is  a  section  of  an  English  form  of  sewer 
cheap  and  strong.  The  bricks  are  laid  with  close  joints  inside  and  an  exterior 
coating  of  cement  plaster. 

This  form  of  construction  is  not  uncommon  here  with  a  central  pipe  of 
vitrified  stoneware.  The  concrete  backing  is  very  desirable  to  withstand  the 
shock  of  heavy  moving  loads,  especially  for  pipes  of  large  diameter. 

Fig.  1107  is  the  usual  form  of 
egg-shaped  pipe,  of  which  the  pro- 
portions are  given  in  the  table. 

Thickness  of  brickwork,  8"; 
boards  shown  at  bottom  only  used 
in  cases  of  soft  earth  for  convenience 


EGG-SHAPED   SEWERS. 


Equal  to  a 
circular 
sewer  of 

D  inches. 

D  and  R' 
inches. 

R"  inches. 

Di»m«ter. 

24  in. 

19-8 

29-8 

5-0 

30 

24-8 

37-2 

6-2 

36 

29-8 

44.7 

7-4 

42 

34-8 

52-1 

8-7 

48 

39-7 

59-5 

9-9 

54 

44-6 

67-0 

11-2 

60 

49-6 

74-4 

12-4 

of  construction.  For  area  of  egg- 
shaped  sewer  of  above  section,  multi- 
ply Rs  by  4-6. 

In  general,  brick  sewers  are  only 
well  packed  in  earth,  but  when  the 
soil  is  loose  and  it  is  desirable  to  secure  an  extended  base  and  side  supports, 
the  form  Fig.  1108  is  adopted,  which  may  be  in  rubble  masonry  or  concrete, 
and  if  the  earth  cover  is  light  and  the  structure  exposed  to  heavy  moving  loads 
the  masonry  should  be  carried  above  the  arch.  At  the  bottom,  where  the  arch 
is  of  small  radius  and  it  is  difficult  to  get  good  joints  in  the  brickwork,  it  is 
very  common  to  place  inverts  of  vitrified  ware  which  are  sold  for  this  purpose. 
Fig.  1109  is  a  section  of  a  sewer  constructed  in  situ  at  Mount  Vernon,  N.  Y,, 
through  a  long  rock-cut.  Concrete  was  rammed  in  around  an  inverted  centre, 
and  after  it  was  withdrawn  the  face  was  plastered  with  a  very  thin  coat  of 


ENGINEERING  DRAWING. 


469 


FIG.  1108. 


Portland  cement ;  the  invert  is  of  vitrified  ware.  A  plumb  J,  is  inserted  across 
the  sewer  (Fig.  1110)  with  points  for  centres  at  different  heights,  the  radius 
is  uniform,  and  the  arch  turned  as  high  as  convenient  for  the  rock  sides  and 


FIG.  1111. 


FIG.  1109. 


FIG.  1110. 


470 


ENGINEERING  DRAWING. 


street  grades,  either  on  levels  and  offsets  or  by  inclines,  the  object  being  to  se- 
cure space  in  the  sewer,  and  save  the  rock  excavated  for  other  city  purposes. 
Fig.  1111  represents  the  first  joint  from  the  sewer  on  house  branches  curved 

and  with  a  cover  by  means  of  which  any 
obstruction  in  sewer  or  branch  could 
be  better  reached  and  removed. 

Man-holes  are  built  along  the  line 
of  sewers,  usually  from  200  to  400  feet 
apart,  and  at  every  junction  and  change 
of  direction,  to  give  access  to  the  sewers 
for  purposes  of  inspection  and  removal 
of  deposit. 


FIG.  1112. 


SCALE  :    J  *  =  1  foot. 
FIG.  1113. 


In  the  large  Washington  sewer  the  man-hole  is  constructed  on  the  side  of 
the  sewer ;  in  the  Brooklyn  one  the  aperture  of  the  man-hole  comes  within  the 
exterior  wall.  In  most  sewers  it  is  directly  over  them. 

Figs.  1112  and  1113  are  section  and 
plan  of  the  man-hole  at  present  used  by 
the  Croton  Sewer  Department.  It  consists 
of  a  funnel-shaped  brick  wall,  oval  at  the 
bottom  4',  circular  at  top  2'  diameter. 


FIG.  1114. 


Side-walls,  8"  thick,  through  which  the  pipe-sewers  pass  at  the  bottom  of  the 
well.  Across  the  open  space  the  sewer  is  formed  in  brick,  whose  bottom  section 
corresponds  to  that  of  pipe,  side-walls  carried  up  perpendicular  to  top  of  sewer ; 


ENGINEERING  DRAWING. 


471 


the  flat  spaces  at  the  sides  of  sewer  are  flagged.  The  top  of  the  sewer  is  a 
heavy  cast-iron  frame,  fitted  with  a" strong  cover,  which  may  or  may  not  be  per- 
forated, for  ventilation.  In  the  figure  the  main  sewer  is  12"  pipe,  with  a  12" 
branch  entering  at  an  acute  angle,  as  all  branches  and  connections  with  a 
sewer  should.  The  short  lines  on  the  left  vertical  wall  represent  sections  of  U 
staples,  built  in  to  serve  for  a  ladder. 

When  the  T  is  at  right  angles  to  the  through  pipe  it  is  very  convenient  to 
form  the  base,  as  in  Fig.  1114,  in  concrete  to  a  wooden  mould,  with  the  inside 
plastered.  This  form  enables  the  sewer  to  be  seen  in  all  directions  by  a  light 

from  man-hole  to  man-hole.     Curved  pipes 
are  now  seldom  laid ;  angles  are  made  at  the 


FIG.  1116. 


FIG.  1117. 


man-holes,  with  straight  pipe  between.  When  necessary,  catch-basins  (of 
which  Fig.  1115  is  a  vertical  section,  Fig.  1116  a  half  plan  and  a  half  sectional 
plan)  are  placed  at  the  corner  of  the  street  or  at  depressions  of  the  street  gut- 
ters, to  catch  any  heavy  matter  that  might  clog  the  sewer  or  fill  the  dock  slips, 
and  is  removed  by  hand.  The  cast-iron  hood  makes  a  seal,  preventing  the  es- 
cape of  sewer  gas  through  the  sewer  branch.  Fig.  1117  is  a  perspective  draw- 
ing of  the  basin  head  at  the  corner  of  the  street. 

Where,  by  the  difference  of  grades  between  the  main  line  of  sewer  and  the 
branches,  the  latter  are  at  a  considerable  height  above  the  base  of  the  man-hole, 
it  is  best  to  lead  the  branch  down  by  a  vertical  cast-iron  pipe  having  a  cross  at 
the  top  for  access  to  the  branch,  and  an  elbow  at  the  bottom  to  protect  the  ma- 
sonry from  the  effects  of  the  discharge. 

Gas-Supply. — Next  in  importance  to  the  necessities  of  a  city  or  town  for 
water-supply  and  sewerage  is  the  luxury  of  gas-supply.  The  gas-works  should 
always  be  placed  remote  from  the  thickly  populated  part  of  the  city,  for  under 
the  best  regulations  some  gas  (offensive  and  deleterious)  will  escape  in  the  manu- 
facture. They  should  be  placed  at  the  lowest  level,  for  gas,  being  light,  readi- 
ly rises,  and  the  portions  of  the  city  below  the  works  are  supplied  at  less  pres- 
sure than  those  above.  Gas-mains,  like  those  for  water,  are  of  cast-iron,  and  put 
together  in  the  same  way  ;  but,  as  they  have  to  resist  no  pressure  beyond  that  of 
the  earth  in  which  they  are  buried,  they  are  never  made  of  as  great  thickness  as 
those  of  water-pipes,  but  drips  must  be  provided,  and  the  pipe  laid  with  such  in- 
clination to  them  that  the  condensed  tar  may  be  received  in  them  and  pumped  out. 

Owing  to  the  reduction  in  price  complete  systems  of  wrought-iron  gas-pipe 
are  now  laid,  with  the  usual  screw-coupling  and  tested  to  a  pressure  much  in 
excess  of  that  of  the  gas. 


4:72 


ENGINEERING   DRAWING. 


WEIGHT   OP   GAS-PIPES   PER  RUNNING   FOOT. 


3* laibs. 

4" 16   '• 

6" 27   " 

8"..         ..,..  .40   " 


10" 501bs. 

12" 62   " 

16" 103    " 

20"..  .   150   " 


The  holes  for  access  to  the  valves  on  gas-pipes  usually  consist  of  two  pipes, 
the  lower  one  with  a  saddle  base  resting  on  the  pipe,  the  upper  with  a  cap  at 
the  top  which  is  adjustable  to  the  height  of  the  pavement  by  screws  cast  on 
both  pipes,  the  upper  one  being  the  extension. 

Roads  and  highways  are  terms  applied  distinctively  to  routes  of  land  travel 
in  the  country,  though  in  general  they  may  include  city  streets  and  avenues. 
Lines  of  canal,  river,  lake,  and  ocean  transit  are  often  designated  as  highways. 

The  first  requirements  in  the  opening  up  of  a  country  are  good  roads,  which 
must  naturally  be  of  the  cheapest  kind,  but  with  the  increase  of  population 
they  must  be  made  more  and  more  permanent,  and  the  reflex  action  extends  to 
farming  and  mechanical  facilities  and  increase  in  population. 

For  constant  and  continued  use  there  can  be  no  good  road  without  drain- 
age ;  there  may  be  seasons  when  hauling  is  practicable,  but  no  road  will  stay 
good  unless  the  surplus  water  is  got  rid  of,  and  if  the  road  is  well  drained  it 
will  pay  the  farmer  to  extend  the  drainage  to  the  fields  adjacent. 

Fig.  1118  is  a  section  of  a  dirt  road  in  which  there  is  a  central  drain,  and 
above  it  a  4"  layer  of  coarse  straw,  hay,  or  stubble,  the  bed  for  which  has  been 
excavated  on  slopes  toward  the  drain  of  1"  to  2"  to  the  foot.  The  earth  should 
then  be  filled  above  in  layers  and  rolled,  with  slopes  to  the  sides  sufficient  to 


Fio.  1119. 

carry  off  all  the  water  from  the  centre.  The  width  of  a  common  road  should 
be  16  feet,  slopes  of  about  8  inches  to  each  side,  grade  not  to  exceed  9'  to  the 
hundred,  or  about  5°,  and  this  not  continuous,  but  broken  by  changes  of  grade. 
Fig.  1119  is  a  section  of  a  gravel  road  similar  to  the  dirt  road,  but,  as  illus- 
trative of  a  road  with  a  steep  grade,  the  cut  across  the  turf  borders  are  diagonal 
to  turn  the  water  more  readily  into  the  ditches,  while  in  the  level  road  the  cuts 
are  at  right  angles.  If  not  convenient  to  construct  the  drains  in  the  centre  of 
the  road,  they  may  be  placed  at  the  sides  with  the  sub-slopes  discharging  into 
them.  Throughout  our  country  there  is  at  the  present  time  a  strong  move- 


ENGINEERING  DRAWING. 


473 


ment  in  favour  of  good  roads,  and  machinery  has  been  designed  and  constructed 
by  which  the  cost  of  construction  has  been  very  much  reduced,  with  great  im- 
provement in  the  character  of  the  roads. 

Across  marsh  lands  it  is  important  that  the  surface  of  sods  and  roots  should 
not  be  broken,  but  that  the  weight  of  the  roadway  should  be  further  distrib- 
uted by  a  layer  of  brush,  fagots,  or  poles,  on  which  the  layers  of  earth  should 
be  sods  from  the  marsh  taken  distant  from  the  roadway,  compacted  in  layers 
and  finished  like  the  dirt  road,  but  without  gutters,  or  at  such  distance  and 
depth  as  not  to  weaken  the  road  float.  , 

For  country  roads,  wagons  subject  to  heavy  loads  should  have  wide  tires, 
say  4"  tires  for  the  front  wheels  and  6"  for  the  rear  ones,  and  the  paths  of  the 
wheels  should  lap  but  not  track,  the  axles  of  the  rear  wheels  being  longer  than 
those  of  the  fore. 

Near  the  sea,  where  the  soil  is  sand  or  gravel  and  stone  is  not  to  be  had 
readily,  oyster  shells  make  an  admirable  road ;  they  are  arranged  in  layers  like 
Macadam,  and  grinding  together  beneath  rolling  and  travel,  they  make  a  com- 
pact and  solid  cover. 

Macadam  was  the  first  to  reduce  the  construction  of  broken-stone  roads  to 
a  science,  and  has  given  the  name,  in  his  own  and  this  country,  to  all  this  class 
of  roads.  He  says  that  "  the  whole  science  of  artificial  road-making^consists  in 
making  a  dry,  solid  path  on  the  natural  soil,  and  then  keeping  it  dry  by  a  dura- 
ble water-proof  covering."  The  road-bed,  having  been  thoroughly  drained, 
must  be  properly  shaped,  and  sloped  each  way  from  the  centre,  to  discharge  any 
water  that  may  penetrate  it.  Upon  this  bed  a  coating  of  3"  of  clean  broken 
stone,  free  from  earth,  is  to  be  spread  on  a  dry  day.  This  is  then  to  be  rolled, 
or  worked  by  travel  till  it  becomes  almost  consolidated ;  a  second  3"-layer  is 
then  added,  wet  down  so  as  to  unite  more  readily  with  the  first;  this  is  then 
rolled,  or  worked,  and  a  third  and  fourth  layer,  if  necessary,  added.  Macadam's 
standard  for  stone  was  6  ounces  for  the  maximum  weight,  corresponding  to  a 
cube  of  1£",  or  such  as  would  pass  in  any  direction  through  a  2£"  ring.  The 
Telford  road  is  of  broken  stone,  supported  on  a  bottom  course  or  layer  of  stone 
set  by  hand  in  the  form  of  a  close,  firm  pavement. 

Early  in  the  construction  of  the  New  York  Central  Park,  after  trials  of  the 
Macadam  and  Telford  roads,  gravel  was  adopted  and  still  maintains  its  position 
for  these  roads.  The  gravel  road,  of  which  a  cross-section  of  one  half  is  shown 
(Fig.  1120),  consists  of  a  layer  of  rubble-stones,  about  7"  thick,  on  a  well-rolled 
or  packed  bed,  with  a  covering  of  5'  of  clean  gravel.  C  is  the  catch-basin  for 


FIG.  1120. 


474 


ENGINEERING  DRAWING. 


the  reception  of  water  and  deposit  of  silt  from  the  gutters ;  S  is  the  main 
sewer  or  drain,  and  s  a  sewer-pipe  leading  to  a  catch-basin  on  opposite  side  of 
the  road.  In  wider  roads  each  side  has  its  own  main  drain,  and  there  is  no 
cross-pipe  s.  The  road-bed  was  drained  by  drain-tiles  of  from  1£"  to  4"  bore, 
at  a  depth  of  3'  to  3£'  below  the  surface.  The  maximum  grade  of  the  Park 
roads  is  1  in  20. 

In  New  York  the  streets  above  Fourteenth  Street  running  north  and  south 
are  called  avenues,  and  those  at  right  angles,  streets,  and  boulevard  is  applied 
to  very  wide  avenues  in  which  there  are  rows  of  trees.  The  terms  street  and 
avenue,  as  laid  out,  are  the  established  bounds  within  which  no  buildings 
may  be  erected.  The  street,  therefore,  technically  includes  the  street  or  trav- 
elled way  for  carriages,  and  the  side- 
walks and  front  areas.  New  York 
streets  above  Fourteenth  Street  are  60 
and  100  feet  wide,  avenues  100  feet, 
of  which  the  carriage-way  occupies 
one  half  (Fig.  1121),  and  the  sidewalks 
and  area  one  quarter  on  each  side. 
The  space  occupied  by  areas  is  from 

5  to  8  feet,  which  may  be  inclosed  by  iron  fence  ;  the  space  beneath  it  and  the 
sidewalk  to  the  curb  and  used  for  vaults  can  be  leased  from  the  city.  The 
stoop-line  extends  into  the  sidewalk  beyond  the  area-line  some  1'  to  18",.  fixing 
the  limit  for  the  first  step  and  newel  to  a  high  stoop  or  platform.  The  boule- 
vard in  the  old  line  of  upper  Broadway  and  the  Bloomingdale  Eoad  is  150 
feet  wide,  of  which  100  feet  are  to  be  carriage-way,  and  25  feet  on  each  side  for 
sidewalk  and  area,  the  latter  not  to  exceed  7  feet ;  one  row  of  trees  to  be  set 
within  the  sidewalk,  about  2  feet  from  the  curb. 

The  best  grade  is  from  1  in  50  to  1  in  100 ;  this  gives  ample  descent  for  the 
flow  of  water  in  the  gutters.  Many  of  our  street-gutters  have  a  pitch  not  ex- 
ceeding 1  foot  in  the  width  of  a  block,  or  200  feet. 

The  grade  of  a  road  is  described  as  1  in  so  many ;  so  many  feet  to  the  mile, 
or  such  an  angle  with  the  horizon  : 


FIG.  1121. 


Inclination. 

Feet  per  mile. 

Angle. 

Inclination. 

Feet  per  mile. 

Angle. 

linlO 

528 

5°  43' 

1  in   30 

176 

1°  55' 

1  "  11                  462 

5° 

1  "    40 

132 

1°  26' 

1  "  14 

369 

4° 

1  "    50 

106 

1°     9' 

1  "  20 

264 

2°  52' 

1  "    57 

92 

1° 

1  "  29 

184 

2° 

1  "  100 

53 

35" 

The  foot-walks  in  this  city  and  vicinity  are  generally  formed  of  flags,  or 
what  is  here  termed  blue-stone,  laid  on  a  bed  of  sand  or  cement-mortar.  The 
flags  are  from  2"  to  4"  thick.  Stone  thicker,  select  in  quality,  upper  surface 
bush  hammered  or  planed,  close  jointed,  and  covering  the  whole  width  of  the 
sidewalk  in  one  stone,  add  much  to  the  exterior  finish  of  large  houses.  Bricks 
are  often  used  in  towns,  or  places  where  good  flagging  can  $ot  be  readily  ob- 
tained, usually  laid  flatways  on  a  sand-bed.  Granite  is  often  employed  for  side- 
walks in  lengths  equal  to  the  width  of  the  sidewalk,  and  making  a  cover  for  the 


ENGINEERING  DRAWING. 


475 


vault  beneath ;  the  objection  to  it  is  that  by  wear  and  under  certain  atmospheric 
conditions  it  becomes  slippery. 

Cement  face,  with  a  base  of  concrete  and  laid  in  squares  to  admit  of  expan- 
sion, makes  a  good  and  permanent  walk.  For  the  country  a  composition  of 
coal  tar,  or  asphalt  and  gravel,  is  economical  and  satisfactory. 

In  Paris  there  is  no  area  (Fig.  1122) ;  the  sidewalk  comes  up  to  the  house 
or  street-line,  and  there  is  a  space  for  trees  between  sidewalk  and  street-curb. 


This  space  is  available  for  pedestrians,  a  part  being  a  gravel,  asphalt,  or  flagged 
walk.     The  following  are  the  dimensions  according  to  the  law  of  June  5, 1856  : 


Entire  width  of 
boulevard  and 

Width  of 

Width  of 

Width  for 

Rows  of 

DISTANCE  OF 

ROW  FROM 

avenues. 

Street-line. 

Street-curb. 

Metrei. 

26  to  28 

Metrei. 
12 

Metres. 

Metrei. 

1 

Metres. 

5-5  to  6-5 

Metres. 

1-5 

30  "  34 

14 

1 

6-5  "   8-5 

1-5 

36  "  38 
40 

12  to  13 
14 

3-5 

3-5 

8-0  to  8-5 
9-5 

2 
2 

5-0  "  5-5 
6-5 

1-5 
1-5 

1  metre  =  3 -281  feet. 


GRANITE   BLOCK    PAVEMENT   WITH    FOUNDATION    AGREEABLY   TO    NEW   YORK 
CITY   SPECIFICATIONS  (Fig.  1123). 

Stone  blocks  of  granite,  measuring  on  the  upper  surface  not  less  than  8"  nor 
more  than  12"  in  length,  not  less  than  3£"  nor  more  than  4£"  in  width,  not 


FIG.  1123. 


less  than  7"  nor  more  than  8"  in  depth,  blocks  to  be  dressed  to  form  when  laid, 
close-end  joints,  and  side  joints  not  exceeding  1"  in  width. 

Bridge  or  Crossing  Stones. — Each  stone  to  be  not  less  than  4'  nor  more  than 
8'  long  and  2'  wide;  thickness,  from  6"  to  8";  dressed  to  an  even  face  on 'top, 
bottom  bedded,  sides  square  and  full,  ends  cut  to  a  bevel  of  6"  in  2'  not  paral- 
lel with  the  line  of  vehicle  travel. 


476  ENGINEERING  DRAWING. 

Curbstones  shall  not  be  less  than  3'  in  length,  5"  thick,  20"  deep,  matched 
width,  the  top  cut  to  a  bevel  of  1",  front  cut  to  a  fair  line  to  a  depth  of  14", 
ends  from  top  to  bottom  squared. 

The  subsoil  to  be  excavated  and  removed  to  a  depth  of  16"  below  the  top 
line  of  the  proposed  pavement;  roadbed  shall  be  truly  shaped  and  trimmed  to 
the  required  grade,  and  rolled  to  ultimate  resistance  with  a  roller  weighing  not 
less  than  ten  tons.  When  the  roller  can  not  reach  any  portion  of  the  roadbed 
it  shall  be  tamped  or  rolled  with  a  small  roller.  Upon  the  foundation  a  6"  bed 
of  concrete,  except  in  the  space  between  the  rails  known  as  the  horse- ways, 
where  no  concrete  shall  be  laid.  Concrete  of  Portland  cement — one  part  of 
cement,  three  parts  of  sharp  sand,  seven  parts  of  broken  stone  by  measure  ;  or 
one  part  of  cement,  three  parts  of  sand,  four  of  broken  stone,  and  three  of  gravel. 
Of  Rosendale  cement — one  part  of  cement,  two  of  sand,  and  four  of  broken 
stone ;  or  one  of  cement,  two  of  sand,  two  of  broken  stone,  and  two  of  gravel. 

On  this  concrete  foundation,  and  on  the  foundations  of  the  horse-ways  of 
street  railways  (where  no  concrete  shall  be  laid)  shall  be  laid  a  bed  of  clean,  sharp 
sand,  perfectly  free  from  moisture,  not  less  than  1£"  thick,  to  the  depth  neces- 
sary to  bring  the  pavement  to  the  proper  grade  when  properly  rammed.  Upon 
this  bed  of  sand  cross-walks  to  be  laid,  stone  blocks  in  courses  at  right  angles 
with  the  line  of  street,  except  in  intersections  of  streets,  when  the  courses  shall 
be  laid  diagonally.  Each  course  of  blocks  shall  be  of  uniform  depth  and  width, 
so  laid  that  all  end  joints  shall  be  broken  by  a  lap  of  at  least  3" ;  joints  be- 
tween courses  not  more  than  1"  in  width.  As  the  blocks  are  laid  they  shall  be 
covered  immediately  with  clean,  hard,  hot,  dry  gravel,  of  proper  size,  which 
shall  be  brushed  into  the  joints  until  all  the  joints  become  filled ;  gravel  shall 
be  free  from  sand.  Blocks  shall  be  thoroughly  rammed  to  an  unyielding  bear- 
ing, with  uniform  surface,  true  to  the  roadway  grade.  Before  pouring  the 
paving  cement,  the  joints  and  gravel  filling  must  be  made  dry  and  free  from 
dirt.  Paving  cement  shall  be  poured  into  the  joints  while  the  gravel  is  still 
hot  (paving  cement  to  be  heated  to  300°  Fahr.)  until  the  joints  are  filled  flush 
with  the  top  of  the  blocks. 

Paving  cement  to  be  composed  of  twenty  parts  refined  Trinidad  asphalt 
and  three  parts  of  residuum  oil,  mixed  with  a  hundred  parts  of  coal  tar. 

Gutter  stones  are  not  now  used,  the  paving  extending  to  the  curbstone. 

Granite  Pavement  ivithout  Concrete  Bed — Similar  to  the  above,  excepting 
that  the  subsoil  shall  be  excavated  and  removed  to  the  depth  of  10"  below 
the  top  line  of  the  proposed  pavement  when  rolled  or  rammed.  Upon  this 
foundation  shall  be  laid  a  bed  of  clean  sharp  sand,  or  clean  fine  gravel,  to  the 
depth  necessary  to  bring  the  pavement  and  cross-walks  to  the  proper  grade. 
No  ramming  shall  be  done  within  25  feet  of  the  face  of  the  work  being  laid. 
Whenever  the  pavement  shall  have  been  constructed  it  shall  be  covered  with  a 
good  and  sufficient  second  coat  of  clean  sharp  sand,  and  immediately  thoroughly 
rammed  until  the  work  is  made  solid  and  secure;  no  paving  cement  in  the 
joints  of  the  blocks. 

Asphalt  Pavement  with  Concrete  Foundation  (Fig.  1124). — The  subsoil  or 
other  matter  shall  be  excavated  and  removed  to  the  depth  of  9  inches  below  the 
top  line  of  the  proposed  Trinidad  asphalt  pavement,  which  shall  have  a  crown 
not  to  exceed  the  rate  of  5  inches  on  a  roadway  of  30  feet,  9£  inches  below  the 


ENGINEERING  DRAWING. 


477 


top  of  the  proposed  asphalt  pavement,  and  13£  inches  below  the  top  of  the 
stone  block  pavement  adjoining  the- rails,  man-hole  heads,  and  stop-cock  boxes, 


the  entire  road-bed  to  be  thoroughly  rolled  with  a  heavy  roller.  Upon  the 
foundation  thus  prepared  shall  be  laid  a  bed  of  hydraulic  cement  concrete,  6 
inches  in  thickness,  which,  if  necessary,  must  be  protected  from  the  action  of 
the  sun  and  wind  until  set.  Upon  this  foundation  must  be  laid  a  fine  bitumi- 
nous concrete  or  binder  of  clean,  broken  stone  not  exceeding  1£  inch  in  their 
largest  dimensions,  thoroughly  screened,  and  coal-tar  residuum,  commonly 
known  as  No.  4  paving  composition.  The  stone  to  be  heated  by  passing 
through  revolving  heaters,  and  thoroughly  mixed  by  machinery  with  the  pav- 
ing composition  in  the  proportion  of  1  gallon  of  paving  composition  to  1  cubic 
foot  of  stone.  The  binder  to  be  spread  with  hot  iron  rakes  to  true  grade  of 
the  pavement  and  to  such  thickness  that,  after  being  thoroughly  compacted 
by  tamping  and  hand  rolling,  the  surface  shall  have  a  uniform  grade  and  cross- 
section,  and  the  thickness  of  the  binder  at  any  point  shall  be  not  less  than  three 
fourths  of  an  inch,  the  upper  surface  to  be  parallel  with  the  surface  of  the 
pavement  to  be  laid.  Upon  this  foundation  must  be  laid  the  wearing  surface, 
the  basis  of  which,  and  of  paving  cement,  must  be  pure  asphaltum,  unmixed 
with  any  of  the  products  of  coal  tar.  The  wearing  surface  to  be  composed  of 
refined  asphaltum,  heavy  petroleum  oil,  fine  sand  containing  not  more  than 
one  per  cent  of  hydrosilicate  of  alumina  and  fine  powder  of  carbonate  of  lime ; 
asphalt  from  the  Pitch  Lake,  on  the  Island  of  Trinidad ;  petroleum  oil  to  be 
freed  from  all  impurities  and  brought  to  a  specific  gravity  of  from  18  to  22° 
Beaume,  and  a  fire  test  of  250°  Fahr.  The  cement  from  these  two  hydro- 
carbons shall  have  a  fire  test  of  250°  Fahr.,  to  be  composed  of  100  parts  of  pure 
asphalt  and  from  15  to  20  parts  of  petroleum  oil. 
The  pavement  mixture  to  be  composed  of : 

Asphaltic  cement 12  to  15  parts. 

Sand 83  to  70     " 

Pulverized  carbonate  of  lime 5  to  15     " 

Sand  and  asphaltic  cement  to  be  heated  separately  to  about  300°  Fahr.,  the 
carbonate  of  lime  while  cold  to  be  mixed  with  the  hot  sand  and  then  with  the 
asphaltic  cement.  The  pavement  mixture,  at  a  temperature  of  about  250°,  shall 
then  be  carefully  spread  by  means  of  hot  iron  rakes  in  such  manner  as  to  give 
a  uniform  and  regular  grade.  The  surface  shall  then  be  compressed  by  hand 
rollers,  after  which  a  small  amount  of  hydraulic  cement  shall  be  swept  over  it, 
and  it  shall  then  be  thoroughly  compressed  by  a  steam  roller  weighing  not  less 
than  250  pounds  to  the  inch  run,  the  rolling  to  be  not  less  than  five  hours  for 


4:78 


ENGINEERING  DRAWING. 


every  1,000  yards  of  surface.  After  its  ultimate  compression  the  pavement 
must  have  a  thickness  of  not  less  than  2  inches. 

Of  the  powdered  carbonate  of  lime,  5  to  15  per  cent  shall  be  of  an  impalpa- 
ble powder,  the  whole  of  it  to  pass  a  No.  26  screen ;  of  the  sand,  none  to  pass 
a  No.  80  screen ;  and  the  whole  of  it,  a  No.  10  screen. 

Pavements,  Salt  Lake  City,  Utah. — The  streets  are  92  feet  from  curb  to 
curb.  The  pavement  is  practically  in  two  portions — an  asphalted  central  por- 
tion and  two  stone-block  surfaces — arranged  as  shown  in  Fig.  1125.  The 
foundation  of  the  block  pavement  is  10  feet  wide  on  each  side,  is  composed  of 


coarse  sand  laid  on  a  foundation  compacted  by  a  10- 
ton  steam  roller  ;  the  sand  stratum  is  6"  thick.  The 
blocks  are  of  very  hard  sandstone,  and  vary  from 

7"  X  3f  X  7"  to  10"  X  4£"  X  7" ;  they  form  a  pavement  7"  thick,  with 
joints  not  over  f"  wide,  filled  with  fine-screened  gravel  and  grouted  .pitch. 
Before  the  joints  are  poured  the  blocks  are  rammed  with  hammers  weighing 
from  75  to  80  pounds  until  brought  to  a  firm  bed  at  the  proper  level.  The 
asphalted  portion  of  the  street  is  laid  on  a  concrete  foundation  6"  thick. 

Methods  of  laying  Brick  Pavements  (Fig.  1126). — After  excavation   the 
ground  is  compacted  with  rollers  weighing  about  2  tons.     A  foundation  course 


of  sand  or  broken  stone  is  thoroughly  compressed  with  the  roller  to  the  exact 
form  and  crown  of  the  finished  pavement.  On  this  foundation  a  layer  of 
brick  is  laid  flatwise,  with  the  longest  dimension  longitudinal  with  the  road- 
way;  on  this  layer  sufficient  sand  is  spread  to  fill  all  joints  and  then  rolled  or 
rammed  ;  then  a  cushion  of  1"  or  2"  of  sand,  and  on  this  a  layer  of  brick  is  set 
on  edge,  with  the  longest  dimension  across  the  roadway,  which  layer  is  either 
rolled  or  rammed.  After  rolling  is  completed,  any  broken  bricks  are  replaced 
with  whole  ones ;  this  is  also  done  in  the  first  layer.  By  some  a  foundation  is 
preferred  composed  of  8"  to  15"  of  broken  stone,  made  compact  with  rollers 
weighing  from  12  to  15  tons,  and  upon  this  is  spread  a  3"  cushion  of  sand.  A 
crown  of  4"  is  allowed  in  a  roadway  50  feet  wide,  and  3"  in  a  roadway  40  feet 
wide. 

Modulus  of  rupture  in  compression :  First-quality  brick,  1,700  pounds  per 
square  inch  ;  absorption,  1-6  per  cent;  abrasion  under  test  to  be  equal  to  granite. 


ENGINEERING  DRAWING. 


479 


Modulus  of  rupture  in  compression :  Second-quality,  1,500  pounds  per  square 
inch ;  absorption,  5  per  cent ;  abrasion  not  to  exceed  twice  that  of  granite. 
Of  wooden  pavements,  cedar  block  is  the  most  general  (Fig.  1127).     The 


CEDAR  BLOCKS 


2      12LANK 
1"X  12"STRINGER 


FIG.  1127. 


curbstone  is  set  to  the  true  grade,  and  the  ground  between  is  graded  to  the 
true  cross-section  of  the  street.  After  this  the  surface  is  rolled  by  a  heavy 
steam  roller ;  next,  3"  of  coarse  sand  is  spread  over  the  entire  surface.  String- 
ers 1"  x  12"  are  then  laid  across  the  street  from  curb  to  curb,  usually  8"  apart 
and  bedded  in  the  sand  to  the  true  section  of  the  roadway ;  after  the  stringers 
are  in  place  and  well  tamped,  sand  is  levelled  between  flush  to  the  top  of  the 
stringers.  On  the  stringers  and  sand  the  foundation  planks,  1"  to  2"  thick, 
well  seasoned  and  dry,  are  laid  close  together  lengthwise  of  the  street,  the  ends 
abutting  on  the  stringers.  Sometimes  the  foundation  boards  are  dipped  in  hot 
coal  tar  before  laying.  The  paving  blocks  are  sawed  from  peeled  cedar  fence 
posts,  and  run  from  4'  to  8*  diameter.  The  standard  length  is  6",  but  some 
cities  use  blocks  7*  or  8*  long. 

The  cedar  blocks  are  packed  on  end  close  together  upon  the  plank  founda- 
tion, and  with  the  spaces  between  adjoining  blocks  three-sided  rather  than 
more  sides.  Against  the  curb,  or  any  other  straight  vertical  surface,  each 
alternate  block  should  be  split  in  halves  and  the  straight  side  placed  against 
the  curb.  After  the  blocks  are  in  place  the  spaces  between  them  are  filled  with 
gravel  rammed  down  by  iron  rods.  Some  require  that  a  paving  cement,  com- 
posed of  coal  tar  and  asphalt,  be  poured  over  the  whole  surface  of  the  pave- 
ment, and  run  into  the  spaces  between  the  blocks.  The  entire  surface  of  the 
pavement  is  then  covered  with  about  I"  of  fine  roofing  gravel. 

RAILROADS. 

The  necessity  of  a  well-drained  road-bed  is  as  important  beneath  rails  as  on 
a  highway.  The  cuts  should  be  excavated  to  a  depth  of  at  least  2  feet  below 
grade,  with  ditches  at  the  sides  still  deeper,  for  the  discharge  of  water.  The 
embankments  should  not  be  brought  within  2  feet  of  grade;  this  depth  to  be 
left  in  cut  and  on  embankment  for  the  reception  of  ballast.  The  best  ballast 
is  Macadam  stone,  in  which  the  cross-ties  are  to  be  bedded,  and  finer  broken 
stone  packed  between  them.  Good  coarse  gravel  makes  very  good  ballast ;  but 
sand,  although  affording  filtration  for  the  water,  is  easily  disturbed  by  the  pas- 
sage of  the  trains,  raising  a  dust,  an  annoyance  to  travellers,  and  an  injury  to 
the  rolling-stock  by  getting  into  boxes  and  bearings.  The  average  length  of 
sleepers  on  the  4'  8£"  gauge  railways  is  about  8  feet;  bearing  surface,  7"  ;  dis- 
tance between  centres,  2'  to  2'  6",  except  at  joints,  where  they  are  as  close  to 


480 


ENGINEERING  DRAWING. 


each  other  as  the  necessity  of  tamping  beneath  them  will  admit.  Average 
width  of  New  York  railways  of  same  gauge  as  above,  for  single  lines,  in  cuts 
18',  banks  13' ;  for  double  lines,  cuts  31',  banks  26£'. 

Figs.  1128  and  1129  are  two  standard  sections  of  the  permanent  way  of  the 


CROSS    SECTION   GRAVEL  BALLAST. 
FIQ.  1129. 

Pennsylvania  Kailroad,  in  which  the  width  of  cuts  and  top  of  embankments  are 
the  same,  31'  4",  and  other  dimensions  equally  ample. 

Rail  sections  are  of  infinite  variety  and  weights,  adapted  to  the  class  of 
railroads  on  which  they  are  to  be  used,  and  the  loads  and  speed  of  trains  to 
which  they  are  to  be  subjected.  For  roads  of  the  common  gauge,  the  weight  of 
rails  is  from  56  to  100  pounds  per  yard.  The  joints  are  made  with  a  fish-plate. 

Figs.  1130,  1131,  and  1132  are  the  elevation,  section,  and  plan  of  the 
standard  rail-joint  of  the  West  Shore  Railroad. 


FIG.  1130. 


-.          F3~T~    ""-YT 

"--...  L .?  J  ..-•  -        %    • 


Sfin 


|  *4J"/^-- 

^^ 

67  POUND  STB 

j 

FIG.  1181. 


With  the  increase  of  speed  on  railways,  the  tracks  on  the  larger  roads  are 
being  laid  with  rails  of  100  pounds  to  the  yard,  and  wrought-iron  ties  are  being 
tested,  but  experiments  on  them  with  very  heavy  trains  and  high  speeds  have 
not  yet  been  conclusive  as  to  their  adoption. 


ENGINEERING  DRAWING. 
DIMENSIONS  OF  STANDARD   RAILS.* 


481 


POUNDS  PER  YARD. 

A. 

B. 

c. 

D. 

E. 

F. 

G. 

40  

3* 

3| 

14 

i 

1JL 

25 

45                   

3U 

8U 

2 

21 

Hi 

1JL 

f? 

27 

50     

84 

3* 

21 

8 

Sh% 

?t 
7 

55         

iX 

4 

84 

*4 

2U 

111 

re 

JS 

60  

4i 

4± 

24 

M 

m 

1JL 

37 

il 

65  

4* 

4  A 

013 

%$ 

21 

1A 

6i 
1 

70     

4f 

44 

9rt 

If 

glf 

It* 

75  

411 

4|f 

•  2M 

si 

2ff 

1|| 

ii 

80  

5 

5 

2i 

2f 

1| 

if 

85  

&A 

5& 

2A 

*{ 

2f 

ifl 

s 

90  

54 

5| 

2f 

|| 

g4A 

lit 

A 

95 

5-A- 

5ft 

2}4 

!£ 

2SJ 

l£i 

? 

100         

5i 

54 

2f 

§i 

S-/4 

Itl 

s 

*  Dimensions  not  given  in  table  are  constant,  and  are  to  be  taken  from  the  standard  sec- 
tion of  a  70-pound  rail. 

Fig.  1132  is  a  drawing  of  a  standard  70-pound  rail. 


Fia.  1132. 


Figs.  1133,  1134,  and  1135  are  the  front  elevation,  plan,  and  side  elevation 
of  a  New  York  city  cable  conduit  adapted  to  Love's  electric  traction,  one  half 
of  each,  showing  the  construction  of  the  hand  holes  h  on  each  side  at  every 
third  yoke  about  15  feet  centres,  the  other  half  showing  the  intermediate  con- 
struction. Details  of  hand  hole  are  shown  in  Figs.  1136,  1137,  and  1138. 


482 


ENGINEERING  DRAWING. 


There  are  two  copper-wire  conductors  supported  and  well  insulated  beneath 
each  hand  hole,  which  affords  access  to  the  insulator  and  wire.  The  support 
for  the  conductor  is  formed  by  two  iron  rods  made  fast  inside  the  yoke,  carry- 
ing the  mica  block  into  which  the  hook-shaped  conductor  is  inserted. 


! 

-  -,,  , 

1 

!      h 

! 

(  1 

^  "  - 

FIG.  1135. 


FIG.  1134. 


FIG.  1133. 


Under  the  main  body  of  the  car  is  a  thin,  broad  plough  (Figs.  1139  and 
1140),  side  and  front  elevation,  that  passes  through  the  slot  between  the  rails 
with  wires  (as  shown  in  figures)  leading  to  the  trolley,  which  is  brought  in 
contact  with  the  conductor  by  making  connections  with  both  wires  as  it  is 


FIG.  1137. 


ENGINEERING   DRAWING. 


483 


pressed  against  them.  The 
current  forms  a  complete  cir- 
cuit, passing  up  through  one 
wire  and  one  blade  of  the 
plough  to  the  motor;  thence  it 
returns  through  the  other  blade 
and  wire  to  the  power  house. 
None  of  the  current  returns 
through  the  rails  or  escapes 
through  the  ground. 

The  pulleys  shown  (Fig. 
1133)  are  those  belonging  to 
the  cable  traction,  see  Appen- 
dix. Manholes  into  the  con- 
duit are  placed  at  intervals  for 
inserting  the  lower  bar  of  the 
plow,  the  tongue  of  which  is 
raised  through  the  slot,  and 
fastened  by  the  pin  p  to  the 
head  attached  to  the  car. 


FIG.  1139. 


ROOFS    AND    BRIDGES. 


At  pages  490  and  491  will  be  found  illustrations  of  the  trussing  of  wooden 
beams.  These  are  simple  forms,  which  may  be  used  in  roofs  or  bridges,  and 
rules  are  given  for  the  proportion  of  parts.  Rolled  I-beams  or  plate-girders 
will  senve  also  for  floor-beams  and  moderate  spans,  but  with  modern  necessities 
much  more  complicated  structures  are  required. 

On  the  General  Principles  of  Bracing. — Let  Fig.  1141  be  the  elevation  of 
a  common  roof-truss,  and  let  a  weight,  W,  be  placed  at  the  foot  of  one  of  the 
suspension-rods.  Now,  if  the  construction  consisted  merely  of  the  rafter  C'  B, 
and  the  collar-beam  0'  C,  resting  against  some  fixed  point,  then  the  point  B 
would  support  the  whole  downward  pressure  of  the  weight ;  but  in  consequence 
of  the  connection  of  the  parts  of  the  frame,  the  pressure  must  be  resolved  into 
components  in  the  direction  C'  A  and  C'  B  ;  C'  b  will  represent  the  pressure  in 

the  direction  C'  B,  C'  w  the  portion 
of  the  weight  supported  at  B,  C'  a 


FIG.  1141. 


FIG.  1142. 


the  pressure  in  the  direction  C'  A,  and  w  W  the  portion  of  the  weight  sup- 
ported on  A.  The  same  resolution  obtains  to  determine  the  direction  and 
amount  of  force  exerted  on  a  bridge-truss  of  any  number  of  panels,  by  a  weight 
placed  at  any  point  p  of  its  length  (Fig.  1142).  In  either  case,  the  effect  of  the 
oblique  form  C'  A  upon  the  angle  C  is  evidently  to  force  it  upward  ;  that  is,  a 
weight  placed  at  one  side  of  the  frame  has,  as  in  case  of  the  arch,  a  tendency 


484: 


ENGINEERING  DRAWING. 


to  raise  the  other  side.  The  effect  of  this  upward  force  is  a  tension  on  a  por- 
tion of  the  braces,  according  to  the  position  of  the  weight ;  but  as  braces,  from 
the  manner  in  which  they  are  usually  connected  with  the  frame,  are  not  capa- 
ble of  opposing  any  force  of  extension,  it  follows  that  the  only  resistance  is 
that  which  is  due  to  the  weight  of  a  part  of  the  structure. 

Figs.  1143  and  1144  illustrate  the  effects  of  overloading  at  single  points  such 
forms  of  construction.     Such  an  unequal  loading  on  trusses  requires  that  a 


Fio.  1143. 


FIG.  1144. 


FIG.  1145. 


portion  of  the  load  W  be  transferred  to  each  point  of  support  inversely  propor- 
tionate to  the  distances  of  the  weight  from  each  support.  The  above  trusses 
are  not  prepared  to  transfer  this  weight  to  but  one  support.  To  remedy  the 
difficulty,  it  will  be  necessary  to  add  braces  running  in  the  opposite  direction 

as  shown  by  dotted  lines  (Fig.  1145),  at  every  point 

subject  to  the  above  distortion.     These  are  called 

counter-braces. 

To  prevent    the   braces  from   becoming  loose 

when  the  counter-braces  are  in  action,  it  is  always 

customary  to  give  the  braces  and  counter-braces  an  initial  compression,  by  put- 
ting a  moderate  tension  on  the  suspension-rods.  In  this  case,  therefore,  the 
passage  of  a  load  produces  no  additional  strain  upon  any  of  the  timbers,  but 
tends  to  relieve  the  counters.  The  counter-braces  do  not  assist  in  sustaining 
the  weight  of  the  structure ;  on  the  contrary,  the  greater  the  weight  of  the 
structure  itself,  the  more  will  the  counter-braces  be  relieved. 

If,  instead  of  the  counter-braces,  the  braces  themselves  are  made  to  act 
both  as  ties  and  struts,  as  in  some  iron  bridges  and  trusses,  then  the  upward 
force  will  be  counteracted  by  the  tension  of  the  brace. 

If  a  system  be  composed  of  a  series  of  suspension-trusses  (Fig.  1146)  in  which 


FIG.  1146. 

the  load  is  uniformly  distributed,  represent  the  load  at  each  of  the  points,  4,  3, 
2,  1,  2',  etc.,  by  1,  then  the  load  at  4  will  be  supported  ^  upon  a  and  £  upon 
3  ;  hence  the  strut  3  will  have  to  support  a  load  of  1  +  -5  —  To  ;  of  this  £ 
will  be  supported  by  2  and  -J-  by  a ;  f  of  1-5  =  1,  I  -f-  1  =  2,  load  on  strut  2 ; 
f  of  this  load,  or  1-5,  will  be  supported  at  1,  and  since  from  the  opposite  side 


ENGINEERING  DRAWING.  435 

there  is  an  equal  force  exerted  at.l,  therefore  the  strut  1  supports  1  -f-  1-5  -f- 
1-5  =  4. 

c  a 

The  tension  on  the  rod  c-2  =  2  - 

c  1 

"  "  2-3  =  2£  " 

"  "  3-4  =  3    " 


If  this  construction  be  reversed  as  in  a  roof-truss,  the  parts  which  now  act 
as  ties  become  braces,  and  the  braces  ties.  The  force  exerted  on  the  several 
parts  may  be  estimated  in  a  similar  way  as  for  the  suspension-truss.  Neither 
of  these  constructions  would  serve  for  a  bridge-truss,  subject  to  the  passage  of 
heavy  loads,  but  are  only  fit  to  support  uniform  and  equally  distributed  loads. 

To  frame  a  construction  so  that  it  may  be  completely  braced  —  that  is,  under 
the  action  of  any  arrangement  of  forces  —  the  angles  must  not  admit  of  alterd- 
tion,  and  consequently  the  shape  can  not.  The  form 


FIG.  1148.  FIG.  1149. 

should  be  resolvable  into  either  of  the  following  elements  (Figs.  1147,  1148, 
and  1149)  : 

In  these  figures,  lines  -  represent  parts  required  to  resist  compres- 

sion ;  lines  —  -  parts  to  resist  tension  only ;  lines  —  parts  to  re- 

sist both  tension  and  compression. 

In  a  triangle  (Fig.  1147),  an  angle  can  not  increase  or  diminish  without 
the  opposite  angles  also  increasing  or  diminishing.  In  the  form  Fig.  1148  a 
diagonal  must  diminish;  in  Fig.  1149  a  diagonal  must  extend,  in  order  that 
any  change  of  form  may  take  place.  Consequently,  all  these  forms  are  com- 
pletely braced,  as  each  does  not  permit  of  an  effect  taking  place,  which  would 
necessarily  result  from  a  change  of  figure.  Hence,  also,  any  system  composed 
of  these  forms,  properly  connected,  breaking  joint  as  it  were  into  each  other, 
must  be  braced  to  resist  the  action  of  forces  in  any  direction  ;  but  as  in  general 
all  bridge-trusses  are  formed  merely  to  resist  a  downward  pressure,  the  action 
on  the  top  chord  being  always  compression,  it  is  not  necessary  that  these  chords 
should  act  in  both  capacities. 

Most  city  roofs  are  flat ;  the  timbers  are  placed  like  those  of  the  floor  be- 
neath, but  at  greater  distances  between  centres,  as  they  have  less  load  to  sustain. 
The  roof  covering  is  inclined  to  discharge  the  rain  water  ;  and  the  timbers  be- 
neath are  arranged  to  admit  of  this  inclination,  which  may  be  quite  small,  £ 
of  an  inch  to  the  foot ;  but  it  should  be  positive  and  uniform,  to  prevent  the  re- 
tention of  the  water  in  puddles.  It  is  an  advantage  to  hold  the  snowfall,  as  it 
relieves  the  street  of  a  great  encumbrance. 

Figs.  1150,  1151,  and  1152  represent  elevations  or  portions  of  elevations  of 
the  usual  form  of  framed  roofs.  The  same  letters  refer  to  the  same  parts  in 
all  the  figures.  T  T  are  the  tie-beams,  R  R  the  main  rafters,  r  r  the  jack-raf- 
ters, P  P  the  plates,  p  p  the  purlins,  K  K  the  Icing-posts,  k  k  king-bolts,  q  q 
queen-bolts — both  are  called  suspension-bolts — C  the  collar  or  straining  beam, 
B  13  braces  or  struts,  b  b  ridge-boards,  e  corbels. 


486 


ENGINEERING   DRAWING. 


The  pitch  of  the  roof  is  in  the  inclination  of  the  rafters,  and  is  usually  des- 
ignated in  reference  to  the  span,  as  £,  £,  f ,  etc.,  pitch  ;  that  is,  the  height  of 


FIG.  1150. 


the  ridge  above  the  plate  is  £,  £,  f ,  etc.,  of  the  span  of  the  roof  at  the  level  of 
the  plate.     The  steeper  the  pitch  of  the  roof,  the  less  the  thrust  against  the 


FIG.  1151. 


side- walls,  the  less  likely  the  snow  or  water  to  lodge,  and  consequently  the 
tighter  the  roof.  For  roofs  covered  with  shingles  or  slate,  in  this  portion  of 
the  country,  it  is  not  advisable  to  use  less  than  £  pitch  ;  above  that,  the  pitch 
should  be  adapted  to  the  style  of  architecture  adopted.  The  pitch  in  most 
common  use  is  £  the  span. 

Fig.  1150  represents  a  simple  form  of  framed  roof ;  it  consists  of  rafters, 
resting  upon  a  plate  framed  into  the  tie-  or  ceiling-beam  ;  this  beam  is  sup- 
ported by  a  suspension-rod,  k,  from  the  ridge,  if  supported  from  below,  the  rod 
is  omitted.  If  neither  ceiling  nor  attic  floor  are  necessary,  an  iron  tie-rod  con- 
necting the  plates  is  sufficient.  The  rafters  are  to  be  spaced  from  1  to  2  feet 
centres,  and  the  tie-beams  at  intervals  of  from  6  to  8  feet ;  the  roof  cover  to  be 
of  boards  nailed  to  the  rafters.  This  form  of  construction  is  sufficient  for  any 
roof  of  less  than  25  feet  span,  and  of  the  usual  pitch,  and  may  be  used  for  a 
40-foot  span  by  increasing  the  depth  of  the  rafters;  deep  rafters, should  always 
be  bridged.  By  the  introduction  of  a  purlin  extending  beneath  the  centre 


ENGINEERING   DRAWING. 


487 


of  the  rafter,  supported  by  a  brace  to  the  foot  of  the  suspension-rod,  as  shown 
in  dotted  line,  the  depth  of  the  rafters  may  be  reduced.     If  the  tie-beam, 


FIG.  1152. 


which  is  also  a  ceiling  and  floor  beam,  be  below  the  plate  some  2  to  4  feet  the 
thrust  of  the  roof  is  resisted  (Fig.  1153)  by  bolts,  b  b,  passing  through  the  plate 
and  the  beam,  and  by  a  collar-plank,  C,  spiked  on  the  sides  of  the  rafters,  high 
enough  above  the  beam  for  head-room.  For  roofs  f  pitch  and  under  20  feet 
span  the  bolts  are  unnecessary,  the  collar  alone  being  sufficient. 

Fig.  1151  represents  a  roof,  a  larger  span  than  Fig.  1150  ;  the  frame  may 
be  made  very  strong  and  safe  for  roofs  of  60  feet  span.  King-bolts  or  suspen- 
sion-rods are  now  oftener  used  than  posts,  with  a  small 
triangular  block  of  hard  wood  or  iron,  at  the  foot  of 
the  bolts,  for  the  support  of  the  braces.  The  objec- 
tion to  this  form  of  roof  is  that  the  framing  occupies 
all  the  space  in  the  attic ;  on  this  account  the  form, 
Fig.  1152,  is  preferred  for  roofs  of  the  same  span,  and 
is  also  applicable  to  roofs  of  at  least  75  feet  span,  by 

the  addition  of  a  brace  to  the  rafter  from  the  foot  of  the  queen-bolt.  The  col- 
lar-beam (Fig.  1155)  is  also  trussed  by  the  framing  similar  to  Fig.  1151. 

In  many  church  and  barn  roofs 
the  tie-beam  is  cut  off   (Fig.  1154), 


T 

FIG.  1153. 


FIG.  1154. 


FIG.  1155. 


488 


ENGINEERING  DRAWING. 


the  queen-post  being  supported  on  a  post,  or  itself  extending  to  the  base,  with 
a  short  tie-rod  framed  into  it  from  the  plate. 

Figs.  1156  and  1157  are  representations  of  the  feet  of  rafters  on  an  enlarged 
scale.     In  Fig.  1156  the  end  of  the  rafter  does  not  project  beyond  the  face  of 
the  plate ;  the  cove  is  formed  by  a  small  tri- 
angular, or  any  desirable  form  of  plank,  se- 


FIG.  1156. 


FIG.  1157. 


FIG.  1158. 


cured  to  the  plate.  The  form  given  to  the  foot  of  the  rafter  is  called  a  crow- 
foot. In  Fig.  1157  the  rafter  itself  projects  beyond  the  plate  to  form  the  cov- 
ing. Fig.  1158  represents  a  front  and  side  elevation  and  plan  of  the  foot  of 
a  main  rafter,  showing  the  form  of  tenon,  in  this  case  double ;  a  bolt,  passing 
through  the  rafter  and  beam,  retains  the  foot  of  the 
former  in  its  place.  Fig.  1159  represents  the  foot  of  a 
main  rafter,  with  a  wooden  shoe  too  short  at  a,  outside 
of  the  rafter  ;  it  should  be  framed  as  in  Fig.  1158.  • 


FIG.  1159. 


r ,  _,,    ir^ri 

Jo       n       o    I 

/  '  ^'     '  -1  '  t 


FIG.  1160. 


FIQ  1161. 


FIG.  1162. 


Roofs  may  be  very  neatly  and  strongly  framed  by  the  introduction  of  cast- 
iron  shoes  and  abutting  plates  for  the  ends  of  the  braces  and  rafters.    Fig.  1160 


FIG.  1163. 


FIG.  1164. 


represents  the  elevation  and  plan  of  a  cast-iron  king-head  for  a  roof  similar  to 
Fig.  1151  ;  Fig.  1161,  that  of  the  brace-shoe ;  Fig.  1162,  that  of  the  rafter-shoe 


ENGINEERING  DRAWING. 


489 


FIG.  1165. 


for  the  same  roof ;  Fig.  11G3,  the  front  and  side  elevation  of  the.  queen-head 
of  roof  similar  to  Fig.  1152  ;  and  Fig.  1164,  elevation  and  plan  of  queen  brace- 
shoe.  Fig.  1165  represents  the  section  of  a  rafter-shoe 
for  a  tie-rod ;  the  side  flanges  are  shown  in  dotted  line. 

On  the  size  and  the  proportions  of  the  different 
members  of  a  roof  :  Tie-beams,  usually  serving  a  double 
purpose,  are  affected  by  two  strains  :  one  in  the  direc- 
tion of  their  length,  from  the  thrust  of  the  rafters  ;  the 
other  a  cross-strain,  from  the  weight  of  the  floor  and 

ceiling.  In  estimating  the  size  necessary  for  the  beam  the  thrust  need  not  be 
considered,  because  it  is  always  abundantly  strong  to  resist  this  strain,  and  the 
dimensions  are  to  be  determined  as  for  a  floor-beam  merely,  each  point  of  sus- 
pension being  a  support.  When  tie-rods  are  used,  the  strain  is  in  the  direction 
of  their  length  only,  and  their  dimensions  can  be  calculated,  knowing  the  pitch, 
span,  and  weight  of  the  roof  per  square  foot,  and  the  distance  apart  of  the  ties, 
or  the  amount  of  surface  retained  by  each  tie. 

The  weight  of  the  wood-work  of  the  roof  may  be  estimated  at  40  pounds 
per  cubic  foot ;  slate  at  7  to  9  pounds,  shingles  at  1^-  to  2  pounds  per  square 
foot.  The  force  of  the  wind  may  be  assumed  at  15  pounds  per  square  foot. 
The  excess  of  strength  in  the  timbers  of  the  roof,  as  allowed  in  all  calculations, 
will  be  sufficient  for  any  accidental  and  transient  force  beyond  this.  Knowing 
the  weights,  pressures,  and  their  directions  on  parts  of  a  roof,  their  stresses  may 
be  determined  by  the  parallelogram  of  forces  and  dimensions  proportioned  to 
the  strength  of  the  materials  of  which  the  roof  is  composed.  It  will  generally 
be  sufficient  for  the  draughtsman  to  have  practical  examples  of  construction  to 
draw  from.  Dimensions  are  therefore  given  of  the  parts  of  wooden  roofs  already 
illustrated.  Beams  are  usually  proportioned  to  the  weight  that  they  are  to  sus- 
tain in  floors  and  load,  but  where  tie-rods  are  used,  the  stress  upon  them  may 
be  determined  by  the  following  rule  : 

Rule. — Multiply  one  half  the  weight  of  the  roof  and  load  by  one  half 
the  span,  and  divide  the  product  by  the  rise  or  height  of  ridge  above 
eaves. 

Gwilt,  in  his  "Architecture,"  recommends  the  following  dimensions  for  por- 
tions of  a  roof : 


Span. 

Form  of  Roof,, 

Rafters. 

Braces. 

Posts. 

Collar-beams. 

Feet. 

Inches. 

Inches. 

Inchei. 

Inchtl. 

25 

Fig.  1151, 

5x4 

5x3 

5x5 

30 

i< 

6x4 

6x3 

6x6 

35 
45 

Fig.  1152, 

5x4 
6x5 

4x2 
5x3 

4x4 
6x6 

7x4 
7x6 

50 

2  sets  of  queen-posts, 

8x6 

5x3 

j    8x8 
]    8x4 

9x6 

60 

it                   u 

8x8 

6x3 

j  10x8 
]  10x4 

11x6 

These  dimensions,  for  rafters,  are  somewhat  less  than  the  usual  practice  in 
this  country  ;  no  calculations  seem  to  have  been  made  for  using  the  attic.  An 
average  of  framed  roofs  here  would  give  the  following  dimensions  nearly  :  30 
feet  span,  8x5  inches ;  40  feet,  9  x  6  ;  50  feet,  10  x  7  ;  60  feet,  11x8;  col- 


490 


ENGINEERING  DRAWING. 


lar-beams  the  same  size  as  main  rafters.     Roof -frames  from  8  to  12  feet  from 
centre  to  centre. 

Dimensions  for  jack-rafters,  15  to  18  inches  apart : 


For  a  bearing  of  12  feet 6x3  inches. 

«  "  10    "    .      .  9x3       " 


For  a  bearing  of    8  feet. . .     4x3  inches. 
20    "    .    .   10x3       " 


Purlins  : 

Length  of  bearing. 

Distances  apart  in  Feet. 

Feet. 
8 

10 
12 

6 
7x5 
9x5 
10x6 

8 
8x5 
10x5 
11x6 

10 
9x5 
10x6 
12x7 

12 
9x6 
11x6 
13x8 

The  pressure  on  the  plates  is  transverse  from  the  thrust  of  the  rafters,  but 
in  all  forms  except  Fig.  1150,  owing  to  the  notching  of  the  rafters  on  the  pur- 
lins, this  pressure  is  inconsiderable.  The  usual  size  of  plates  for  Figs.  1150 
and  1151  is  6  X  6  inches.  The  dimensions  of  rafters  depend  on  the  distances 
between  their  supports  and  between  centres.  The  depth  in  all  such  cases  to  be 
greater  than  the  width ;  2  to  6  inches  may  be  taken  as  the  width,  8  to  12  for 
the  depth. 

In  the  framing  of  roofs  it  is  now  customary,  for  roofs  of  mills,  to  omit  pur- 
lins, jack-rafters,  and  plates,  and  make  the  roof-boards  of  plank  stiff  enough  to 
supply  their  places,  from  2"  to  3"  thick  (according  to  the  space  between  the 
frames),  tongued  and  grooved,  and  strongly  spiked  to  the  main  rafters.  There 
is  no  need  of  plates ;  the  plank  forms  a  deep  beam,  and,  if  the  ends  of  the 
frame  are  secured,  there  is  no  need  of  intermediate  ties. 

Joinings. — As  timber  can  not  always  be  obtained  of  sufficient  lengths  for 
the  different  portions  of  a  frame,  or  to  tie  the  walls  of  a  building,  it  is  often 
necessary  to  unite  two  or  more  pieces  together  by  the  ends,  called  scarfing  or 
lapping.  Fig.  1166  is  a  most  common  means  of  lapping  or  halving  employed 
when  there  is  not  much  longitudinal  stress,  and  when  a  post  is  to  be  placed 
beneath  the  lower  joint. 

For  beams  with  a  butt  joint  under  the  last  condition  joint  bolts  (Fig.  1167) 
are  often  used  in  which  the  ends  of  the  timber-  are  squared  and  held  together 
by  bolts  inserted  in  holes  central  of  the  beams  with  the  nuts  in  side-pockets,  in 
which  one  is  screwed  up  by  turning  the  bolt  and  the  other  by  a  cold  chisel. 

Fig.  1168  is  a  long  scarf,  in  which  the  parts  are  bolted  through  and  strapped, 
suitable  for  tie-beams.  Joints  (Figs.  1169,  1170,  and  1171)  are  also. often  made 

V 


FIG.  1166. 


FIG.  1167. 


FIG.  1168. 


by  abutting  the  pieces  together  and  bolting  splicing-pieces  on  each  side  ;  still 
further  security  is  given  by  cutting  grooves  in  both  timbers  and  pieces  and 
driving  in  keys,  k  k. 

Iron  Roofs. — Roofs  of  less  than  30  feet  span  are  often  made  of  corrugated 
iron  alone,  curved  into  a  suitable  arc,  and  tied  by  bolts  passing  through  -the 
iron  about  2  to  4  feet  above  the  eaves. 


ENGINEERING   DRAWING. 


491 


Fig.  1172  represents  the  half  eleyation  of  an  iron  roof  of  a  forge  at  Paris  ; 
Figs.  1173,  1174,  and  1175,  details  on"  a  larger  scale.     This  is  a  common  type  of 


FIG.  1169. 


f       •! 

8    i1  - 

a    T 

,i     i       1 

1; 
!' 

—  m  ^  — 

;! 

—  5  It  U  » 

9  j!  E 

>\ 

£•  —  '•       • 

HI 


e  o  » 

o  o  o    » 


FIG.  1170 


FIG.  1171. 


iron  roof,  consisting  of  main  rafters,  R,  of  the  I-section  (Fig.  1175),  trussed  by 
a  suspension-rod,  and  tied  by  another  rod.  The  purlins  are  also  of  I-iron,  se- 
cured to  the  rafters  by  pieces  of  angle-iron  on  each  side  ;  and  the  roof  is  cov- 
ered with  either  sheet-iron  resting  on  jack-rafters,  or  corrugated  iron  extending 


from  purlin  to  purlin.     The  rafter-shoe,  A,  and  the  strut,  S,  are  of  cast- 
iron  ;  all  the  other  portions  of  the  roof  are  of  wrought-iron.     In  Ameri- 
can practice  it  is  usual  to  make  the  strut  of  wrought-iron,  with  a  single 
pin  connection  at  its  foot,  instead  of  as  in  the  figure. 
The  surface  coverec1.  by  this  particular  roof  is  53  metres  (164  feet)  long  and 

30  metres  (98£  feet)  w'de.     There  are  eleven  frames,  including  the  two  at  the 

ends,  which  form  the  gables. 


492 


ENGINEERING  DRAWING. 


The  following  are  the  details  of  the  dimensions  and  weights  of  the  different 
parts  : 

Pounds. 

2  rafters,  0'72  feet  deep ;  length  together,  99-1  feet 1,751 

5  rods,  0-13  feet  diameter ;  length  together,  131-4  feet 882 

16  bolts,  0-13  feet  diameter 79 

8  bridle-straps,  0-24  x  0-05 123 

2  pieces,  0-46  thick,  connecting  the  rafters  at  the  ridge,  i  gg 

4  pieces,  0'46  thick,  at  the  foot  of  the  strut )  " 

4  pieces,  0*36  thick,  uniting  the  rafters  at  the  junction  in  the  strut — together 

with  their  bolts  and  nuts 176 

2  cast-iron  struts 308 

2  rafter-shoes 287 

Total  of  one  frame 3,694 

16  purlins,  1  ridge-iron,  each  0'46  deep,  17'2  long 2,985 

Bolts  for  the  same 64 

16  jack-rafters,  I-iron,  (M6  deep 2,489 

"Weight  of  iron  covering,  including  laps,  per  square  foot 2-88 

Eoofs  are  sometimes  made  with  deep  corrugated  main  rafters  with  flat  iron 
between,  or  purlins  and  corrugated  iron  for  the  covering.     The  great  objec- 
tion to  iron  roofs  lies  in  the  con- 
densation of  the  interior  air  by  the 
outer  cold,   or,   as    it  is    termed, 
sweating ;   on    this   account,    they 
are  seldom  used  for  other  buildings 


than  boiler-houses  or  depots,  except  a  ceil- 
ing be  made  below  to  prevent  the  contact 
of  the  air  inside  with  the  iron. 

Fig.  1176  is  an  elevation  of  one  of  the 


FIG.  1174. 


s 


FIG.  1175. 


three  panels  of  one  of 

the  cast-iron  girders  fo/  connecting  the  columns,  and  carry- 
ing the  transverse  main  gutters,  which  supported  the  roof 
of  the  Crystal  Palace  of  the  English  Exposition  of  1851. 
Figs.  1177  to  1181  are  sections  of  various  parts  on  an  en- 
larged scale.  The  depth  of  the  girder  was  3  feet,  and  its 
length  was  23  feet  3f  inches.  Tin  sectional  area  of  the 
bottom  rail  and  flange  in  the  centre  (Fig.  1178)  was  6f 
square  inches ;  the  width  of  both  bottom  and  top  rail  (Fig. 


ENGINEERING  DRAWING. 


493 


1177)  was  reduced  to  3  inches  at  their  extremities.  The  weight  of  these  girders 
was  about  1,000  pounds,  and  they  were  proved  by  a  pressure  of  9  tons,  dis- 
tributed on  the  centre  panel. 


FIG.  lire. 


A  second  series  of  girders  were  made  of  similar  form,  but  of  increased  di- 
mensions in  the  section  of  their  parts.     Their  weight  averaged  about  1,350 


FIG.  1179. 


FIG.  1180. 


FIG.  1181. 


pounds,  and  were  proved  to  15  tons.  A  third  series  weighed  about  2,000 
pounds,  and  were  proved  to  22%  tons. 

Figs.  1182  and  1183  are  sections  and  details  of  the  trusses  for  sustaining  the 
roof  and  floor  of  the  English  High  and  Latin  School  Gymnasium,  Boston, 
Massachusetts.  The  object  of  sustaining  the  gymnasium -floor  by  rods  was  to 
secure  a  drill-hall  for  the  military  exercises  of  the  school,  and  trusses  were  de- 
signed to  have  sufficient  strength  to  resist  the  vibration  of  the  floor.  As  the 
trusses  were  to  be  in  sight,  a  central  cloumn  of  cast-iron  was  introduced  to  sus- 
tain the  centre  of  the  top  chord,  with  lattice  between  the  main  diagonals  to 
enable  them  to  act  as  counters,  and  a  3^-inch  gas-pipe  for  horizontal  bracing- 
struts.  The  floor-sustaining  rods  all  have  upset  ends,  and  their  tops  pass 
through  ornamental  foliated  castings,  but  their  connection  with  the  trusses  is 
wholly  of  wrought-iron. 

The  top  chords  consist  of  two  9-inch  channel-irons  weighing  50  pounds  per 


494 


ENGINEERING  DRAWING. 


yard,  and  one  plate  12  X  f  inches.     The  end-posts  have  the  same  section. 
The  bottom  chord  consists  of  four  bars  2$  X  I  inch  at  the  shallow  end  of  the 


Fm.  1183. 


truss,  and  four  bars  2£  X  f  of  an  inch  at  the  deep  end  of  the  truss.  The  diago- 
nals are  two  bars  3x1  inch  at  deep  end  of  truss,  and  two  bars  3  X  £  inch  at 
shallow  end  of  truss.  The  pins  are  all  2^  inches  diameter.  The  trusses  were  de- 
signed and  constructed  by  D.  H.  Andrews,  C.  E.,  of  the  Boston  Bridge  Works. 

In  order  to  secure  free  space  in  the  room  beneath  the  roof,  a  roof  or  bridge 
truss  may  be  constructed  above,  and  the  roof  framed  as  a  floor  suspended  from 
it,  with  such  pitch  as  is  requisite  to  shed  rainfall. 

Figs.  1184  to  1189  are  the  elevation  and  details  for  an  iron  roof-truss,  for 
wood,  slate,  or  corrugated  iron  covers,  built  by  the  Missouri  Valley  Bridge  and 
Iron  Works,  A.  S.  Tulloch,  engineer. 

Fig.  1190  is  a  half  cross-section  of  a  two-story  freight-shed  for  the  New 
York,  Lake  Erie  and  Western  Eailroad,  a  simple  and  cheap  construction  of 
wood,  readily  framed  and  put  together.  The  shed  rests  upon  a  pile-dock. 
The  platform  for  the  reception  of  freight  is  4  feet  above  the  dock-planking 
and  about  26  feet  wide,  with  occasional  inclined  runs  for  the  transfer  of  freight 
to  or  from  vessels. 


ENGINEERING  DRAWING. 


495 


TY 


496 


ENGINEERING  DRAWING. 


CROSS-SECTION  OF  ONE   HALF  OF  A  FREIGHT-SHED,  NEW  YORK,   LAKE  ERIE 
AND  WESTERN  RAILROAD. 


ENGINEERING  DRAWING. 


497 


Fig.  1191  is  a  section  of  the  Baltimore  and  Ohio  coaling  bins  for  loco- 
motives. 

Piers. — Fig.  1192  is  an  elevation  of  a  pile-pier  for  a  bridge.  Tenons  are 
cut  on  the  top  of  the  piles,  and  a  cap  (a)  mortised  on.  The  two  outer  piles 


FIG.  1191. 


driven  in  an  inclined  position,  and  the  heads  bolted  to  the  piles  adjacent.  The 
piles  are  made  into  a  strong  frame  laterally  by  the  planks  b  and  c,  and  plank- 
braces  dd  on  each  side  of  the  piles,  bolted  through.  The  string-pieces  of  the 


n     n       rr 


n       n     n. 


5^1 


ii 


Jc 


FIQ.  1192. 


bridge  rest  on  the  cap.     Longitudinal  braces  are  often  used,  their  lower  ends 
resting  on  the  plank  b — which  should  be,  then,  notched  on  to  the  piles — and 
their  upper  ends  coming  together,  or  with  a  straining-piece  between,  beneath 
33 


498 


ENGINEERING  DRAWING. 


the  string-pieces,  acting  not  only  as  supports  to  the  load,  but  also  as  braces  to 
prevent  a  movement  forward  of  the  frames.  As  the  tendency  of  a  moving 
train  is  to  push  forward  the  structure  on  which  it  is  supported,  in  railway- 
bridges  especially,  great  care  is  taken  to  brace  the  structure  in  every  way — ver- 
tically and  horizontally,  laterally  and  longitudinally.  If  the  plank  c  be  a  tim- 
ber-sill, and  the  piles  beneath  be  replaced  by  a  masonry-pier,  the  structure  will 
represent  a  common  form  of  trestle. 

Fig.  1193  is  an  illustration  of  a  trestle-bent  supporting  a  span  of  the  Brook- 
lyn Elevated  Kailroad  over  its  coal-yard.     The  timber  is  of  yellow  pine  of  the 


FIG.  1193. 


dimensions  shown  ;  the  ties  are  extended  beyond  the  guard-rail  on  one  side  to 
support  a  plank  walk.  The  bent  is  about  15  feet  high. 

Bridge- Trusses. — Whatever  maybe  the  form  of  truss  or  arrangement  of 
the  framing,  provided  its  weight  is  supported  only  at  the  ends,  the  tension  of 
the  lower  chord,  or  the  compression  of  the  upper  chord  at  centre,  may  be  de- 
termined by  this  common  rule  : 

Rule. — The  sum  of  the  total  weight  of  the  truss,  and  the  maximum  dis- 
tributed load  which  it  will  be  called  on  to  bear,  multiplied  by  the  length  of  the 
span,  and  divided  by  8  times  the  depth  of  the  truss  in  the  middle,  the  quo- 


ENGINEERING  DRAWING. 


499 


tient  will  V  the  tension  of  lower  chord  and  compression  of  upper  at  the  mid- 
dle. In  net  rly  all  the  forms  of  diagonal  bracing,  if  the  uniform  load  be  con- 
sidered as  acting  from  the  centre  toward  each  abutment,  each  tie  or  brace 
sustains  the  whole  weight  between  it  and  the  centre,  and  the  strain  is  this 
weight  multiplied  by  the  length  of  tie  or  brace,  divided  by  its  height.  Any 
diagonals,  equally  distant  from  the  centre,  sustain  all  the  intermediate  load  :  if 
rods,  as  in  Fig.  1195,  by  tension ;  if  braces,  as  in  Fig.  1194,  by  compression. 
It  follows,  therefore,  that  in  all  these  trusses  the  upper  and  lower  chords 


Fio.  1194. 


FIG.  1195. 


should  be  stronger  at  the  centre  than  at  the  ends,  while  diagonals  should  be 
largest  at  the  abutments.  Unless  the  weight  of  the  bridge  is  great  compared 
with  the  moving  loads,  counter-braces  become  necessary. 

The  general  rule  adopted  in  the  construction  of  the  Howe  truss  is,  to  make 
the  height  of  the  truss  one  eighth  of  the  length  up  to  60  feet  span ;  above  this 
span  the  trusses  are  21  feet  high,  to  admit  of  a  system  of  lateral  bracing,  with 
head  clearance  for  a  person  standing  on  the  top  of  a  freight-car.  From  175 
feet  to  250  feet  span,  height  of  truss  gradually  increased  up  to  25  feet.  Moving 
load  for  single-track  railroad-bridge  calculated  at  2  tons  per  running  foot. 

Wooden  Truss- Bridges. — Fig.  1194  is  the  elevation  of  a  few  panels  of  a 
Howe  truss,  and  Fig.  1195  of  a  Pratt  truss.  The  Howe  truss  is  by  far  the  most 
popular  of  all  wooden  trusses,  being  readily  framed  and  put  together,  uniting 
great  strength  with  simplicity  of  construction. 

Fig.  1196  is  the  side  elevation  of  three  of  the  five  panels  of  a  Howe  truss 
highway-bridge  of  the  New  York,  Lake  Erie  and  Western  Railroad.  Fig.  1197 
is  a  cross-section.  There  is  a  section  of  3"  plank  laid  close,  and  another  beneath, 
laid  with  spaces ;  these  planks  are  laid  diagonally  across  the  floor-beams,  and 
at  right  angles  to  each  other,  to  act  as  lateral  bracing.  Fig.  1198  is  the  details 
of  the  abutment  end  of  bridge ;  the  foot  of  the  brace  rests  on  a  cast-iron  shoe. 
The  length  over  all — that  is,  including  the  portions  on  the  abutment — is  81'  2", 
or  75  feet  between  abutments,  usually  designated  as  the  span. 

Figs.  1199,  1200,  and  1201  are  the  side  elevation,  floor  cross-section,  and! 
plan  of  floor  and  bottom  chord  of  three  of  the  twelve  panels  of  a  single-track 
railway  Howe  truss.  Their  length  is  each  10'  10^-".  The  centre  braces  are- 
two,  7"  X  10" ;  the  centre  rods  three,  1£"  diameter.  The  counters,  each  one- 
6"  X  8" ;  lateral  brace,  top  and  bottom,  6"  X  6" ;  rods  !£" ;  top  chord,  four 
pieces,  7"  X  12" ;  bottom  chord,  four  pieces,  7"  X  15" ;  floor-beams,  7"  X  16". 
The  shoes,  splices,  and  blocks  between  chord-timbers  are  of  cast-iron.  In  the 
earlier  practice  the  angle-blocks  were  of  oak,  and  the  splices  made  as  in  Fig.. 
1202.  Both  were  satisfactory. 


500 


ENGINEERING  DRAWING. 


ENGINEERING  DRAWING. 


501 


77 


\ 


FIG.  1201. 


502 


ENGINEERING  DRAWING. 


ENGINEERING  DRAWING. 


503 


) 

i 

_i 

Cj  —  '           '    '           "~ 

Combination  Truss.— Fig.  1203  is  the  elevation  and  details  of  a  combina- 
tion or  composite  truss,  which  owes  its  name  to  the  use  of  the  two  materials, 
wood  and  wrought-iron,  the 
tension  members  being  of 
iron  and  the  compression  of 
wood.  This  class  is  entirely 
American  in  practice,  and 
embodies  an  essentially  Amer-  Fio.  1202. 

ican  feature, pin  connections. 

The  bridge  illustrated  is  a  double  intersection  combination  through  bridge,  de- 
signed by  L.  L.  Buck,  0.  E.,  for  the  Northern  Pacific  Eailroad  crossing  the 
Yakima  River  in  the  State  of  Washington.  The  span  is  300  feet  between  cen- 
tres of  end  pins,  and  is  divided  into  15  panels  of  20  feet  each.  The  height  from 
centre  to  centre  of  chords  is  40  feet,  and  width  20  feet  from  centre  to  centre. 

The  cheapness  of  timber  and  the  distance  from  which  iron  had  to  be 
secured  made  it  advisable  to  construct  this  form  of  bridge.  The  timbers 
are  heavy  and  framed,  so  that  no  two  pieces  are  in  direct  contact,  and  provision 
has  been  made  by  which  iron  can  at  any  time  be  substituted  for  the  wood. 

Iron  Bridges. — When  the  span  is  of  moderate  extent,  the  load  can  be  safely 
carried  by  beams  put  together  at  the  works  and  transferred  to  the  road  in 
complete  form.  Plate  or  lattice  girders  are  used,  put  together  with  rivets. 

Fig.  1204  is  a  plan  side  and  end  elevation  of  a  plate-girder  bridge  on  the 
New  York,  New  Haven  and  Hartford  Railroad.  The  bridge  is  for  a  single  line 
of  rails,  crossing  a  highway  on  a  skew.  The  following  is  the  bill  of  material : 

LIST  OF   MATERIAL  FOR  PLATE-GIRDER  BRIDGE,   WOODMONT,  CONN. 


NUMBER. 

Section. 

Length. 

Weight,  pounds. 

32 

6"x6"    xft'Ls. 

47'     1" 

40,530 

8 

5"  x  3|"  x  |"    Ls. 

15'  10" 

2,140 

4 

5"  x  3"    x  jY  Ls. 

19'     9" 

884 

8 

4"x3"   xf"    Ls. 

15'  10" 

1,063 

68 

3"x3"    xf"    Ls. 

15'  10" 

OQ'     1A" 

7,538 

O  w-ij' 

14 
4 

U             4t               U            1( 

yy  10 
23'     0" 

-6,0/CO 

644 

4 

11         it          «        « 

27'    0" 

756 

4 

3£"  x  -f-J  "  bars. 

24'    6" 

786 

38 

3"    xf}'     " 

24'    6" 

6,405 

Total  Ls  and  bars 

63,572 

16 

8 

48"    x  T7/  plate. 
48"   xf" 

15'     8i" 

15'  sr 

17,590 
7,419 

16 

20±"  x  1" 

2'     0* 

1,880 

1 

15"    xf" 

25'     6" 

478 

1 

10'     3" 

192 

6 

14"    xf" 

18'     3" 

1,916 

1 

23'     0" 

402 

16 

i 

21'    7" 

6,043 

16 

4 

4'     1" 

1,143 

16 

4 

1'     5" 

396 

16 

14"     XrY 

26'  10" 

8,766 

32 

•*-           **      b 

23'     5f" 

15,342 

2 

4 

29'     0" 

1,184 

4 

1°*"  x  -7  " 

24'     6" 

1,786 

2 

12'    xf" 

22'     6" 

675 

Total  weight 

of  bridge,  exclusive  of  rivet  he 

128,784 

504: 


ENGINEERING  DRAWING. 


o  Oooooooooooo    o 


5(0,8 


,5(0,8  xj%  x,8  "'mi  Z 
",.%  ',8  '.8  »T  o 


E  E  K 


ENGINEERING  DRAWING. 


505 


Figs.  1205, 1206,  and  1207  are  plans,  elevations,  and  details  of  a  plate-girder 
river  bridge  built  for  the  New  York,  New  Haven  and  Hartford  Railroad  by  the 
Berlin  Iron  Bridge  Company  within  the  limits  of  the  builders'  yards.  It  is  a 
single-track  bridge  102'  9"  from  end  to  end  of  girders  fixed  at  one  end  and  sup- 
ported on  rollers  at  the  other. 

Figs.  1208,  1209,  and  1210  are  respectively  the  outside  elevation,  top  lateral 
bracing,  and  cross-frame  of  a  single-track  lattice-deck  span  designed  by  the 
Pho3nix  Bridge  Company.  The  bridge  is  70  feet  long  over  all,  and  divided 
into  four  panels,  two  of  which  are  shown  in  the  figure ;  there  are  five  cross- 
frames  attached  to  the  vertical  posts.  Each  truss  is  built  in  two  sections, 
spliced  as  shown,  the  blackened  circles  indicating  holes  through  which  the 
connecting  rivets  will  be  driven  in  the  field.  The  girders  are  7'  11"  deep,  and 
placed  6'  6"  apart.  The  ties  of  the  railroad  rest  immediately  on  the  top  chord. 

BILL  OF  MATERIAL. 

Two  lattice  girders  and  bracing  (Figs.  1208,  1209,  1210). 


DESCRIPTION. 

Sections. 

Sizes. 

Length. 

Weight 
per  foot. 

No.  of 
pieces. 

Remarks. 

Weight, 
pounds. 

Top  chords  

Angles. 

a 

Plates. 

t 
t 

i 

it 
u 

u 
H 

at  4 

6x4 
6x4 
6x4 
6x4 
6x4 
5x31 
5x3£ 
4x3 
5  x  3^ 
5x31 

5  x  31 
3x3 
3x3 
3x3 
3x3 
3x3 
12x   f 
12x    f 
12x   f 
12x   f 
12x   f 
12  x   ft 
llx   f 
8x    i 
6x   H 
12x   f 
10  x    f 
10  x   | 
10  x   ft 
9x   f 
9x   | 
9x   ft 
7x   ft 
10  x   f 
9x   f 
9x   ft 
6x   H 
6x   i 
3x   ft 

32'    4" 
37'    7" 
32'    4" 
37'    7" 
11'    7" 
11'   3" 
11'    3" 
7'  10" 
9'    4" 
9'    4" 

0'    9" 
5'    5" 
9'    7" 
9'    3" 
8'    9" 
6'    2" 
32'    5" 
37'   8" 
15'    9" 
21'    0" 
2'    0" 
2'    2" 
2'    2" 
2'    2" 
11'    6" 
1'   8' 
1'    4" 
1'    2" 

r  o" 

1'    4" 
0'    6" 
1'   0" 
0'    8" 
2'    1" 
2'    1" 
1'    9" 
0'    9" 
1'    0" 
0'    9" 

16-3 
16-3 
15-0 
15-0 
16-7 
9-0 
9-0 
6-7 
14-0 
11-3 

10-0 
6-0 
6-0 
6-0 
6-0 
6-0 
30-0 
30-0 
30-0 
30-0 
30-0 
17-5 
13-8 
13-3 
13-8 
30-0 
12-5 
12-5 
10-4 
11-3 
11-3 
9-4 
7-3 
12-5 
11-3 
9-4 
13-8 
10-0 
1-9 

4 
4 
4 
4 
8 
8 
8 
20 
2 
6 

2 
4 
2 
6 
10 
10 
2 
2 
2 
2 
4 
4 
8 
8 
8 
4 
2 
2 
20 
4 
4 
6 
5 
2 
2 
4 
8 
8 
8 

2,106 
2,452 
1,938 
2,256 
1,547 
792 
792 
1,049 
261 
633 

14 

129 
115 
333 
525 
372 
1,945 
2,262 
945 
1,260 
240 
152 
242 
234 
1,270 
204 
25 
23 
208 
38 
16 
40 
24 
52 
39 
66 
83 
80 
13 
593 

Bottom  chords      

u                 u 

Diagonals  

Cut. 

u 

Verticals  

Top  laterals  

Cut. 

« 

Top  lateral. 

Connecting  angles  for 
end  bottom  laterals. 
Struts  

Bottom  laterals 

Cross  bracing 

Top  and  bottom  struts. 
Web  for  top  chord  

Web  for  bottom  chord. 

U             U                 It                      .1 

Splice  plates  

u              u 

U                    !( 

Diagonals  

Wall  plates  

Gussets  

Cut. 

H 

Sway  frame. 
Cut. 
Top  lateral  cut. 
Bottom  lateral  cut. 
Sway  frame. 
Top  lateral. 
Top  lateral  cut. 
Bottom  lateral. 

<t 

i 

Fillers..  . 

« 

1,482  pairs  rivet  heads 
Total 

25,368 

506 


ENGINEERING  DRAWING. 


%<x — *-. 


.*.ti«»nu 

*.»  si  Su'iailps  I. 


I,  ^^^BiBB^adboEES 


T 


S    £ 

"\«  G 
2X"  ® 


•n 

^3 


o 
o 

Z    jri 


ENGINEERING  DRAWING. 


507 


3 


/ 

'QA  'cLJH  "1 

508 


ENGINEERING  DRAWING. 


ENGINEERING  DRAWING. 


509 


510 


ENGINEERING  DRAWING. 


Fig.  1211  is  a  partial  plan  and  elevation  of  a  highway  bridge  built  by  the 
King  Bridge  Company.  It  is  pin  connected,  with  floor-beams  riveted  to  the 
posts  above  the  pin.  Fig.  1212  is  a  section,  and  Fig.  1213  the  end  post,  with 
part  of  the  portal  bracing.  The  lateral  bracing  of  both  top  and  bottom  chords 
is  designed  to  take  the  stresses  arising  from  wind  pressure.  Each  system  forms 
with  the  respective  chords  of  both  trusses  an  independent  truss,  for  which  the 
stresses  are  calculated  and  the  members  proportioned.  The  wind  stresses  of 
the  upper  system  are  carried  through  the  portal  bracing  and  end  posts  to  the 
abutments,  and  those  of  the  lower  lateral  bracing  immediately  to  the  end  shoes 
and  abutments ;  the  floor-beams  are  compression  members. 

Fig.  1214  contains  drawings  in  detail  of  a  railroad  bridge  through  span  on 
the  Lima  and  Oroya  Kailroad,  and  is  a  good  example  of  the  usual  American 
practice.  It  is  a  single-intersection  Pratt  truss  through  span,  built  of  iron  and 
steel.  The  length  from  centre  to  centre  of  end  pins  is  180  feet,  with  eight 
panels,  each  22  feet  6  inches ;  depth  of  truss  26  feet  and  distance  between 
trusses  16  feet.  The  bridge  is  of  the  pin-connected  type,  the  tension  members 
being  steel  eye-bars,  and  the  compression  members  built  sections  of  plates  and 
angles.  The  floor- beams  are  riveted  to  the  posts  above  the  pins. 

Fig.  1215  is  a  side  elevation  of  an  angle  connection  of  end  brace  and  top  chord. 

Conventional  signs  of  riveting  will  be  found  in  the  Appendix. 

Fig.  1216  is  a  standard  pin-nut,  on  sale  in  sizes  from  1||"  to  7-^''  diameter 


Fio.  1215. 


FIG.  1216. 


of  pin;  Fig.  1215  is  an  example  of  its  use.  Fig.  1217  is  a  side  and  top  eleva- 
tion of  a  standard  clevis,  in  sizes,  changing  by  eighths  from  £"  to  3"  diam- 
eter of  bar. 

Figs.  1218,  1219,  and  1220  are  elevation,  plan,  and  detail  of  a  turn-table  as 

made  by  the  Passaic  Boiling  Mill  Company. 
The  table  is  entirely  centre-bearing,  and 
rests  on  a  hard  steel  base.  The  girders  are 
strongly  built  of  plates  and  angles  and  cover- 
plates,  and  connected  to  each  other  by 
frames  and  lateral  angle  bracing.  The  sizes 
vary  from  40  to  60  feet  in  length. 

Figs.  1221,  1222,  and  1223  are  section 
and  details  of  a  turn-table  as  made  by  the 
Greenleaf  Manufacturing  Company.  The 
conspicuous  feature  of  this  centre  is  the 
nest  of  rollers,  shown  on  a  larger  scale  in  Fig.  1222.  The  rolls  and  bearings 
are  made  of  good  quality  tool  steel  and  are  2^  inches  in  length  and  of  the 


FIG.  1217. 


ENGINEERING  DRAWING. 


511 


FIG.  1219. 


same  diameter  on  the  large  end  and  1^-  inch  in  diameter  on  the  small  end, 
and  run  free  in  the.  annular  groove.  Fig.  1223  is  the  end  carriage  of  the  same 
table. 


FIG.  1220. 


Fio.  1223. 


512 


ENGINEERING  DRAWING. 


1 11!11 

I  Jill  i 
o 


i 


ENGINEERING   DRAWING. 


513 


Figs.  1224  to  1228  are  illustrations  of  a  landing-bridge  common  at  New 
York  city  ferries.     Fig.  1224  is  a  longitudinal  section,  showing  a  section  of  the 

float,/,  with  its  lever  shown  at  one 
side  of  the  float  and  stone  coun- 
terpoise to  balance  the  weight  of  the 
bridge.  Fig.  1225  is  the  front  ele- 
vation, and  Fig.  1226  the  plan,  one 
half  in  planking  and  one  half  in 
framing.  There  are  two  chain- 
barrels,  on  each  side  of  the  bridge, 


FIG.  1229. 


FIG.  1230. 


worked  by  hand-wheels ;  on  the  outer  ones  are  the  chains  by  which  the  boat  is 
drawn  up  to  the  bridge ;  on  the  inner  ones  the  chains  by  which  the  bridge  is 
adjusted  to  the  load  on  the  boat,  and  by  which  a  part  of  the  weight  of  the 
bridge  is  held,  the  upper  ends  of  the  chains  being  attached  to  the  frame  over- 
34 


514 


ENGINEERING  DRAWING. 


head.  The  details  (Figs.  1227  and  1228)  in  section  and  plan  explain  the  con- 
struction of  the  land-hinge ;  a  cushion  of  rubber  is  introduced  into  the  joint 
to  modify  the  shock  caused  by  the  boat  striking  the  bridge,  and  a  flap  of 
wrought-iron  to  cover  the  joint,  for  protection  to  travel,  and  security  from  dirt. 


FIG.  1231. 


For  motives  of  economy  in  cost  or  space,  it  has  become  very  common  among 
engineers  to  construct  bridges  with  frequent  wrought-iron  piers  or  trestles  of 
great  height  rather  than  extended  truss  spans ;  one  of  the  most  remarkable  of 
these  is  the  Kinzua  Viaduct,  of  which  Fig.  1229  represents  a  single  pier  in  per- 
spective, with  details,  Fig.  1230. 

Fig.  1231  is  a  section  of  the  roadway  of  the  Eivermont  Bridge,  Lynchburg, 
Va.,  supported  by  similar  piers. 

Fig.  1232  is  the  elevation  of  a  bridge  over  the  Rio  Galisteo,  Apache  Canon, 
on  the  line  of  the  N.  M.  &  S.  P.  R.  R.  The  ends  of  the  bridge  rest  on  abut- 
ments on  opposite  sides  of  the  canon.  The  centre  line  of  the  track  is  on  a  ten- 
degree  curve,  and  is  14£  inches  off  the  centre  line  of  the  plate  girders  at  the 
centre  and  at  both  ends  of  the  span. 

Fig.  1233  is  an  elevation  of  one  bent  of  the  Third  Avenue  Elevated  Road, 
and  Fig.  1234  of  post  and  foundation  on  a  line  of  cross-section. 

The  foundations  for  the  columns  supporting  the  iron  structure  are  simply 
blocks  of  concrete,  capped  with  a  block  of  granite,  to  which  the  bases  of  the 
wrought-iron  columns  are  bolted.  In  soft  material  nine  piles  were  driven, 
capped  with  12-inch  timbers,  and  concrete  filled  in  around  them.  On  sandy 
bottom  concrete  was  placed  about  6  feet  below  the  surface.  On  a  portion  of 
the  line  a  right  of  way  50  feet  wide  was  secured  ;  the  tracks  were  supported  on 
plate  girders  resting  upon  piers  of  brick  masonry,  with  foundations  of  concrete 
below  the  surface  of  the  ground.  The  brick  piers  were  capped  with  granite. 


ENGINEERING  DRAWING. 


515 


Fig.  1235  is  an  elevation  and.  half  plan  of  the  foundations  of  a  post  on  the 
Brooklyn  Elevated  Kailroad,  with  a  base  of  cast-iron,  and  Fig.  1236  a  similar 


FIG.  1232. 


one,  with  a  wrought-iron  base.  In  neither  is  there  any  cap  except  that  con- 
nected with  the  post  base,  and  the  anchorage  is  to  cast-iron  plates  wholly  with- 
in the  masonry,  which  is  of  concrete. 

Fig.  1237  is  a  plan  of  one  of  the  stone  piers  of  the  railway  bridge  across 
the  Susquehanna  at  Havre  de  Grace.     To  lessen  as  much  as  possible  the  ob- 


c 

1       II      II       I/ 

J 

\ 

7~           ~^i 

"\                                     f 

S          i  —  — 

•  15-  >!«  13.5  * 

-<  23:  —»- 

FIG.  1233. 

struction  to  the  flow  of  the  stream,  it  is  usual  to  make  both  extremities  of  the 
piers  pointed  or  rounded.  Sometimes  the  points  are  right  angles ;  sometimes 
angles  of  60°;  often  a  semicircle,  the  width  of  the  pier  being  the  diameter; 
occasionally  pointed  arches,  of  which  the  radii  are  the  width  of  the  pier,  the 
centres  being  alternately  in  one  side,  and  their  arcs  tangent  to  the  opposite 
side.  None  of  the  stoneg  break  joint  at  the  angle  ;  this  is  important  in  oppos- 
ing resistance  to  drift-wood  and  ice.  It  is  not  unusual,  in  very  exposed  places, 
to  make  distinct  ice-breakers  above  each  pier  usually  of  strong  crib-work,  with 
a  plank-slope  upstream  of  45°,  and  with  a  width  somewhat  greater  than  that 
of  the  pier. 

Fig.  1238  is  the  plan  and  Fig.  1239  the  side  elevation  of  a  pier  of  a  bridge 
across  the  Missouri,  on  the  Northern  Pacific  Railroad  at  Bismarck,  designed  and 


516 


ENGINEERING  DRAWING. 


constructed  by  George  S.  Morison,  C.  E.  In  this  design  both  ends  of  the  pier 
are  rounded,  but  the  upper  extremity  is  extended  beyond  the  main  body  of  the 
pier,  and  is  inclined  and  plated  with  iron  between  low-  and  high-water  mark. 


FIG.  1235. 


FIG.  1236. 


FIG.  1234. 


FIG.  1237. 


ENGINEERING  DRAWING. 


517 


FIG.  1239. 


518 


ENGINEERING  DRAWING. 


This  is  intended  not  only  to  turn  aside  drift,  but  as  an  ice-breaker ;  the  ice, 
moving  up  the  incline,  is  broken  by  its  own  weight. 

Fig.  1240  is  a  section  of  the  foundation  of  the  Bismarck  bridge,  showing 
the  construction  of  the  inverted  caisson,  similar  to  that  used  for  the  Brooklyn 


FIG.  1240. 

Bridge  piers.  The  caissons  are  74'  long,  26'  wide,  and  17'  high  outside;  the 
working-chamber  7  feet  high.  The  caissons  are  built  of  pine,  sheathed  with 
two  thicknesses  of  3"  oak-plank.  Above  is  crib-work  filled  in  with  Portland 
cement  concrete;  a  a  are  the  air-locks.  The  sand  was  removed  from  the 
caissons  by  water-ejectors. 

Arch  bridges  are  of  stone,  brick,  concrete,  or  metal ;  the  parts  of  the  arch 
exert  a  direct  thrust  upon  the  abutments,  resisted  by  the  inherent  weight  of 
the  latter,  or  its  absolute  fixed  mass,  as  in  the  case  of  natural-rock  abutments. 

Arch  bridges,  in  masonry,  are  arcs  of  circle,  semicircular  (Fig.  1241),  seg- 
mental  (Fig.  1242),  elliptical,  or  described  from  three  or  five  centres  (page  32). 


FIG.  1241. 


FIG.  1242. 


The  stones  forming  the  arch  are  called  voussoirs,  or  arch-stones ;  those  form- 
ing the  exterior  face  are  called  ring-stones,  the  inner  line  of  arch  the  intrados, 
exterior  line  the  extrados.  The  stones  at  the  top,  which  are  those  set  last  and 
complete  the  arch,  are  key-stones.  -  The  courses  from  which  the  arches  spring 
are  called  skew-backs,  and  the  first  course  the  spring  ing-course.  The  masonry 
on  the  shoulders  of  the  arch  is  called  the  spandrel-courses,  or  spandrel-backing. 
The  weight  at  the  crown  of  a  semicircular  arch  tends  to  raise  the  haunches. 


ENGINEERING  DRAWING.  519 

This  is  counteracted  by  the  spandrel-backing,  and  by  the  earth-load,  which 
should  be  carefully  distributed  on  each  side  of  the  arch. 

To  determine  the  depth  of  the  key-stone,  Eankine  gives  the  following  em- 
pirical rule,  which  applies  very  well  to  most  of  the  above  examples  : 

Depth  at  key,  for  an  arch  of  a  series,  in  feet,  =  <y/'17  X  radius  at  crown. 
For  a  single  arch,  =  -v/'12  X  radius  at  crown. 

To  find  the  radius  at  crown  of  a  segmental  arch,  add  together  the  square  of 
half  the  span  and  the  square  of  the  rise,  and  divide  their  sum  by  twice  the  rise  — 

' 


2r 

Thus,  the  Blackwall  Eailway  bridge  has  a  span  of  87  feet,  and  a  rise  of  16  — 
43-5"  +  16a  _  1892-25  +  256  _ 

2  X  16  ~~32~~ 

To  find  the  radius  of  an  elliptical  arch,  on  the  hypothesis  that  it  is  an  arch 
of  five  centres  (Fig.  103,  page  32),  the  half-span  is  a  mean  proportional  be- 
tween the  rise  and  the  radius.  Thus,  for  example,  the  Great  Western  Railway 
bridge  is  128'  span,  and  24-25'  rise  — 

64a  =  24-25  X  R 
4096 


2425 
To  find  the  depth  of  key-stone,  by  rule  above,  as  in  one  of  a  series  — 


d  =  V'l?  *  169  =  V28^3  =  5-33. 

The  depth  of  the  voussoir  is  increased  in  most  bridges  from  the  key-stone 
to  the  springing-course,  but  not  always  ;  it  is  safer  to  increase  the  depth. 

If  an  arch  be  loaded  too  heavily  at  the  crown,  the  lines  of  pressure  pass 
above  the  extrados  of  the  crown  and  below  the  line  of  intrados  at  the  haunches, 
depressing  the  crown  and  raising  the  haunches,  separating  the  arch  into  four 
pieces,  and  vice  versa  if  the  arches  are  overloaded  at  the  haunches.  To  pre- 
vent such  effects,  especially  from  moving  loads,  in  construction  the  arches  are 
loaded  with  masonry  and  earth,  and  this  constant  load  in  such  excess  that  there 
will  be  no  dangerous  loss  of  equilibrium  by  accidental  changes  of  load. 

The  horizontal  thrust  may  be  determined,  according  to  Rankine,  by  the 
following  approximate  rule,  which  seldom  errs  more  than  5  per  cent  : 

The  horizontal  thrust  is  nearly  equal  to  the  weight  supported  between  the 
crown  and  that  part  of  the  soffit  whose  inclination  is  45°.  This  thrust  is  to  be 
resisted  by  the  masonry  of  the  abutment  and  the  earth-load  behind  it. 

Thus,  if  Fig.  1243  be  a  section  of  an  abutment  of  an  arch,  the  horizontal 
thrust  exerted  at  T  is  resisted  by  the  mass  of  masonry  of  the  abutment  ;  the 
tendency  is  to  slide  back  the  abutment  on  its  base  A  C,  or  turn  it  over  on  the 
point  A.  The  sliding  motion  is  resisted  by  friction,  being  a  percentage,  say 
from  |  to  |  of  the  weight  of  the  abutment  and  of  half  the  arch  which  is  sup- 
ported by  this  base  ;  but,  in  turning  over  the  abutment  on  the  point  A,  the  ac- 
tion may  be  considered  that  of  a  lever,  the  force  T  acting  with  a  lever  T  C  to 
raise  the  weight  of  the  abutment  on  a  lever  A  B  (G  being  the  centre  of  gravity, 
and  G  B  the  perpendicular  let  fall  on  the  base),  and  the  weight  of  half  the 
arch  on  the  lever  A  C.  That  is,  to  be  in  equilibrium,  the  horizontal  thrust 


520 


ENGINEERING  DRAWING. 


T  X  T  C  must  be  less  than  the  sum  of  the  weights  of  the  abutment  multiplied 

by  A  B,  and  the  weight  of  the  arch  multiplied  by  A  C. 

Skew  bridges  are  those  in  which  the  abutments  are 
parallel,  but  not  at  right  angles  to  the  centre  line, 
and  the  arches  oblique.  To  construct  these  in  cut 
stone  requires  intelligence  and  education  both  in  the 
designer  and  stone-cutter;  but,  when  the  work  is 
laid  full  in  cement,  so  that  the  joints  are  as  strong  as 
the  material  itself,  this  refinement  of  stone-cutting  is 
not  necessary.  The  arch  may  safely  be  constructed 
as  a  regular  cylinder  of  a  diameter  equal  to  the  rec- 
tangular distance  between  the  abutments,  with  its 
extremity  cut  off  parallel  to  the  upper  line  of  road. 

For  such  an  arch  hard-burned  brick  is  the  best  material,  the  outer  voussoirs 

being  cut  stone. 

In  the  rules  above  given  no  consideration  is  paid  to  the  strength  of  the 

cement  in  which  the  stones  are  bedded.     When  the  cement  is  thoroughly  set, 

the  structure  is  in  a  measure  monolithic,  and  the  thrust  is  inconsiderable. 

Fig.  1244  is  the  elevation  of  one  of  the  stone  arches  of  the  Minneapolis 

U  niou  Kail  way  Viaduct,  with  the  timber  centres  on  which  the  arch  was  turned. 

The  arch  is  nearly  semicircular,  97'82  feet  span,  50  feet  rise ;  width,  28  feet ; 


B 
FIG.  1243. 


Piers  10'  thick  at  springing  line,  5  ribs  to  each  arch. 


FIG.  1244. 


depth  of  arch  at  spring,  40" ;  at  key,  36".  The  piers  are  10  feet  thick  at 
springing  line ;  their  up-stream  ends  are  at  angles  to  the  main  body  of  the 
piers,  and  parallel  to  the  thread  of  the  stream.  The  whole  length  is  2,100  feet, 
of  which  there  are  3  arches  of  40  feet  span,  16  of  80  feet,  and  4  of  100  feet. 
Height  above  water,  65  feet ;  total  height,  82  feet. 

The  centres  were  very  light  frames,  five  to  each  arch ;  the  chords,  timber 
arches,  and  ties  were  each  12"  X  12",  the  central  braces  10"  X  10",  and  the 
shorter  side-braces  8"  X  8"  ;  the  bolts,  single,  1£"  diameter. 


ENGINEERING  DRAWING. 


521 


The  bridge  was  constructed  after  the  designs  and  under  the  direction  of 
Charles  C.  Smith,  0.  E.,  Chief  Engineer  of  the  St.  Paul,  Minneapolis  and 
Manitoba  Kailway,  and  is  an  example  of  a  very  economical  and  stable  con- 
struction. The  piers  are  of  Minnesota  granite,  but  above  springing  line  the 
masonry  is  of  magnesian  limestone.  It  was  commenced  in  February,  1882,  and 
completed  in  November,  1883. 


FIG.  1345. 


Fig.  1245  is  a  half-elevation  and  half -section  of  the  Cabin  John  Bridge  used 
for  supporting  the  Potomac  conduit  on  the  line  of  supply  to  the  city  of  Wash- 
ington. 


LOCATION. 

Material. 

Form  of  arch. 

Span. 

Rise. 

Depth 
at 
crown. 

Depth 
at 
spring. 

Manchester  and  Birmingham  Railroad. 

(1                                It                                   41                                               <( 

London  and  Brighton  Railroad  

Brick. 

Semicircular. 

u 
44 

18 
63 
30 

9 
31-6 
15 

1-6 
3 
1-6 

Uniform. 
2-3 

"         "    Blackwall      "        

H 

Segmental. 

87 

16 

4'H 

Uniform. 

Great  Western  Railroad  

u 

Elliptical. 

128 

24-3 

5 

7*U 

Chestnut  Street  (Philadelphia)  Railroad 
High  Bridge,  Harlem  River,  New  York 
St.  Paul,  Minneapolis  &  Manitoba  Rail- 
road (largest  arch),  at  Minneapolis.  . 
Cabin  John  Washington  Aqueduct..  .  . 
Licking  Aqueduct  and  Ohio  Canal.  .  .  . 
Monocacy      "          

Stone. 

u 

Segmental. 
Semicircular. 

Segmental. 

44 

Elliptical. 

60 

80 

97-8 
220 
90 
54 

18 
40 

50 
57-3 
15 
9 

2-6 

2-8 

3 
4-2 
2-10 
2-6 

3-4 

Hutcheson    "          

it 

Segmental. 

79 

13-6 

3-6 

4-6 

Chemin  du  Per  du  Nord,  sur  1'Oise  
D'Enghien  Railroad  du  Nord  

tt 

Semicircular. 

82-5 
24-4 

13-5 
12-2 

4-6 
1-4 

Du  Crochet  Railroad  

44 

13-2 

6-6 

l-7i 

Experimental  arch,  designed  and  built 
by  M.  Vaudrav,  Paris.  .  . 

tf 

Seermental. 

124 

6-11 

2-8 

3-7 

The  arch  last  in  the  list  was  a  very  bold  specimen  of  engineering,  built  as 
an  experiment,  preliminary  to  the  construction  of  a  bridge  over  the  Seine.  It 
was  made  of  cut  stone,  laid  in  Portland  cement,  with  joints  of  £ ",  and  left  to 
set  four  mouths ;  the  arch  was  12'  wide ;  the  centres  rested  on  posts  in  wrought- 
iron  boxes  filled  with  sand,  and,  as  the  centring  was  eased  by  the  running  out 
of  the  sand,  the  crown  came  down  TV ;  the  joints  of  one  of  the  skew-backs 
opening  -^^  during  the  first  day,  it  came  down  T£/.  It  was  then  loaded 
with  a  distributed  weight  of  360  tons ;  under  this  load  the  crown  settled  ^ 
more.  Since  then  nothing  has  stirred,  although  it  was  afterward  tested  by 
allowing  five  tons  to  fall  vertically  1'  6"  on  the  roadway  over  the  key-stone. 
This  bridge  will  not  come  within  any  of  the  rules  laid  down  for  other  construe- 


522 


ENGINEERING  DRAWING. 


tions.     The  rise  is  about  ^  the  span,  although  the  usual  practice  for  segmental 
and  elliptical  arches  is  more  than  {-,  or  within  the  limits  of  £  and  £. 

Melan  concrete  arch,  Stockbridge,  Mass.  (Figs.  1246  and  1247),  is  a  seg- 
mental arch  of  100  feet  span  and  -fa  rise. 


The  iron  in  the  arch  consisted  of  bent  ribs  of  7-inch,  15-lb.  I-beams,  spaced 
28  inches  apart  and  raised  about  1£  to  2  inches  from  the  soffit.  The  concrete 

in  the  abutments  (1  cement,  3  sand,  and  6 
stone)  was  put  in  first  with  the  adjoining 
wing  walls  to  such  a  height  as  to  inclose 
the  ends  of  the  iron  ribs,  which  abutted 
against  an  iron  cross-angle  previously 
bolted  to  them. 

The  concrete  in  the  arch  is  9  inches 
thick  at  the  crown  and  30  inches  at  the 
haunches.  The  concreting  of  the  arch 
was  done  in  dne  day.  Then  the  concrete 
filling,  the  face  and  wing  walls,  and  finally 
the  coping  were  built. 

The  bridge  is  a  concrete  monolith,  the 
coping  forming  one  piece  with  the  arch. 
The  iron  railing  is  embedded  in  the  con- 
crete. 

After  striking  the  centres  the  arch  settled  about  |  inch  at  the  abutments 
and  f  inch  at  the  centre. 

The  bridge  was  built  for  $1,475. 

In  suspension- bridges  the  platform  of  the  bridge  is  suspended  from  cables, 
or  chains,  the  ends  of  which  are  securely  anchored  within  the  natural  or  arti- 
ficial abutments. 

The  curve  of  a  suspended  chain  is  that  known  as  the  catenary,  and,  if  the 
whole  weight  of  the  structure  were  in  the  chain  itself,  this  would  be  the  curve 
of  the  chains  of  a  suspension-bridge  ;  but,  as  a  large  part  of  the  weight  and  the 
whole  of  the  loading  lies  in  the  platform,  the  curve  approaches  that  of  the 
parabola,  and  in  all  calculations  it  is  so  regarded. 


FIG.  1847. 


ENGINEERING  DRAWING. 


523 


Let  Fig.  1248  represent  a  suspension-bridge,  in  which  A,  B,  0,  are  points  in 
a  parabolic  curve. 

Rule. — Add  together  four  times  the  square  of  the  deflection  (E  B)s  and  the 
square  of  half-span  (A  E)a,  and  take  the  square  root  of  this  sum ;  multiply  this 


FIG.  1248. 


result  by  the  total  weight  of  one  chain  and  all  that  is  suspended  from  it,  in- 
cluding the  distributed  load,  and  divide  this  product  by  four  times  the  deflec- 
tion (E  B)  of  the  cable  at  the  centre,  and  the  result  will  be  the  tension  on  one 
chain,  at  each  point  of  support,  A  and  C.  The  angles  made  by  the  chain  at 
the  point  of  support — viz.,  angle  POL  and  the  angle  of  the  back-stays,  or  con- 
tinuation of  the  chain  (angle  L  C  N) — should  be  equal  to  each  other,  in  order 
that  there  be  no  tendency  to  overturn  the  tower  0  L  and  A  F. 


BRIDGES. 

Main 
spans. 

Deflection 
of  chain  or 
cable. 

No.  of 
chains  and 
cables. 

Total  effective 
section  of 
cable  in 
square  inches. 

Mean  weight 
of  cable  per 
foot  of  span 
(pounds). 

Fixed  load 
per  ft.  of 
span  (Ibs.). 

Breadthof 
platform 
in  feet. 

Menai  

570 

43 

16 

260 

880 

28 

Chelsea  

348 

29 

4 

230 

767 

47 

Pesth  

666 

47-6 

4 

507 

1,690 

9,892 

46 

Bamberg..  .  . 

211 

14-1 

4 

40-2 

137 

1,581 

30-5 

Freyburg  .  .  . 

870 

63 

4 

49 

167 

760 

21-25 

Niagara  Falls 

821 

54  and  64 

4 

241-6 

820 

2,032 

24 

Cincinnati.  .  . 

1,057 

89 

2 

172-6 

516 

2,580 

36 

Brooklyn..  .  . 

1,595-5 

128-5 

4 

188 

501-3 

5,865 

85 

BOILER-SETTING. 

Fig.  1249  is  a  longitudinal  section,  Fig.  1250  a  plan  with  section  of  wall, 
and  Fig.  1251  an  elevation  half-front  and  half-sectional  of  a  boiler  and  setting 
as  recommended  by  the  Hartford  branch  of  the  Hartford  Steam-Boiler  and  In- 
spection Company,  showing  the  interior  bracing,  steam  and  water  connections, 
and  brickwork.  There  are  ten  braces  in  each  head,  secured  to  pieces  of  T-iron, 
placed  radially,  as  shown  in  dotted  lines  (Fig.  1251).  The  feed-pipe  is  through 
the  front-head,  just  above  the  line  of  tubes,  extending  to  the  back  of  the  boiler, 
with  a  perforated  branch  across  it,  that  the  water  may  be  warmed  in  its  passage 
and  distributed.  The  front  is  a  projecting  cut-away  front,  the  boiler-head  being 
nearly  on  a  line  with  the  front  below,  different  from  that  given  in  Fig.  918, 
where  the  lower  part  of  the  shell  projects  beyond  the  head  of  the  boiler,  and 
the  cast-iron  front  covers  the  end.  The  doors  giving  apcess  to  the  tubes  are 
usually  semicircular,  and  hung  on  the  top  diameter,  but  it  will  be  found  more 
convenient  to  form  them  in  two  quadrants,  and  hung  so  as  to  move  horizontally. 
The  boilers  are  to  be  protected  against  radiation  by  a  covering  of  ashes,  or  a 
brick  arch,  resting  on  the  side- walls. 


524: 


ENGINEERING  DRAWING. 


In  the  figure  the  man-hole  frame  is 
riveted  to  the  inside  of  the  boiler ;  fre- 
quently it  is  on  the  outside.  In  many 
positions  the  man  -  hole  should  be 
placed  in  the  back-head,  as  easier  of 
access.  With  the  blow-off  in  the  flue 
(Fig.  1249)  it  is  well  to  make  it  a  circu- 
lating pipe  by  connecting  an  inch-pipe 
inside  the  valve  with  the  upper  water- 
space  of  the  boiler. 

Figs.  1252, 1253,  and  1254  are  draw- 
ings of  boiler  as  made  by  the  Fishkill 
Landing  Machine  Company.  The 
boilers  are  suspended  between  vertical 
side  -  walls.  The  side- walls  here  are 
composed  of  bearing  walls,  air  spaces, 
and  an  inside  4"  wall,  which  is  exposed 


FIG.  1251. 


ENGINEERING  DRAWING. 


525 


FIG.  1253. 


FIG.  1254. 


OOOOOOOOO 

OOOOOOODO 
OOOOOOOOO 
OOOOOOOOO 


OOOOOOOOO 
OOOOOOOOO 
OOOOOOOOO 
OOOOOOOOO 

ooo      oo 


526  ENGINEERING  DRAWING. 

to  the  heat  of  the  gases  from  combustion.  The  fire-box  is  lined  with  fire-brick 
to  the  height  of  the  centre  of  the  boiler,  and  also  the  exposed  surface  of  the 
bridge  wall.  A  covering  of  thin  corrugated  iron  extends  from  wall  to  wall  over 
the  boiler,  and  supports  a  thick  cover  of  ashes. 

The  boiler  is  built  without  dome,  but  of  full  diameter  to  give  steam  capa- 
city ;  the  dry  pipe  of  light  iron  (gutter  or  |J  shape)  extends  the  whole  length 
of  the  upper  part  of  the  boiler,  to  which  it  is  riveted,  but  with  a  washer  be- 
tween it  so  as  to  leave  open  joints  of  about  •£"  for  the  admission  of  steam.  The 
pipes  are  laid  out  in  fan  lines  to  offer  as  much  surface  as  possible  to  the  flame 
and  to  admit  of  ready  cleaning.  There  are  two  man-holes,  one  above  the  tubes 
where  easiest  of  access,  and  one  beneath  in  the  front-head  with  a  hand-hole  in 
the  back-head.  The  breeching  is  of  cast-iron,  attached  to  the  boiler,  with  doors 
opening  laterally ;  the  smoke-pipe  leads  out  from  the  top  with  a  damper  at 
the  bottom ;  the  size  of  the  smoke-pipe  is  proportioned  to  the  number  and  size 
of  tubes,  according  to  the  tables  given  in  the  Appendix. 

The  furnace  doors  are  hung  to  the  sides  of  the  frames  to  expose  the  full 
width  of  opening  for  cleaning,  and  smaller  doors  are  hung  on  the  main  doors 
for  firing. 

CHIMNEYS. 

Figs.  1255  and  1256  are  sections  of  a  small  circular  chimney,  about  100  feet 
high,  in  which  the  buttresses  are  within  the  outer  shell,  supporting  but  not  at- 
tached to  a  central  flue ;  these  flues  may  be  made  of  brick  glazed  ware  or  con- 
crete. This  chimney  is  without  outside  buttresses,  panels,  or  ornaments,  and 
offers  the  least  possible  resistance  to  wind. 

For  chimneys  of  small  diameter  it  is  difficult  to  obtain  circular  brick, 
but  the  chimney  may  be  made  octagonal  of  any  face,  with  a  strong  bond, 
by  corner  brick,  from  brickyards  and  terra-cotta  works.  Chimneys  of  the 
above  section,  100  feet  high,  with  bottom  corners  rounded,  will  give  ample 
draft  with  an  area  of  chimney-flue  of  two  square  inches  for  every  pound  of 
anthracite  per  hour  burned  upon  the  grate. 

If  the  chimney  is  of  less  height  it  is  well  to  increase  the  section  in  propor- 
tion to  the  reduction,  but  the  top  should  be  always  above  buildings,  trees,  etc., 
and  remote  from  obstructions  that  would  check  the  draft.  Chimneys  should 
have  flues  at  least  16"  diameter,  and  there  is  no  objection  to  flues  of  larger  area 
than  given  by  rule  above ;  but  it  is  indispensable  for  a  sure  draft  that  all  flues 
should  have  corners  rounded  without  abrupt  changes  in  area  or  direction. 

Fig.  1257  is  a  sectional  elevation  of  a  chimney  160  feet  high,  from  John  T. 
Henthorne,  M.  E.,  with  a  cross-section  (Fig.  1258)  midway  of  the  height. 

Figs.  1259, 1260,  and  1261  are  sectional  elevation,  front  elevation,  and  cross- 
sections  of  a  chimney  of  large  dimensions,  built  by  Mr.  Henthorne  for  the 
Narragansett  Electric  Light  Works,  Providence,  E.  I. 

Fig.  1262  is  a  vertical  section  of  a  chimney  at  the  Eidgewood  Pumping- 
engine  House,  Brooklyn,  N.  Y.,  and  Fig.  1263  an  elevation  at  the  point  where 
the  square  base  is  changed  into  an  octagonal. 

Fig.  1264  is  the  cross-section  of  a  buttressed  chimney  at  100  feet  above  base, 
built  for  the  Calumet  &  Hecla  Mining  Company,  and  designed  by  E.  D. 
Leavitt,  Jr.,  M.  E.  The  whole  height  of  the  chimney  is  150  feet.  The  but- 
tress walls  are  16"  and  12"  thick,  that  of  the  body  12"  and  8",  and  of  the  cen- 


ENGINEERING  DRAWING. 


iH'H 

•j.— ->'«--J,j 


FIG.  1256. 


...J... 


FIG.  1358. 


FIG.  1255. 


FIG.  1257. 


528 


ENGINEERING  DRAWING. 


(V. 


-h 


\--b 


FIG.  1239. 


FIG.  1260. 


FIG.  1261. 


ENGINEERING   DRAWING. 


529 


530 


ENGINEERING  DRAWING. 


l_ 

' 

i 

1 

i 

i 

' 

i 

i 

i 

1 

, 

ID 

FIG.  1266. 


FIG. 12G7. 


tral  flue  8"  and  4",  offsetting  into 
each  other  by  1"  offsets ;  the  taper 
is  4  inches  to  10  feet  on  each  side. 
Fig.  1265  is  a  half  elevation  and 
half  section  of  the  cap  and  the 
cover  of  the  interior  flue  by  which 
its  expansion  is  permitted. 

Figs.  1266  and  1267  are  eleva- 
tion and  section  of  a  wrought-iron 
chimney  stack,  such  as  are  now  in 
common  use ;  they  are  brick-lined, 
with  a  spread  base  well  anchored 
and  without  other  stays. 

In  most  chimneys  an  interior 
and  independent  flue  is  used, 
which  may  expand  without  dis- 
turbing and  cracking  the  exterior 
shell.  Chimneys  are  built  of  va- 
rious sections,  uniform  throughout, 
with  flues  tapering  to  the  top,  or 
increasing  in  section,  bell-mouthed, 
some,  like  a  lamp  chimney,  con- 
tracted at  the  entrance ;  all  draw 
well  if  without  abrupt  changes  in 
section  and  direction,  and  adapted 
to  the  position.  Chimneys  are 
less  likely  to  be  overturned  by  the 
wind,  the  nearer  the  section  to  the 
circular  and  the  smoother  in  out- 
line, and  the  fewer  the  projections. 

ON   THE   LOCATION   OF    MACHINES. 

The  construction  of  buildings 
for  mills  and  manufactories  (if 
any  aesthetic  effect  is  intended)  is 
usually  left  to  the  architect,  but 
the  necessities  of  the  construction, 
the  weights  to  be  supported,  and 
the  space  to  be  occupied,  must  be 
supplied  by  the  mechanical  en- 
gineer or  millwright. 

In  the  arrangement  of  a  manu- 
factory or  workshop  it  is  of  the 
utmost  importance  to  know  how 
to  place  the  machinery,  both  as  to 
economy  of  space  and  also  of  work- 
ing. Where  a  new  building  is  to 
be  constructed  for  a  specific  pur- 


ENGINEERING  DRAWING. 


531 


pose  of  manufacture,  it  will  be  found  best  to  arrange  the  necessary  machines 
as  they  should  be,  and  then  build  the  edifice  to  suit  them.  For  defining  the 
position  of  a  machine,  the  space  it  occupies  in  plan  and  elevation,  the  position 
of  the  driven  pulley  or  gear,  of  the  operative,  and  the  spaces  for  the  working 
and  access  to  parts,  are  required.  To  illustrate  this  subject,  take  a  two-story 
weaving-room,  of  which  Fig.  1268  is  an  elevation  and  Fig.  1269  a  plan. 


Lay  down  the  outlines  of  an  interior  angle  of  the  building,  and  dot  in,  or 
draw  in  red  or  blue,  the  position  and  width  of  beams.  This  last  is  of  impor- 
tance, as  no  driving-pulley  can  come  beneath  the  beam,  and  this  is  also  the  posi- 


532 


ENGINEEKING  DBA  WING. 


FIG.  1869. 


ENGINEERING   DRAWING.  533 

tion  for  the  hanger.  Lay  off  the  width  of  the  alleys  and  of  the  machines.  The 
first  alley,  or  nearest  the  side- wall;  is  a  back  alley ;  that  is,  where  the  operative 
does  not  stand,  and  so  on  alternate  alleys.  Draw  the  lines  of  shafting  central 
to  the  alleys,  as  in  this  position  the  belts  are  least  in  the  way.  One  operative  * 
usually  tends  four  looms ;  they  are  therefore  generally  arranged  in  sets  of  four, 
two  on  each  side  of  the  main  alley,  where  the  operative  stands ;  the  twos  are 
placed  as  close  to  each  other  as  possible,  say  one  inch  between  the  lays,  a  small 
cross-alley  being  left  between  them  and  the  next  set.  Lay  off  next  the  alley 
necessary  at.the  end  of  the  room,  and  space  off  the  length  of  two  rows  of  looms 
with  alleys  at  the  end  of  alternate  looms,  and  mark  the  position  of  the  pulleys. 
Looms  are  generally  rights  and  lefts,  so  that  the  pulleys  of  both  looms  come  in 
the  space  where  there  is  no  alley.  Should  the  pulley  come  beneath  a  beam, 
the  loom  must  be  either  moved  to  avoid  it,  or  the  pulley  may  be  shifted  to  the 
opposite  end  of  the  loom.  Parallel  with  the  pulleys  on  the  looms  draw  the 
driving-pulleys  on  the  shafts/  that  is,  k  parallel  'with  &,  b  with  Z»,  /  with  /,  and 
so  on.  Draw  the  third  and  fourth  rows  of  looms ;  since  the  second  and  third 
rows  are  driven  from  the  same  shaft ;  if  they  are  placed  on  the  same  line,  it  will 
be  impossible  to  drive  both  from  the  same  end,  and,  as  this  is  important,  move 
the  third  row  the  width  of  the  pulley  #,  and,  for  the  sake  of  uniformity,  the 
fourth  row  also.  Lay  off  the  length  of  looms  and  position  of  pulleys  as  before, 
and  parallel  with  the  pulleys  the  driving-pulleys  on  the  shaft,  that  is,  c  against 
c,  g  against  #,  and  so  on.  Having  in  this  way  plotted  in  all  the  looms,  every 
alternate  set  being  on  a  line  with  the  third  and  fourth  row,  if  there  are  to  be 
looms  on  the  story  above,  proceed  to  lay  down  the  position  of  the  looms  on  this 
floor;  and  since  for  economy  of  shafting  it  is  usual  to  drive  from  the  lines  in 
the  lower  rooms,  to  avoid  errors,  interference  of  belts  and  pulleys,  plot  the 
upper  room  on  the  same  paper  or  board  as  the  lower  room,  in  two  different 
colored  inks,  or  drawing  the  machines  in  one  room  in  deep  and  in  the  other 
in  light  line,  as  shown  in  Fig.  1269.  If  the  width  of  the  rooms  is  the  same, 
the  lateral  lines  of  looms  and  alleys  are  the  same,  and  it  is  only  necessary, 
therefore,  to  fix  the  end  lines.  As  the  first  loom  in  the  outer  row  of  looms, 
in  the  lower  room,  occupies  for  its  belt  the  position  k  on  the  shaft,  the  loom 
in  the  upper  room  must  be  moved  either  one  way  or  the  other  to  avoid 
this ;  thus  the  position  i  of  the  pulley  on  the  loom  must  be  made  parallel 
to  the  pulley  i  on  the  shaft,  so  in  the  other  looms  a  to  a,  e  to  e,  d  to  d, 
and  h  to  h. 

Besides  the  plan,  it  is  often  necessary,  and  always  convenient,  to  draw  a 
sectional  elevation  (Fig.  1268)  of  the  rooms,  with  the  relative  positions  of  the 
driving-pulleys  and  those  on  the  machines,  to  determine  the  length  of  the  belts, 
and  also  to  see  that  their  position  is  in  every  way  the  most  convenient  possi- 
ble. In  the  figure,  one  of  the  lower  belts  should  have  been  a  cross-belt,  and 
one  of  the  upper  ones  straight :  had  the  belts  to  the  second  row  of  looms  in  the 
upper  story  been  drawn  (as  they  should  have  been)  straight,  the  belt  would 
have  interfered  a  little  with  the  alley,  and  it  would  have  been  better  to  have 
moved  the  driving-shaft  a  trifle  toward  the  wall. 

From  this  illustration  of  the  location  of  machines,  knowing  all  the  require- 
ments, in  a  similar  way  any  machinery  may  be  arranged  with  economy  of  space,      v 
materials,  power,  and  attendance.     These  last  two  items  are  of  the  more  iui-  •*   \ 


534 


ENGINEERING  DRAWING. 


>©• — * 


ENGINEERING  DRAWING. 


535 


portance  as  they  involve  a  daily  expense,  where  the  others  are  almost  entirely 
in  the  first  outlay. 

Machine  Foundations. — Figs.  1270,  1271,  and  1272  are  side,  end  elevations, 
and  plan  of  the  foundation  of  the  stationary  steam-engine.  F  is  the  cast-iron 
frame  or  bed-plate  of  the  engine;  B  the  granite  bed  of  the  engine,  or  coping  of 
foundation  ;  P  the  stone  or  brick  pier,  laid  full  in  cement.  The  sides  and  sur- 
faces of  granite  exposed  are  usually  fine-hammered,  the  upper  bed  or  build  to 
receive  the  engine-frame,  hammer-dressed  and  set  level.  Strong  wrought  iron 
bolts  pass  through  frame,  bed,  and  pier,  with  nuts  at  each  end,  and  the  whole 
is  strongly  bolted  together.  Pockets  are  left  in  the  pier  near  the  bottom  for 
access  to  nuts,  and  these  pockets  are  covered  by  granite  caps  or  iron  plates. 

Few  stationary  steam  engines  are  now  built  with  bed-plates  extending  the 
whole  length  of  the  engines,  but  the  illustration  is  applicable  to  the  partial 
plates  supporting  the  cylinder  and  pillow-block,  and  to  engines  and  machines 
for  which  heavy  foundations  are  necessary.  It  is  not  an  uncommon  practice, 
instead  of  granite  caps,  to  use  timber,  to  cushion  the  shocks  and  blows  incident 
to  most  machinery. 

Tunnels. — Figs.  1273  to  1282  are  illustrations,  with  description,  taken  from 
"  Tunneling,"  a  standard  work  on  this  subject  by  H.  S.  Drinker,  C.  E. 


Fio.  1273. 


Figs.  1273  to  1278  illustrate  the  principles  of  timbering  applied  to  drivings 
gallery  through  running  material.  Figs.  1273  and  1274  are  parts  of  the  con- 
struction on  a  large  scale,  with  the  technical  names  of  the  parts.  Each  frame  is 
called  a  timber-set.  Suppose  a  leading  set  (Figs.  1275  and  1276)  is  in  place, 
close  to  the  face,  and  that  the  leading  ends  of  the  poling-boards  resting  above 
this  leading  set  are  held  up  from  the  collar  by  wedges  sufficiently  high  to  allow 
the  insertion  of  the  new  poling-boards.  In  Fig.  1276  the  sets  e  e,  standing  mid- 
way between  the  front  and  the  hind  ends  of  the  poling-boards,  serve  as  middle 
sets  between  the  main  sets  dd.  By  referring  to  the  plan  (Fig.  1278)  of  a  gal- 
lery thus  timbered  it  will  be  seen  that  the  side-poling  has  to  be  wedged  out  at 
its  leading  end,  just  as  the  roof-poling  is  wedged  up,  and  the  space  to  be  filled 
across  the  top  by  the  roof-poling  is  wider  over  a  front  main-set  than  over  a  back 


536 


ENGINEERING   DRAWING. 


one.  The  two  outer  top  poling-boards  (Fig.  1273)  are  therefore  made  wider  at 
their  leading  ends  than  at  their  back  ends.  The  miners  begin  by  inserting  the 
roof-poling  at  either  corner  of  the  face,  removing  the  extreme  end-wedges  be- 
tween the  collars  and  the  poling,  and  driving  into  this  space  the  new  poling- 
boards  (i.  e.,  the  ones  shown  in  Fig.  1273).  Though  the  wedges  between  the 
collar  and  the  poling-boards  serve  well  enough  to  keep  back  the  material,  it 
would  be  dangerous  thus  to  take  any  of  them  out  were  there  no  other  guard 
for  the  poling,  as  the  board  just  above  the  wedge  removed  would  be  pressed 
down ;  a  run  might  also  be  started,  and  all  the  other  wedges  forced  out,  when 
the  poling-boards  would  snap  down  on  the  leading  collar,  and  perhaps  break 


FIG.  1275. 

off;  in  any  event,  it  would  be  a  matter  of  great  trouble  to  get  them  wedged  up 
again.  In  order  to  guard  against  this  trouble,  a  cross-board  or  plank  a  (Fig. 
1274)  is  placed  just  under  the  poling-boards,  and  over  the  wedges.  Then,  when 
one  wedge  is  removed,  this  cross-connection  holds  in  place  the  poling-board 

that  is   immediately   above  the  wedge 
removed,  until   the  new  board  can  be 


FIG.  1277. 


put  in ;  it  also  stays  the  tendency  to  any  general  movement.     The  new  poling- 
board  being  inserted,  it  is  driven  ahead  six  or  twelve  inches,  and  then  tern- 


ENGINEERING   DRAWING. 


537 


FIG.  1279. 
(Section  of  Fig.  1281,  through  A  B,  looking  west.) 

HOOSAC  TUNNEL. 
Timbering  and  arching  through  soft  ground  at  the  West  End.    Scale,  10'  =  1". 


FIG.  1280. 


538 


ENGINEERING  DRAWING. 


West. 


East. 


FIG.  1281. 

HOOSAC  TUNNEL. 
West  End.    Scale,  10'  =  1". 


FIG.  1282. 


ENGINEERING  DRAWING.  539 

porarily  stayed  by  wedges,  b  (Fig.  1277).  The  corner  roof-polings  being  thus 
in  place,  the  middle  ones  (Fig.  1273)  are  similarly  inserted.  Then  the  top 
retaining-board  in  the  face  is  cut  out,  and  the  material  allowed  to  flow  into  the 
heading  through  the  space.  As  room  is  thus  given  ahead,  the  poling-boards 
are  gradually  driven  forward,  say  24  or  30  inches,  or  about  half  the  length  of 
a  board.  Whenever  they  are  thus  tapped,  the  wedges  b  (Fig.  1274)  must  be 
loosened,  and  then  tightened  again  after  the  driving.  The  side-poling  is  simi- 
larly advanced ;  as  space  is  gained  ahead,  it  must  be  protected  by  new  face- 
boarding,  stayed  by  stretchers.  Thus  the  work  can  be  gradually  carried  down 
to  the  floor  of  the  heading  by  successively  taking  out  the  face-boards.  Often 
the  floor  of  the  gallery  also  has  to  be  planked,  and,  in  very  extreme  cases,  to 
be  poled  similarly  to  the  roof  and  sides. 

While  inserting  the  new  poling-board  for  half  its  length  the  boards  have 
been  held  in  place  by  the  double  support  offered  by  a  and  b.  The  face  retain- 
ing-boards  are  kept  back  by  a  vertical  plank  laid  across  them,  and  stayed  by 
stretchers.  On  this  newly  excavated  chamber  the  outside  pressure  will  be 
great,  acting,  as  it  does,  on  the  front  half  length  of  the  poling-board  c  a,  and,  if 
the  remaining  work  is  not  rapidly  executed,  the  front  ends  of  the  boards  may 
be  snapped  beyond  a ;  then,  if  it  were  attempted  to  drive  the  remaining  portion 
of  the  board  on,  as  soon  as  its  back  end  left  b  it  would  snap  between  a  and  b. 
A  middle  set  is  therefore  required  at  once.  The  middle  set  being  in  position, 
the  work  of  excavating  the  face  can  be  proceeded  with  as  before.  The  face- 
boards  are  removed,  one  by  one,  from  top  to  bottom,  and  the  polings  are  driven 
in  to  their  full  length ;  then  in  the  new  length  ahead  the  next  main  set  is 
erected.  Such  are  the  general  principles  of  heading-driving  through  running 
ground,  or  sheet-piling  in  tunnelling. 

Figs.  1279  to  1282  show  the  English  system  of  bar-timbering,  as  used  at 
the  Hoosac  Tunnel  for  the  soft  ground  at  the  west  end.  The  material  was  of 
the  worst  character,  and  was  exceedingly  difficult  to  drive  through.  Figs.  1279 
and  1280  are  cross-sections,  the  one  looking  west  from  A  B,  the  other  east. 
Fig.  1281  is  a  longitudinal  section.  Fig.  1282  is  a  cross-section  of  the  tunnel 
as  completed  with  an  invert,  and  the  bars  not  drawn  but  bricked  in. 

Railway  Stock. — Figs.  1283  and  1284  are  the  elevation  and  plan  of  a  stand- 
ard box-car  of  the  New  York  Central  and  Hudson  Eiver  Railroad. 

Figs.  1285  to  1288  are  the  plan  and  elevations  of  the  truck  for  the 
same  car. 

Figs.  1289,  1290,  and  1291  are  end-elevations  and  cross-sections,  Figs.  1292 
and  1293  longitudinal  sections,  and  Fig.  1294  plan  of  a  standard  passenger-car 
of  the  Pennsylvania  Eailroad. 

Fig.  1295  is  a  plan  and  section  of  a  pair  of  wrought-iron  plates  which  sup- 
port a  car  body  in  the  centre  of  the  truck.  There  are  two— the  body  centre- 
plate  and  the  truck  centre- plate.  The  centre-pin  or  king-bolt,  not  shown,  carries 
none  of  the  strain  except  in  emergencies. 

Figs.  1296  to  1299  are  elevations,  in  full  and  parts,  and  Fig.  1300  a  plan  of 
the  trucks  of  the  above  car. 

In  the  figures,  both  of  standard  box  and  passenger  cars,  the  elevations  and 
plans  are  usually  broken,  to  show  the  construction.  When  the  two  sides  or 
two  ends  of  a  car  or  truck  are  similar,  it  has  not  been  considered  necessary  to 


540 


ENGINEERING    DRAWING. 


ENGINEERING  DRAWING. 


541 


8 


canters  or  gidp  Door-1 


!<- Centers  of  Swing  Hangers  4'-S"- -*>  ! 


K- Centers  or  SWinj  |  HAiiger  Bearing  4'-3 ^J 

< Spring  PlanK  2'-  lOVz" ,N  n 

K Transom  3-3" --X-  — Swing  Doistor.  2  - io!i* 1 —  >i 

<•  —  — '  Ccnterof  £"pn"4ig  2-4''    •  — >f 
•* Between  Centers  of  Journal  Bearing  6-3 •> 


FIG.  1288.  ^. Axle  e'-' 

End  Devation. 
Track  Gauge    if'-D'/^' 


542 


ENGINEERING  DRAWING. 


f**U  \  I— ^^jizz^C. — 11}  \^J,  ?' 


FIG.  1295. 


ENGINEERING  DRAWING. 


543 


3-l'Y "*  — * -3-l'/»' 

FIG.  1297.   ' 


FIG.  1300. 


ENGINEERING  DRAWING. 


A..  ._iffl.-Xl- 


ENGINEERING  DRAWING. 


545 


show  both,  but  the  figure  is  completed  with  a  section  of  the  other  part,  through 
a  different  plane. 

The  following  letters  of  reference  and  technical  names  of  similar  parts 
apply  equally  to  all  the  figures  : 

k.  Draw-  bar. 

I,  Journal-box.  * 

-   m,  Pedestal. 

n,  Pedestal  tie-bar. 


Sill. 

End-sill. 

Intermediate  floor-timbers. 

Centre  floor-timbers. 


Sill  knee-iron  or  strap.  o, 

d,  Body  bolster.  p, 

e,  Body  bolster  truss-rod.  p' 
/,    Truck  side-bearing.  q, 
g,    Centre  plate,  body  or  truck.-  r, 
h,   Check-chain  on  the  truck,  hooking  into  s, 
h',  Check-chain  eye  on  the  car.  t, 
i,    Body  truss-rod.  to, 
i,   Body  truss-rod  queen-post.  v, 
j,     Cross-frame  tie-timber. 


Pedestal  stay-rod. 

Pedestal  arch-bar. 

Pedestal  inverted  arch-bar. 

Transom. 

Truck  bolster. 

Spring-plank. 

Swing-hanger. 

Safety-beam. 

Equalizing-bar. 


Fig.  1301  is  a  plan  and  elevation  of  the  frame  of  a  locomotive  as  designed 
by  Mr.  Robert  Buchanan  of  the  New  York  Central  and  Hudson  River  Railroad. 
The  distinguishing  feature  is  the  American  "  bar  "  frame,  while  the  plate  frame 
may  be  called  the  English  practice.  The  latter  admits  of  a  wider  fire-box  be- 
tween the  frames,  but  in  the  American  example  the  fire-box  is  entirely  above 
the  frames. 

The  Wave-line  Principle  of  Ship-  Construction,  from  Russell's  "  Naval  Archi- 


FIG.  1302. 


tecture."— The  general  doctrines  arrived  at  by  J.  Scott  Russell,  F.  R.  S.,  from 
numerous  and  long-continued  experiments  and  practical  tests,  is  "  that  the 
form  of  least  resistance  for  the  water-line  of  the  bow  is  horizontally  the  curve 
of  versed  sines,  and  that  the  form  of  least  resistance  for  the  stern  of  the  vessel 
is  the  cycloid  ;  and  you  can  either  adopt  the  said  cycloid  vertically  or  horizon- 
tally, or  you  can  adopt  it  partly  vertically  and  partly  horizontally,  according  to 
the  use  of  the  vessel  or  the  depth  of  water." 

"  That  the  length  of  entrance,  or  fore  body,  should  be  f ,  and  that  of  the 
run,  or  after  body,  f ." 
36 


546 


ENGINEERING  DRAWING. 

"  When  it  is  required  to  construct  the  water-lines  of  the 
bow  of  a  ship  of  which  the  breadth  and  the  length  of  the  bow 
are  given,  so  as  to  give  the  vessel  the  form  of  least  resistance 
to  passage  through  the  water,  or  to  obtain  the  highest  velocity 
with  a  given  power  :  Take  the  greatest  breadth,  M  M  (Fig. 
1302),  on  the  main  section  of  construction  at  midship-breadth, 
and  halve  this  breadth,  MO;  at  right  angles  to  M  M  at  0 
draw  the  centre  line  of  the  length  of  the  bow,  0  X  ;  on  each 
half-breadth  describe  a  half-circle,  dividing  its  circumference 
into,  say,  eight  equal  parts.  Divide  the  length  0  X  into  the 
same  number  of  equal  parts.  The  divisions  of  the  circle^ 
reckoned  successively  from  the  extreme  breadth,  indicate  the 
breadths  of  the  water-line  at  the  successive  corresponding 
points  of  the  line  of  length.  Through  .the  divisions  of  the 


FIG.  1303. 

circles  draw  lines  parallel  to  0  X,  and  through  the  divisions 
of  0  X  lines  parallel  to  M  M.  These,  intersecting  one  an- 
other, show  the  successive  points  in  the  required  water-line. 
The  line  traced  through  all  these  points  is  the  wave  water- 
line  of  least  resistance  for  a  given  length  of  bow  and  breadth 
of  body." 

To  construct  the  water-lines  of  the  after  body  or  run  of  a 
ship  (Fig.  1304),  the  mid-section  (Fig.  1303)  being  given  : 
The  bow  is  constructed  as  in  Fig.  1302,  but  with  12  divisions' 
on  the  centre  line  ;  for  the  run  lay  off  8  divisions,  each  equal 
to  those  of  the  bow  ;  divide  the  half  circle  into  8  equal  parts,. 
and  draw  chords  to  these  divisions  from  0  to  1,  2,  3,  4.  From 
the  point  1  on  the  centre  line  lay  off  an  inclined  line  equal 
and  parallel  to  the  chord  0  1 ;  the  point  1'  will  be  in  the  water- 
line.  In  the  same  way  from  the  point  2  draw  an  inclined  line 
parallel  and  equal  to  the  chord  0  2,  for  2',  and  determine  in 
the  same  way  the  points  3',  4',  5',  6',  7'.  The  other  circles 
drawn  in  the  figure  are  described  on  semi-diameters  of  the 
mid-section  at  different  levels,  and  the  points  of  their  wave- 
lines  are  determined  on  the  same  inclined  lines  1  1',  2  2',  but 
the  lengths  are  those  of  the  chords  of  the  different  circles. 
In  Fig.  1303,  the  elevations  of  the  mid  body,  the  curved  lines 
of  sections  are  projected  from  the  plan. 

Fig.  1305  is  a  body  plan  of  a  vessel  adapted  to  speed ; 
Fig.  1306  of  one  adapted  to  freight. 

"  To  determine  the  after  body  it  is  expedient  to  construct. 


ENGINEERING  DRAWING. 


547 


a  vertical  wave-line  on  the  run  as  well  as  a  horizontal  one,  and  in  designing 
shallow  vessels  to  give  more  weight  to  the  vertical  wave-line." 

"  The  wave  system  destroys  all  idea  of  any  proportion  of  breadth  to  length 
being  required  for  speed.  An  absolute  length  is  required  for  entrance  and  run, 
but,  these  being  formed  in  accordance  with  the  wave  principle  for  any  given 
speed,  the  breadth  may  have  any  proportion  to  that  which  the  uses  of  the  ship 
and  the  intentions  of  the  constructor  require." 

"  The  wave  system  allows  us  to  give  the  vessel  as  much  length  as  we  please. 
It  is  by  this  means  that  we  can  give  to  a  vessel  of  the  wave  form  the  capacity 
we  may  require,  but  which  the  ends  may  not  admit.  Thus,  the  Great  Eastern, 


FIG.  1305. 


FIG.  1306. 


which  is  a  pure  example  of  the  wave  form,  has  an  entrance  or  fore  body  of 
330',  a  run  or  after  body  of  220',  and  a  middle  body  of  120',  which  was  made 
of  this  length  merely  to  obtain  the  capacity  required.  The  lengths  of  the  fore 
and  after  body  are  indicated  by  the  required  speed,  and  if  the  beam  is  fixed, 
it  is  only  by  means  of  a  due  length  of  middle  body  that  the  required  capacity, 
stability,  and  such  other  qualities  are  to  be  given  as  will  make  a  ship,  as  a  whole, 
suit  its  use." 

Length  of  entrance  of  a  vessel  for  a  10-mile  speed  should  be  42  feet,  of  run 
30  feet ;  for  a  20-mile  speed,  168  and  120  feet ;  that  is,  the  lengths  increase  as 
the  squares  of  the  speed. 

Under  Isometrical  Drawing  is  given  an  illustration  of  a  vessel  constructed 
on  wave-lines. 


ARCHITECTURAL  CONSTRUCTION. 

IT  is  the  duty  of  an  architect  to  design  a  building  to  be  suitable  and  con- 
venient for  the  purposes  for  which  it  is  intended  ;  to  select  and  dispose  of  the 
materials  of  which  it  is  composed  to  withstand  securely  and  permanently  the 
stresses  and  wear  to  which  they  may  be  subjected  ;  to  arrange  the  parts  to  pro- 
duce the  artistic  effects  consistent  with  the  use  of  the  building  and  its  location, 
and  to  apply  such  appropriate  ornament  as  may  express  the  purpose  and  har- 
monize with  the  construction. 

In  domestic  architecture,  by  far  the  most  extensive  branch  of  the  profession, 
most  persons  can  give  some  idea  of  the  kind  of  building  which  they  wish  to 
have  constructed,  and  perhaps  express  by  line  the  general  arrangement  of 
rooms ;  but  it  is  left  to  the  architect  to  settle  the  style  of  building  appropriate 
to  the  position,  to  adapt  the  dimensions  and  positions  of  rooms  and  passages  to 
the  requirements,  to  determine  the  thickness  of  walls  and  partitions,  and  arrange 
for  drainage,  heating,  and  ventilating.  The  graphical  representation  is  left  to 
the  draughtsman,  and  his  assistance  is  the  more  valuable  if  he  is  not  only  con- 
versant with  practical  details,  but  understands  the  best  proportions  of  parts,  the 
necessities  of  construction,  and  the  requirements  of  building  laws. 

The  draughtsman  usually  commences  his  education  with  the  copying  of 
drawings.  For  this  purpose,  in  Figs.  1307  to  1310,  inclusive,  are  given  plans 
and  elevations  of  a  simple  house,  showing  the  drawings  necessary  to  get  a  clear 
comprehension  of  plans  and  elevation ;  but  for  an  estimate  and  for  constructive 
purposes  it  is  necessary  in  addition  to  draw  elevations  of  the  remaining  sides 
and  one  or  more  longitudinal  and  transverse  sections  showing  the  framing  and 
general  construction;  details  drawn  to  a  large  scale  are  also  required,  from  which 
and  the  specifications  the  building  may  be  erected. 

The  size  of  the  page  has  compelled  the  titles  to  be  put  within  the  body  of 
the  drawings  ;  after  copying,  place  them  outside,  and  give  ample  margin.  In 
all  scale  drawings  the  scale  should  form  a  part  of  the  title.  On  Fig.  1311  the 
section  and  end-elevation  are  given  together.  This  is  also  for  economy  of  space, 
but  should  be  copied  by  the  draughtsman  in  two  distinct  drawings,  each  of  the 
full  width  of  the  building. 

Instead  of  hatching  the  walls  and  partitions,  as  in  the  examples  given,  these 
are  often  indicated  in  solid  black,  or  in  colour,  brick  walls  by  carmine,  wooden 
walls  and  partitions  by  burnt  sienna,  other  materials  by  colours  as  nearly  repre- 
senting them  as  possible,  which  may  be  purchased  in  pans  under  the  name  of 
technical  water  colours. 

Plate  XIII  is  an  illustration  in  colour  of  a  plan  and  ceiling  from  a  design 
of  Arthur  Gilman,  architect. 

548 


ARCHITECTURAL  DRAWING. 


549 


550 


ARCHITECTURAL  DRAWING. 


ARCHITECTURAL  DRAWING. 


551 


552 


AECHITEOTUEAL   DRAWING. 


_J 


o 

IP 


ARCHITECTURAL  DRAWING. 


553 


SECTION. 


FIG  1311. 


554 


ARCHITECTURAL  CONSTRUCTION. 


Details  of  Construction. — Foundations  in  variety  and  requirements  are 
treated  fully  under  "  Engineering  Drawing,"  but  for  common  structures  the 
draughtsman,  if  there  are  examples  in  the  vicinity  of  the  proposed  structure,  will 
conform  to  the  teachings  of  practice,  or  to  the  building  laws,  if  there  are  any  in 
force.  In  general,  for  small  buildings,  cellar-walls,  if  of  stone  laid  in  mortar, 
should  not  be  less  than  18"  thick  ;  if  of  brick,  16",  arid  the  base  6"  to  12"  wider. 


OD          D       D        D         D         O         D 


T 


m 


T 


I 


FIG.  1312. 


FIG.  1313 


FIG.  1314. 


Figs.  1312  to  1314  represent  the  side  and  end  elevations  and  plan  of  a  tim- 
ber frame  building,  of  common  construction,  supported  on  brick  or  stone  walls, 


ARCHITECTURAL  CONSTRUCTION. 


555 


in  which  s  s  are  the  sides,  V  V  the  floor-beams,  1 1  trimmer-beams,  and  h  the 
header.  The  beams,  J  5,  framed  into  the  header  are  called  tail-beams;  pp  are 
posts,  which  are  distinguished  by  their  position,  as  corners,  intermediate  and 
window  posts ;  p'  p'  studs,  g  g  girts,  c  c  plates,  d  d  braces,  and  r  r  rafters. 

Usual  dimensions  of  timber  for  frame  of  common  dwelling-houses :  sills 
G"  X  8",  posts  4"  X  8",  studs  2"  X  4"  or  3"  X  4",  girts  6"  X  the  depth  of  floor- 
joists,  plates  4"  X  6" ;  the  floor-joists  (J,  Fig.  1315)  are  notched  into  the  girts. 
The  posts  and  studs  are  tenoned  into  the  sills  and  girts.  Fig.  1316  represents  a 


FIG.  1315. 


I  c 


FIG.  1316. 


FIG.  1318. 


tenon,  b  c,  in  side  and  end  elevation,  and  mortise,  a ;  the  portions  of  the  end  of 
the  stud  resting  on  the  beam  are  called  the  shoulders  of  the  tenon. 

The  frame  is  covered  with  boards  usually  1"  thick,  laid  either  horizontally 
or  diagonally,  and  nailed  strongly  to  the  posts  or  studs.  Fig.  1317  is  the  ele- 
vation of  the  end  frame  of  a  house,  showing  by  breaks  the  diagonal  cover  of 
boards  and  the  inner  lathing.  The  lower  story  is  sheathed  or  ceiled  with  nar- 
row boards,  the  upper  shingled. 

In  the  balloon  or  spike  frame  the  stiffness  depends  on  the  nailing,  and  mor- 


556 


ARCHITECTURAL  CONSTRUCTION. 


CEILING  LINE 


3*X  *"                ,       . 

(3  X  4 

3*X  4* 

Vx  4" 

2*X  4* 

FLOOR  LINE 

FIG.  1319. 

FIG.  1320. 


FIG.  1321. 


N 


tise  and  tenon  are  omitted,  and  the  girts  supplied  by 
a  board  a  3"  or  4"  x  1*  let  into  the  studs  (Fig.  1318) 
and  firmly  nailed  to  them.  The  studs  are  nailed  to 
the  plates  and  sills. 

The  studs  at  all  door-openings  should  be  set  at 
least  2*  wider  and  3*  higher  than  the  size  of  the  fin- 
ished opening.  It  is  not  unusual  to  have  double  studs 
(2"  x  4")  to  inclose  these  openings  (Fig.  1319).  This 
leaves  the  doorway  more  or  less  independent  of  the 
partition.  Partition  studs  are  of  smaller  dimensions 
than  those  of  the  frame,  but  are  set  like  them  and 
usually  12"  and  16"  centres,  adapted  to  the  length  of 
the  lath  (48").  The  sizes  of  the  studs  are  generally 
2  X  4,  3  X  5,  or  3  X  6  inches,  according  to  the  height 
of  the  partition ;  for  very  high  partitions,  greater 
depth  may  be  required  for  the  studs,  but  three  inches 
will  be  sufficient  width. 

Partitions  are  usually  cut  in  between  sills  placed 
on  the  floor-beams  (Fig.  1320),  and  similar  caps  above, 
beneath  the  beams.  Where  partitions  of  the  second 
story  are  directly  above  those  on  the  first  story  it  is 
better  to  foot  the  studs  on  the  caps  of  the  latter,  and 
not  on  the  beams  (Fig.  1321).  Where  there  are  double 
floors,  the  sills  are  placed  on  the  bottom  floor,  or  on 
the  floor  without  a  sill.  It  may  be  important  that  the 
partitions  should  be  self-sustaining.  This  is  effected 
by  simple  bridging,  well  nailed  to  the  studs,  as  shown 
in  Fig.  1322,  or  by  herring-bone  bridge,  as  shown  in 
plan  of  floor  (Fig.  1330),  or  by  a  system  of  trussing, 
as  in  Fig.  1323.  This  method  of  trussing  must  vary 
with  the  position  of  opening.  The  foot  of  the  braces 
should  rest  on  a  positive  support.  The  bridging 
should  be  accurately  cut  and  firmly  nailed.  Bridging 
distributes  the  weight  of  the  partition,  but  trussing 
concentrates  it  at  the  ends  of  the  braces. 

Walls  in  Masonry. — For  walls  above  the  cellar,  it 
will  be  found  difficult  to  lay  stone  walls  in  mortar, 


FIG.  1322. 


FIG.  1323. 


ARCHITECTURAL   CONSTRUCTION. 


55T 


with  fair  bond  and  face,  less  than  16"  thick.     Brick  walls  may  be  as  thin  as  8" 
for  exteriors,  and  for  partitions  4".,     Brick  walls  are  usually  bonded  by  head- 
ing-courses every  fifth  to  seventh  course.     Where  the  outside 
course  is  pressed  or  face  brick,  these  are  laid  on  stretchers,  and 
the  bond  with  the  backing  may  be  thin  strap-iron,  laid  in  the 
joints,  or,  by  cutting  off  the  interior  corners  of  the  face-course, 
say  every  fifth  course,  and  laying  common  brick  diagonally  of 
the  wall  resting  in  this  clipped  corner  (Fig.  1324).     The  face  of 
buildings  is  often  built  of  thin  ashlar,  which  is  secured  with 
iron  anchors  to  the  brick  backing. 

In  most  cities  there  are  building  acts  in  force  defining  the 
kinds  of  material  and  thickness  of  walls  and  foundations,  to 
which  all  constructions  within  their  limits  must  conform. 

Openings  in  masonry-walls  are  covered  by  lintels  or  arches, 
or  both.     It  is  usual  to  place  a  stone  or  cast-iron  lintel  in  the 
exterior  face  over  openings  for  doors  and  windows,  with  a  wooden  lintel  inside 
(Fig.  1325),  and  a  relieving  arch  above.     For  larger  openings,  brick  arches  are 
turned  on  cast-iron  skew-backs, 
of  which  the  thrust  is  resisted 


FIG.  1324. 


FIG.  1325. 


FIG.  1326. 


by  a  tie-bolt  (Fig.  1326),  or  cast-iron  lintels,  box  girders,  j^-  or  rolled  I-beams. 

But  it  is  to  be  observed  that,  when  the  cement  is  set,  there  is  little  or  no  thrust 
from  the  arch.  The  whole  dead  work,  or  masonry  without 
an  opening,  forms  a  monolithic  beam,  and,  if  there  is  depth 
enough  of  this,  the  arch  is  of  no  account.  It  is  the  custom 
in  the  north  of  Italy  to  construct  flat  lintels  of  brick,  of  con- 
siderable span,  depending  entirely  on  the  mortar  for  strength. 


FIG.  1327. 


FIG.  1328. 


FIG.  1329. 


To  distribute  the  weight  of  piers  over  the  foundation  of  walls  with  open- 
ings, it  is  very  common  to  construct  inverted  arches  beneath  spans  or  open- 
ings. In  old  houses  it  was  not  unusual  to  make  the  exterior  arches  of  an 


558 


ARCHITECTURAL  CONSTRUCTION. 


opening  flat  or  rectangular  in  outline,  with  the  joints  radial.     This  is  now  rele- 
gated to  ornamental  construction. 

Concrete  Walls. — It  is  common  in  many  places  where  brick  and  stone  are 
expensive  and  gravel  is  abundant  to  make  walls  of  concrete,  in  proportions  of 


FIG.  1330. 

one  of  cement  to  five  to  seven  of  gravel.  The  space  requisite  for  the  wall  is 
inclosed  with  plank,  and  is  filled  in  with  concrete,  well  rammed.  Figs.  1327 
and  1328  are  plans  of  concrete  walls  with  inclosing  plank,  and  Fig.  1329  an 
elevation.  The  planks  are  held  by  bolts  passing  through  wall  and  plank,  all  of 
which  are  removed  after  the  wall  is  set,  and  the  bolt-holes  are  then  filled  with 
cement.  The  thickness  of  walls  should  be  a  little  in  excess  of  those  of  brick. 

Flooring. — The  timbers  which  support  the  flooring-boards  and  ceiling  of  a 
room  are  called  the  naked  flooring. 

The  simplest  form  of  flooring,  and  the  one  usually  adopted  in  the  construc- 
tion of  city  houses  and  stores,  is  represented  in  plan  and  section  (Fig.  1330). 
It  consists  of  a  single  series  of  beams  or  deep  joists,  reaching  from  wall  to  wall. 
As  a  lateral  brace  between  each  set  of  beams  a  system  of  bridging  is  adopted, 
of  which  the  best  is  the  herring-bone  bridging,  formed  of  short  pieces  of  joists 
about  2x3,  crossing  each  other,  and  nailed  securely  to  the  tops  and  bottoms 
of  the  several  beams,  represented  by  a  and  b ;  and  wherever  a  flue  occurs,  or  a 
stairway  or  well-hole  prevents  one  or  more  joists  from  resting  on  the  wall,  a 
header,  H,  is  framed  across  the  space  into  the  outer  beams  or  trimmer-beams 
T  T,  and  the  beams  cut  off  or  tail-beams  are  framed  into  the  header. 

Whenever  the  distances  between  the  walls  exceed  the  length  that  can  safely 
be  given  to  floor-joists  in  one  piece,  an  intermediate  beam  or  girder,  running  lon- 
gitudinally, is  introduced,  on  which  the  joist  may  be  set  (Fig.  1331),  notched  on 
(Fig.  1332),  or  boxed  in  (Fig.  1333),  or  both  boxed  and  notched.  They  may 
also  be  framed  in  with  tenon  and  mortise ;  the  best  form  is  the  tusJc-tenon 


ARCHITECTURAL  CONSTRUCTION. 


559 


\ 


FIG.  1331. 


FIG.  1332. 


FIG.  1333. 


FIG.  1334. 


(Fig.  1334).  Flooring  is  still  further  varied,  by  framing  with  girders  longi- 
tudinally ;  beams  crosswise,  and  framed  into  or  resting  on  the  girders ;  and 
joists  framed  into  the  beams,  running  the  same  direction  as  the  girders.  When 
the  joists  are  not  flush  or  level  with  the  bottom  of  the 
beams  or  girders,  either  in  the  finish  the  beams  will 
show,  or  ceiling-joists  or  furrings  will  have  to  be  intro- 
duced. 

The  width  of  beams  as  sold  in  the  market  is  from  2" 
to  6" ;  those  for  common  houses  and  spans  are  2",  but 
for  more  important  buildings  and  structures  3"  to  4". 
The  depth  of  beams  and  distances  between  centres  may  be  determined  from 
the  weight  to  be  supported  (that  is,  load  per  square  foot  by  the  number  of 
feet,  including  that  of  the  floor),  and  from  the  table,  page  239  ;  but  this  table 
gives  the  central  load,  which  is  one  half  the  distributed  load. 

The  following  table  gives  the  load  per  square  foot  for  different  characters  of 
buildings ;  for  floors  of — 

Dwellings 40  pounds  per  square  foot. 

Churches  and  public  halls 80  "  "  "  " 

Warehouses  and  general  merchandise 250  "  "  "  " 

Factories 200  to  400  "  "  "  " 

Snow,  30  inches  deep 16  "  "  "  " 

Maximum  wind  pressure 50  "  "  "  " 

Roofs  for  wind  and  snow 30  "  "  "  " 

For  slate 45  "  "  " 

Plastering 8  " 

Timber  on  sale  is  seldom  found  sawed  to  fractional  dimensions  of  an  inch 
or  in  lengths  to  fractions  of  feet. 

Trimmer-beams  and  headers  should  be  of  greater  width  than  the  other 
beams,  depending  on  the  distance  of  the  headers  from  the  wall,  and  the  num- 
ber of  tail-beams  framed  into  the  trimmers ;  by  the  New  York  Building  Act  all 
headers  must  be  hung  in  stirrup-irons  (Fig.  1335),  and  not  framed. 

Beams  must  be  anchored  to  the  walls  and  to  each  other  when  there  are 
two  lengths  meeting  on  girders.  The  straps  to  be  not  less  than  1£"  X  f", 
spiked  to  sides,  on  top,  or  bottom  of  beam.  The  anchors  and  beams  to  make  a 


FIG.  1336. 


FIG.  1335. 


FIG.  1337. 


tie  across  the  building  about  every  6  feet.     Figs.  1336  and  1337  are  common 
forms  of  ties  between  beams  or  between  beams  and  walls.     Fig.  1338  is  an 


560 


ARCHITECTURAL  CONSTRUCTION. 


anchor  between  beams  and  embracing  a  column.     Fig.  1339  is  a  spear-anchor 
between  beams  and  wall ;  the  angle  is  driven  into  the  beam.     In  warehouses  it 

is  usual  to  carry  anchors 
through  the  wall  with  large 
washers,  often  ornamental, 
and  nut  on  the  outside. 

Wooden  beams  built  into 
walls  must  have  an  air  space 


FIG.  1338. 


FIG.  1339. 


round  them  with  ends  cut  diagonally  and  anchored  to  the  walls  (Fig.  1340). 
The  air  spaces  at  the  sides  are  for  ventilation,  and  with  the  diagonal  cuts  at  the 
ends  permit  the  beams  weakened  by  fire  to  fall  without  disturbing  the  walls. 
Cast-iron  boxes  and  plates  for  ends  of  beams  can  be  purchased,  with  flanges 
for  anchors  to  walls  and  beams. 

Floors. — In  New  York  it  is  usual  to  lay  single  floors  of  tongued  and  grooved 
boards  directly  on  the  beams,  but  in  the  Eastern  States  double  floors  are  more 
common.  The  first  floor  consists  of  an  inferior  kind  of  boards,  as  hemlock, 
unmatched,  laid  during  the  progress  of  the  work  as  a  sort  of  staging  for  the 
carpenter  and  mason,  and,  in  finishing,  a  second  course  is  laid  on  them  of 'better 
material,  generally  tongued  and  grooved,  but  sometimes  only  jointed.  Ceilings 
should  always  be  furred,  and  the  laths  be  nailed  to  the  strips.  Furring-strips 
usually  are  of  inch  board,  2"  wide,  and  12"  from  centre  to  centre,  nailed  cross- 
wise from  joist  to  joist. 

In  dwellings  it  is  desirable  to  isolate  the  floors  of  each  story,  so  that  noise, 
vermin,  smells,  and  fire  may  be  cut  off.  The  first  is  usually  done  by  deafening, 
which  consists  (Fig.  1341)  of  a  sub-floor,  resting  on  cleats,  nailed  to  the  beams 

and  about  4"  below  the  floor.  This  space 
is  filled  with  lime-mortar,  weakened  by  a 
mixture  of  sand  or  gravel,  but  strong 


FIG.  1340. 


FIG.  1341. 


enough  to  set.     If  the  timber  is  green,  the  contact  of  the  mortar  is  apt  to  pro- 
duce dry  rot. 

Deafening  may  be  secured  to  great  extent  by  double  floors,  with  two  or  three 
thicknesses  of  carpet  paper  or  sheathing  quilt  between.  When  small  vermin, 
like  cockroaches,  can  pass,  stenches  and  fire  can  find  their  way.  To  prevent 
which,  begin  at  the  cellar  and  cut  off  all  access  to  space  between  plastering  and 
floor;  if  the  ceiling  is  plastered,  fill  in  between  studs  tightly  with  strips  of 


ARCHITECTURAL  CONSTRUCTION. 


561 


board,  and  above  them  a  course  of  brick  in  cement. 
Fibrous  hemlock  boards  prevent  the  gnawing  of  rats 
and  mice. 

The  fireproof  of  old  builders  consisted  simply  of 
plain  cylindrical  or  groined  arches  (Fig.  1342)  in 
stone  or  brick  masonry  or  concrete. 

Figs.  1343  to  1347  are  illustrations  of  Roman 
constructions  in  masonry,  from  "  Dictionnaire  Rai- 
sonne  de  1'Architecture,"  par  M.  Viollet  Le  Due. 

Fig.  1343  is  a  perspective  view  of  a  cylindrical  arch  in  process  of  construc- 
tion.    The  centres  A  and  lagging  B  are  quite  light,  as  the  full  load  of  the  arch 


FIG.  1342. 


1344. 


FIG.  1343 


is  never  borne  by  them.  On  the  lagging,  B,  a  cover  of  flat  tile,  C,  is  laid  in  ce- 
ment, and  above  ribs,  D  D,  and  girts,  E  E,  in  brick  masonry,  shown  on  a  larger 
scale  in  Fig.  1344,  with  the  plank  P  used  for  the  support  of  the  girt  bricks  E, 
which  is  removed  after  the  mortar  is  set.  The  panels  are  now  filled  with  concrete. 
37 


562 


ARCHITECTURAL  CONSTRUCTION. 


Fig.  1345  represents  rib  and  portions  of 
girts  of  a  groin  shown  in  plan,  Fig.  1346, 
efg  h  being  that  of  the  rib ;  K,  a  timber  of 
the  centre. 

A  similar  construction  also  obtained  for 
domes,  the  girts  being  of  the  same  width  as 
the  ribs,  and  sunk  panels  formed  by  furr- 
ing up  on  the  wooden  lagging  of  the  cen- 
tres. 

Fig.  1347  is  a  perspective  of  a  donre,  in 
which  the  brick  skeleton,  ribs,  and  girts 
are  curved,  with  panels,  B  B,  of  concrete. 

In  Italy  ceilings  are  made  in  single 
courses  of  brick,  groined,  and  laid  without 
centres,  the  arcs  being  described  on  the 
side-walls,  and  the  bricks  laid  in  plaster  to 
a  line.  The  spandrels  may  be  levelled  up 
with  concrete,  when  rooms  above  are  to  be 
occupied,  but  often  there  is  only  the 

brick  arch  forming  the  ceiling  of  the  principal  rooms,  with  a  light  wooden 

roof  above. 


FIG.  1346. 


FIG.  1345. 


FIG.  1347. 


ARCHITECTURAL  CONSTRUCTION. 


563 


The  sizes  of  Italian  brick  are  2"  X  4"  X  10"  and  If  X  4"  X  12" ;  when 
there  is  no  load  above,  these  are  laid  flatwise  in  the  arch. 

In  one  of  the  warehouses  of  the  Appleton  Manufacturing  Company  at 
Brooklyn  the  floor  was  constructed  of  groined  arches  in  concrete,  supported  on 
brick  side- walls  and  piers.  Piers  were  2'  square  and  13'  centres ;  the  arches 
finished  for  a  floor  above  were  21"  deep  at  the  spring  and  9"  at  the  key.  Ceil- 
ing was  plastered  and  the  room  beneath  occupied  as  a  warehouse.  In  the  room 
above  a  wooden  floor  was  laid  and  used  as  a  printery,  and  has  been  occupied 
for  many  years.  There  has  been  found  one  objection  to  the  concrete — that 
water  in  quantity  spilt  on  the  upper  floor  sipes  through,  to  prevent  which  there 
should  have  been  on  the  concrete  floor  a  thin  coat  of  Portland  cement  or  of 
asphalt. 

The  first  fireproof  buildings  in  use  here  were  like  the  example  above  of  the 
Appleton  warehouse,  with  supports  and  arches  entirely  in  masonry.  The  latter 
were  usually  cylindrical  or  segmental,  plain  or  groined.  The  depth  taken  for 
the  construction  and  the  floor  space  occupied  by  the  supports  were  objection- 
able, but  as  fireproof  constructions  they  were  the  best. 

The  erection  of  high  buildings,  the  large  and  valuable  stocks  often  carried 
in  stores  and  warehouses,  have  involved  the  necessity  of  forms  of  fireproof  con- 
structions which  will  prevent  the  spreading  of  conflagrations  and  secure  the 
contents  of  a  building,  but  it  must  be  understood  that  no  construction  has  yet 
been  invented  that  will  prevent  the  destruction  of  a  building  by  fire  whose 
contents  are  large  masses  of  combustibles ;  the  buildings  should  be  called  fire- 
resisting  rather  than  fireproof.  The  first  buildings  designed  for  this  purpose 
consisted  of  iron  I-beams,  brick  arches,  and  concrete  spandrels,  with  wooden 
floors  above.  This,  aside  from  its  weight,  was  satisfactory,  but  a  skew-back  tile 
and  plaster  were  necessary  to  protect  the  bottom  flange  of  the  iron  beam.  The 
tie-rod,  when  necessary,  was  concealed  in  the  arch. 

In  another  form  of  construction,  instead  of  using  a  movable  centre,  a 
crimped  sheet-iron  arch  was  used,  which  was  left  in  and  made  a  part  of  the 
structure,  above  which  there  was  a  concrete  filling  to  the  level  of  the  top  of  the 
beam. 

To  reduce  the  weight  of  brick  and  increase  their  fire  resistance,  brick  are 
now  made  hollow,  with  flat  surfaces  below  for  the  reception  of  plastering,  and 
above  for  the  wooden  floors  (Fig.  1348).  Such  floorings  weigh  only  about  one 
half  that  of  solid  brick  arches,  and  therefore  admit  of  beams  of  less  weight  per 


FIG.  1348. 


square  foot  of  floor,  either  by  the  reduction  of  the  weight  of  the  beam  or  an 
increase  of  span.  A  thin  layer  of  concrete  is  put  on  the  top  of  the  brick,  and 
wooden  strips  embedded  to  nail  the  floor  to. 

By  mixing  sawdust  with  the  clay,  which  is  burned  out  in  the  firing,  the 
product  becomes  a  very  light,  porous,  and  firm  substance,  which  can  be  cut 


564 


ARCHITECTURAL  CONSTRUCTION. 


with  the  saw  and  will  hold  a  nail.    Porous  brick,  hollow,  with  thicker  ribs  than 
the  tiles,  are  sawed  to  voussoir  joints  and  laid  between  I-beams  as  flat  arches. 


Fio.  1349. 


FIG.  1350. 


For  ceilings,  porous  tiles  about  2"  thick  rest  on  iron  straps  suspended  from 
wooden  beams  (Fig.  1349),  or  on  the  flanges  of  j_-irons  in  a  bed  of  mortar  (Fig. 
1350),   the   thickness    of   the   plaster    finish   beneath 
affording    some    protection    to    the   iron    straps   and 
flanges  from  fire. 

Iron  posts  not  protected  are  not  as  safe  as  wooden 
ones.  Cast-iron  posts  may  be  cast  with  a  surface  of 
nails  or  projections  for  plaster  of  common  mortar,  or  of 
cement,  with  a  finish  of  Keene's  cement,  which  admits 
of  washing.  Figs.  1351  and  1352  are  elevation  and 
section  of  a  Phoenix  column  with  a  porous  terra-cotta 
covering;  Figs.  1353  and  1354,  a  similar  covering  ap- 
plied to  a  square  and  round  post. 

Fig.  1355  shows  in  perspective  the  applications  of 
hollow  brick  to  the  lining  of  exterior  walls  bonding 
with  the  common-sized  brick  and  equal  in  crushing 
strength ;  they  supply  the  place  of  a  course,  and  the 
moisture  will  not  strike  through. 


FIG.  1351. 


FIG.  1352. 


FIG.  1353. 


FIG.  1354. 


FIG.  1355. 


Fig.  1356  is  another  form  applied  di- 
rectly to  the  face  of  a  wall  secured  by 
flat-headed  nails  driven  into  the  joints  of 
the  brickwork. 

Fig.  1357  shows  the  mode  of  setting 
hollow  brick  for  a  partition ;  where  it  is 
necessary  that  nails  should  be  driven, 
porous  brick  should  be  inserted. 

Improvements  in  material,  especially 
the  use  of  rolled  steel  instead  of  wrought- 


ARCHITECTURAL   CONSTRUCTION. 


565 


iroii,  led  to  a  skeleton  construction  which  consists  of  rolled  steel,  wrought-  or 
cast-iron  columns  supporting  a  frame  of  rolled  steel,  beams  and  girders,  set 
and  framed  before  any  of  the  masonry  except  the  foundation  walls  are  laid. 

The  next  in  order  of  construction  are 
the  side  and  end  walls,  of  which  the 
masonry  may  be  wholly  or  partially  self- 
sustaining  or  merely  a  screen  or  cur- 
tain extending  from  the  top  of  any 
wall  girder  to  the  under  side  of  the  next 
girders  above.  The  outside  posts  in 


FIG.  1357. 
FlO.  1356. 

the  last  case  as  well  as  the  inside,  therefore,  sustain  all  the  dead  and  live  load. 
The  dead  loads  include  material  used  in  actual  construction,  or  fixtures  and 
machinery  which  form  a  permanent  part  of  the  necessities  of  occupation.  Live 
loads  are  the  weight  of  occupants,  furniture,  goods,  stores,  and  movables. 


Tie  Kocfs 


Co/. 


-O 


CJ 


FIG.  1358. 


Fig.  1358  is  a  floor  plan  of  girders  and  beams  of  the  standard  form;  columns 
are  preferably  of  rolled  steel,  but  often  of  cast-iron.  In  all  the  walls,  centrally 
between  walls  and  columns,  and  between  columns,  girders  are  framed  on  which 
the  beams  rest  and  to  which  they  are  usually  fastened. 


566 


ARCHITECTURAL  CONSTRUCTION. 


Under  the  head  of  "  Engineering  Drawing  "  foundations  are  shown  with  the 
bases  of  these  columns  and  the  iron  grillage  on  which  they  are  supported.  All 
the  parts  are  proportioned  to  the  loads  which  they  are  to  sustain. 

The  iron  surface  of  all  columns,  girders,  and  beams  must  be  protected  from 


FIG.  1359. 

fire,  commonly  by  brick  —  common,  hollow,  or  porous,  and  of  thickness  not  less 
than  4".  The  floors  are  usually  flat  arches  of  hollow  brick  (Fig.  1348)  in  which 
the  skew-back  extends  below  the  flanges  of  beams  and  girders  to  sustain  the 
plaster  protection. 

Besides  the  flat  arches  of  hollow  brick  and  of  porous  brick,  concrete  has  been 
used  for  beams  and  flooring,  but,  as  the  material  has  comparatively  little  tensile 
strength,  the  bottom  tension  of  a  concrete  beam  has  been  met  by  steel  rods  or 
wire  anchored  and  embedded  in  the  material.  Twisted  bars  of  wrought-iron 
from  •£"  to  2"  square  have  been  introduced  by  E.  E.  Ransome,  of  San  Francisco,  to 
strengthen  flat  floors  of  considerable  span,  and,  as  they  can  not  slip,  the  anchor- 
age is  well  and  uniformly  distributed.  Experiments  by  Kirkaldy  for  Mr.  "Hyatt 
demonstrated  that  the  expansion  and  contraction  of  concrete  and  of  iron  is 
equal  under  changes  of  temperature. 

Metropolitan  Fire  Proofing  Company  of  this  city  make  use  of  the  I-beam 
frame  and  tension  rods  or  wires  of  galvanized  iron  (Fig.  1359)  which  are  em- 
bedded in  a  concrete  composed  very  largely  of  plaster-of-Paris  cement  and  a 
little  sand,  with  crushed  coke,  cork,  or  sawdust. 

Figs.  1360,  1361,  and  1362  are  plan 
and  elevations  of  one  of  the  standard 
connections  of  I-beams  and  Z-bars 
from  the  hand-book  of  the  Carnegie 
Steel  Company. 

Figs.  1363  and  1364  is  a  cross-pin- 
tle connection  of  girders  and  struts  of 
the  Phoenix  Iron  Company  with  their 
usual  steel  column. 

Figs.  1365  and  1366  is  a  cast-iron 
pintle  connection  of  the  same  company. 
Figs.    1367,   1368,   and    1369    are 
drawings  of  a  cast-iron  joint  detail. 


FIG.  1362. 


- 


•  Itr-1 


FIG.  i860. 


In  the  present  form  of  framing 
steel  skeletons,  rivets  are  preferred  to 
bolts,  and  much  depends  on  their 
strength  in  shear. 

Fig.  1370  is  a  plate  of  the  standard 
connection  of  angles  for  I-beams  from 
the  Carnegie  Company. 


ARCHITECTURAL  CONSTRUCTION. 


567 


FIG.  1363. 


FIG.  1365. 


FIG.  1368. 


Fio.  1367. 


FIG.  1369. 


FIG.  1371. 


568 


ARCHITECTURAL  CONSTRUCTION. 


Fig.  1371  is  a  section  of  the  wall  of  the  New  Street  front  of  the  Manhattan 
Life  Insurance  Company  of  New  York,  showing  the  position  of  wall  girders. 
The  front  is  176'  X  254'  high,  with  five  posts,  including  the  corner  ones. 

The  great  objections  made  to  the  skeleton-frame  construction  are  that  the 


STANDARD  CONNECTION  ANGLES. 
FOR  I  BEAMS. 


for3"lJ61bs. 
for  4"!  [?  Ibs. 


for  5" I  j  10  Ibs. 
Ibs. 


CHANNELS, 
for  is''c  — 33  N>s> 


for8"c  jn  Ibs. 
for  g'C  J 14  Ibs. 


Connections  for  3,4,5,  and  6  I-beams  apply  also  to  Channels. 
All  holes  for  %  Bolts  or  Rivets. 
FIG.  1370. 

iron  is  liable  to  rust  in  position  where  it  can  not  be  seen,  but  it  is  met  by  care  in 
cleansing  the  iron,  in  boiling  in  oil  and  painting,  or  by  the  Smith  process  used 
in  protecting  cast-iron  pipes,  and,  second,  the  want  of  protection  against  wind 
strains  and  a  proper  system  of  bracing  without  interfering  with  the  occupancy 
of  the  building.  The  section  of  walls  (Figs.  1372  and  1373)  shows  the  dimen- 


ARCHITECTURAL  CONSTRUCTION. 


569 


FIG.  1372. 


FIG.  1373. 


sions  required  by  the  Building  Depart- 
ment of  New  York  city  for  the  skeleton 
construction  and  for  plain  walls  with- 
out it. 

If  the  wall  construction  follows 
promptly  that  of  the  steel  frame,  and 
it  is  temporarily  held  by  tie  rods,  a 
mortar  set  will  be  secured  which  will 
resist  the  usual  wind  stresses.  For 
buildings  entirely  of  brick  masonry,  it 
is  usual  to  introduce  wooden  braces — 
as  the  work  progresses — which  are  re- 
moved when  fully  closed  in. 


FIG.  1374. 


FIG.  1375. 


In  New  England  there  has  been  introduced  what  are  called  fire-retarding 
constructions  for  mills,  of  which  the  beams,  posts,  and  floors  are  of  wood.     The 


FIG.  1376. 


570 


ARCHITECTURAL  CONSTRUCTION. 


principle  of  the  construc- 
tion is  to  consolidate  the 
material  in  such  a  way 
that  a  fire  can  be  held  long 
enough  in  any  room  in 
which  it  may  originate  till 
the  water  and  appliances 
under  the  management  of 
an  established  fire  depart- 


FIG.  1377. 


ment  connected  with  the  mills  or  public  can  get  it 
under  control. 

Figs.  1374  and  1375  are  elevation  and  section  of 
post,  beams,  and  floors  which  show  the  details  of  con- 


Fio.  1378. 


Fio.  1379. 

struction,  and  Fig.  1376  of  a  mill  showing  a  floor  and 
a  roof.  The  ceiling  must  be  high  posted  and  the 
windows  wide,  and  set  well  up  to  the  ceiling  to  admit 
of  light  into  a  wide  mill.  When  there  is  plenty  of 
ground  space,  it  is  in  most  industries  safer  from  fire 
and  more  economical  in  management  to  have  a  one- 
story  mill  (Fig.  1377),  of  which  details  are  shown  in 
Figs.  1378  and  1379.  A  one-story  mill  may  be  of  any 
dimension  required,  as  the  central  spaces  are  lighted 
by  monitor  decks.  The  principle  of  all  this  construc- 
tion is  that  there  should  be  no  spaces  where  dust  may 
collect ;  in  the  floors  the  material  is  close,  but  if  the 


ARCHITECTURAL  CONSTRUCTION. 


571 


timber  be  not  seasoned  or  kiln-dried,  as  there  is  no  circulation  of  air,  it  may  dry 
rot.     The  posts  have  a  bore  through  the  centre  and  holes  connecting  with  it  at 


FIG.  1380. 


top  and  bottom  to  provide  air  circulation,  and  it  is  better  not  to  paint  any  of 
the  exposed  timber  until  all  the  moisture  is  dried  out. 

In  mills  sheathing  is  preferable  to  plastering,  as  this  last  may  break  and  pieces 
fall  into  the  machinery;  but  Fig.  1380  shows  a  form  of  construction  that  has 
served  well  for  warehouses,  and  is  safer  and  more  ornamental  than  the  usual 
timber  constructions.  The  lathing  consists  of  wire  cloth  fastened  with  staples, 
stapled  through  furring  strips  £' '  to  •£",  and  then  the  usual  three-coat  plaster. 

Doors. — In  stud-partitions,  the  openings  for  doors  are  framed  as  in  Fig. 
1319,  the  door-frame  being  independent  of  the  studs. 

Fig.  1381  represents  the  elevation  and  Fig.  1382  the  horizontal  section  of  a 
common  inside-door.  A  A  are  the  stiles,  B,  0,  H,  D,  the  bottom,  lock,  parting, 
and  top  rail,  E  the  panels,  and  F  the  muntin  ;  the  combination  of  mouldings 
and  offsets  around  the  door,  G,  is  called  the  architrave j  in  the  section,  a  a  are 
the  partition-studs,  b  b  the  door-jambs. 

Fig.  1383  represents  the  forms  of  the  parts  of  a  door,  and  the  way  in  which 
they  are  put  together.  When  the  tenons  are  to  be  slipped  into  the  mortises, 
they  are  covered  with  hot  glue,  and,  after  being  closed  up,  keys  are  driven  in. 

With  regard  to  the  proportions  of  internal  doors,  they  should  depend  in 
some  degree  on  the  size  of  the  apartments  ;  in  a  small  room  a  large  door  always 
gives  it  a  diminutive  appearance,  but  doors  leading  from  the  same  room  or 
passage,  which  are  brought  into  the.  same  view,  should  be  of  uniform  height. 
The  smaller  doors  which  are  found  on  sale  are  2  feet  4  inches  X  6  feet ;  for 
water-closets,  or  very  small  pantries,  they  are  sometimes  made  as  narrow  as  15 
inches,  but  any  less  height  than  6  feet  will  not  afford  requisite  head-room  ; 
2  feet  9  inches  X  7  feet,  3  feet  X  7  feet  6  inches,  or  3  feet  6  inches  X  8  feet, 
are  well-proportioned,  six-panelled  doors.  But  the  apparent  proportions  of  a 
door  may  be  varied  by  the  omission  of  the  parting-rail,  making  the  door  four- 
panelled,  or  narrowed  still  more  by  the  omission  of  the  lock-rail,  making  a  two- 
panelled  door.  Sometimes  the  muntin  is  omitted,  making  but  one  panel ;  but 
this,  of  course,  will  not  add  to  the  appearance  of  width,  but  the  reverse.  Wide 
panels  are  objectionable,  as  they  are  apt  to  shrink  from  the  mouldings  and 
crack.  The  mouldings  are  generally  planted  on,  and  nailed  to  the  stiles  and 
rails,  but  sometimes  formed  on  the  latter. 


572 


ARCHITECTURAL  CONSTRUCTION. 


When  the  width  of  the  door  exceeds  four  feet,  it  is  generally  made  in  two 
parts,  each  part  being  hung  to  its  side  of  the  frame,  or  one  part  hung  to  the 

other,  so  as  to  fold  back  like  a 
shutter;  or  the  parts  may  be 
made  to  slide  back  into  pockets 


G 

D 

E 

H 

F 

E 

O 

0 

C 

A 

A 

S 

FIG.  1381. 

123  4-tt 

FIG.  1382. 


FIG.  1383. 


or  grooves  in  the  partition.  The  doors  may  be  supported  on  wheels,  and  run 
on  tracks  at  the  floor-level;  or  the  tracks  may  be  above  the  doors,  and  the 
doors  suspended  ;  or  they  may  be  supported  by  levers,  and  be  moved  parallel 
without  rollers  ;  all  these  appliances  can  be  purchased. 

Figs.  1384,  1385,  and  1386  are  the  elevation,  vertical  and  horizontal  sections 
of  a  pair  of  slid  ing-doors.  There  are  no  knobs,  but  countersunk  pulls  to  the 
doors,  that  they  may  be  slid  entirely  within  the  pockets,  with  a  special  handle 
in  the  locks  at  the  edges  of  the  doors  for  withdrawing  them. 

Figs.  1387  and  1388  are  vertical  and  horizontal  sections  of  the  same  doors 
hung  on  butts  or  hinges. 

Figs.  1389  and  1390  are  the  elevation  and  horizontal  section  of  an  antas- 
finished  outside-door,  with  the  side-lights  C  C,  and  a  top,  fan,  or  transom  light 
B.  The  bar  A  is  called  a  transom,  and  this  term  is  applied  generally  to  hori- 
zontal bars  extending  across  openings,  or  even  across  rooms. 

Fig.  1391  is  the  elevation  of  an  outside  folding-door.  The  plan  (Fig.  1392) 
shows  a  vestibule,  V,  and  an  interior  door.  The  outer  doors  open,  as  shown  by 
the  arcs,  and  fold  back  into  the  pockets  or  recesses,  p  p,  in  the  wall.  This  is  a 
very  common  form  of  doors  for  first-class  houses  in  this  city.  The  fan-lights 
are  made  semicircular,  and  also  the  head  of  the  upper  panels  of  the  door  ;  these 


ARCHITECTURAL  CONSTRUCTION. 


573 


panels  in  the  interior  or  vestibule  door  are  of  glass.  Of  late  the  outer  doors  are 
extensively  used  as  storm  doors,  glazed  with  plate  glass  exposing  the  vestibule, 
and  hung  with  spring  butts  and  ornamental  in  finish. 


FIG.  1386. 


Windows  are  usually  understood  to  be  glazed  apertures.     The  sashes  may 
be  stationary,  but  for  most  positions  they  are  made  to  open  either  by  sliding 


574: 


ARCHITECTURAL  CONSTRUCTION. 


vertically,  or  laterally,  or  like  doors.     The  first  is  the  common  form  of  window, 
and  the  sashes  are  generally  balanced  by  weights ;  the  second,  except  in  a  cheap 


FIG.  1387. 


FEET 

form  in  mechanics'  shops,  are  seldom  used  ;  the  third,  often  used 
for  access  to  balconies  or  between  rooms,  are  called  casements,  or 
French  windows. 

Figs.  1393  and  1394  are  the  outside  elevation  and  horizontal 
section  of  one  half  of  a  common 


FIG.  1390. 


FIG.  1392. 


box-frame,  and  Fig.  1395  a  vertical  section  of  the  same  in  a  wooden 
frame  house.  S  is  the  sill  of  the  sash-frame,  W  the  frame-sill, 
with  a  wash  to  discharge  the  water,  B  the  bottom  rail  of  the  sash, 
M  the  meeting  rails,  T  the  top  rail,  H  the  head  of  the  sash-frame, 
and  A  the  architrave  similar  to  that  around  doors.  Instead  of 
two  sills,  S  and  W,  one  is  often  used,  and  inclined  to  form  the  wash.  D  is  the 
common  outside  blind.  In  the  sectional  plan  (Fig.  1400),  C  C'  are  the  win- 
dow-stiles, F  the  pulley -stile,  w  w  the  sash-weights,  p  the  parting  strip,  and  D  D 
double-fold  shutters. 

Figs.  1396  and  1397  are  the  interior  elevation  and  vertical  section  of  a  box- 
frame  window  in  a  masonry  wall ;  Fig.  1398  is  an  exterior  view  of  the  same 


ARCHITECTURAL  CONSTRUCTION. 


D 


FIQ.  1393. 


M 


<B 


FEET 


FIG.  1394. 


Fio.  1395. 


576 


ARCHITECTURAL  CONSTRUCTION. 


window,  and  Pig.  1399  a  horizontal  section.  In 
masonry  walls  the  sills  are  usually  of  stone,  as 
shown  in  Fig.  1397,  with  a  lap  of  the  window 
frame  on  it.  In  setting  the  sill,  one  course  of  brick 
is  left  out  beneath  the  central  portion  to  admit  of 
settlement  in  the  walls  without  stress  to  the  sill. 


o 


B  : 


E  3 


FIG.  1396. 


FIG.  1397. 


ARCHITECTURAL  CONSTRUCTION. 


In  brickwork,  the 
height  of  sill  and 
cap  corresponds 
to  a  determinate 
number  of  courses, 
so  that  it  may  not 
be  necessary  to 
split  brick  in  set- 
ting them. 

Unless  the  win- 
dows begin  from, 
or  nearly  from, 
the  floor,  the  point 
a  (Fig.  1395)  may 
be  fixed  at  a  height 
of  about  30  inches 
above  the  floor, 
and  the  top  of  the 
window  sufficient- 
ly below  the  ceil- 
ing to  allow  space 
for  the  architrave 
or  other  finish 
above  the  window, 
and  for  the  cornice 
of  the  room,  if 
there  be  any  ;  .a 
little  space  be- 
tween these  adds 
to  the  effect.  For 
common  windows, 
the  width  of  the 
sash  is  4  inches 
more  than  that  of 
the  glass,  and  the 
height  G  inches 
more  ;  thus  the 
sash  of  a  window 

3  lights  wide  and 

4  lights    high,  of 
12"  X  16"  glass,  is 
3     feet    4    inches 
wide  and  5  feet  10 
inches    high.      In 
plate  -  glass    win- 
dows   more  width 
is    taken    for   the 
stiles     and     rails. 

38 


FIG.  1398. 


Fie.  1399. 


578 


ARCHITECTURAL   CONSTRUCTION. 


The  usual  sizes  of  cylinder  glass  are  7"  X  9"  up  to  24"  X  36",  but  single  thick 
glass  may.  be  had  up  to  40"  X  60" ;  double  thick,  48"  X  62".  Plate  glass, 
polished  or  rough,  may  be  had  of  a  size  as  large  as  14  X  8  feet. 

In  Fig.  1393  the 
blind  D  is  hinged  to 
the  hanging  stile,  and 
is  closed  within  the 
opening  in  the  mason- 
ry. The  slats  are 


.  1400. 


1101. 


FIG.  1402. 


movable  on  pin  tenons, 

and  those  of  each  half, 

upper    and   lower,  are 

connected  by  a  central 

bar,  so  that   they    are 

moved    together,    and 

adjusted  at  any  angle  to  the  light.     In  Fig.  1399  the  blinds  are  inside,  4-fold, 

and  folding  back  into  pockets.     It  is  more  usual  to  make  the  pockets  for  the 

blinds  inclined  to  the  window,  as  in-  Fig.  1400,  giving  to  the  interior  more 

light,  or  ampler  space  for  curtains. 

Fig.  1401  is  the  outside  elevation  of  a  French  window  or  casement. 

Fig.  1402  represents  the  sectional  elevation  of  the  same  window,  in  broken 
lines,  and  on  a  larger  scale ;  the  same  letters  designate  similar  parts  as  in  Fig. 
1395.  A  transom-bar  is  often  framed  between  the  meeting-rails,  and  in  this 
case  the  upper  sash  may  be  movable;  in  Fig.  1402  it  is  fixed.  An  upright, 
called  a  mullion,  is  often  introduced  in  the  centre,  against  which  the  sash  shuts. 

For  use  as  doors,  the  lower  sashes  should  not  be  less  than  5  feet  6  inches 
high.  In  these  forms  of  sash  the  rails  and  stiles  are  wide,  and  for  equal  aper- 
tures. French  windows  when  closed  admit  light.  The  chief  objection  to  this 
window  lies  in  the  difficulty  of  keeping  out  the  rain  at  the  bottom  in  a  driving 
storm.  To  obviate  this,  the  small  moulding  d,  with  a  drip  or  undercut,  is  nailed 
to  the  bottom  rail ;  but  the  more  effectual  means  is  the  patent  weather-strip, 
the  same  as  used  on  outside  doors. 

Dormer  or  attic  windows  are  framed  and  set  as  in  an  upright  stud-partition. 

Stairs  consist  of  the  tread  or  step  on  which  to  set  the  feet,  and  risers,  up- 


ARCHITECTURAL  CONSTRUCTION. 


579 


right  pieces  supporting  the  treads — each  tread  and  riser  forms  a  stair.  If  the 
treads  are  parallel  they  are  called  fliers  ;  if  less  at  one  end  than  the  other,  they 
are  called  winders,  f  and  w  (Fig.  1409).  The  top  step,  or  any  intermediate 
wide  step,  for  the  purpose  of  resting,  is  called  a  landing  ;  the  height  from  the 
top  of  the  nearest  step  to  the  ceiling  above  the  headway  ;  the  rounded  edge  of 
the  step  a  nosing  (a,  Fig.  1403) ;  and  if  a  small  hollow  or  cavetto  (b)  be  glued 
in  the  angle  of  the  nosing  and  riser,  it  is  called  a  moulded  nosing.  The  pieces 
which  support  the  ends  of  the  stairs  are  the  strings  (Fig.  1404) ;  that  against 
the  wall  the  wall-string,  the  other  the 
outer  string.  Besides  these  strings, 
pieces  of  timber  are  framed  and  placed 
beneath  the  fliers,  when  the  stairs  are 


a  ^ 


FIG.  1404. 


wide  (Fig.  1405),  called  carriages.     Sometimes  the  strings,  instead  of  being 
notched  out  to  receive  the  steps,  have  the  upper  and  lower  edges  parallel,  with 

grooves  cut  in  the  inner  faces  to 
receive  the  ends  of  their  steps  and 


FIG.  1405. 


FIG.  1406. 


risers  (Fig.  1406).  These  are  called  housed  strings.  Steps  and  risers  are  se- 
cured in  the  grooves  by  wedges  covered  with  glue,  and  driven  in.  For  the 
rough,  strong  strings  of  warehouses  the  carriages  are  made  of  plank,  with 
grooves  to  receive  plank-treads,  and  without  risers. 

Figs.  1407  and  1408  are  elevation  and  plan  of  a  straight  run  of  stairs,  both 
partly  in  section.  N  is  the  newel-post,  n  a  baluster,  h  the  hand-rail,  iv  the 
well.  In  the  section  of  the  floors,  cleats  are  shown  nailed  to  the  beams ;  on 
these  short  boards  are  nailed  to  form  a  box  for  the  reception  of  mortar  for  the 
deafening.  The  opening  represented  in  the  plan  (which  must  occur  between 
the  outer  strings,  if  they  are  not  perpendicular  over  each  other)  is  called  the 
well  (W,  Fig.  1409). 

The  breadth  of  tread  in  general  use  is  from  9  to  12  inches;  in  the  best 
staircases,  it  should  never  be  less  than  11  inches,  nor  more  than  15.  The 
height  of  the  riser  should  be  the  more,  the  less  the  width  of  the  tread  ;  for 
a  15-inch  tread  the  riser  should  be  5  inches  high ;  for  12  inches,  6.J- ;  for  9 
inches,  8.  In  laying  out  the  plan  of  stairs,  having  determined  the  starting- 


580 


ARCHITECTURAL  CONSTRUCTION. 


point,  either  at  bottom  or  top,  as  the  case  may  be,  find  exactly  the  height  of 
the  story ;  divide  this  by  the  height  you  suppose  the  riser  should  be.     Thus 


Fro.  1408. 

(Fig.  1410),  if  the  height  of  the  story  and  thickness  of  floor  be  9  feet,  and  we 
suppose  the  riser  should  be  7  inches  high,  then  108  inches,  divided  by  7  =  15f 

It  is  clear  that  there  must  be  a  full  number  of  steps,  either  16  or  15  ;  to 
be  ntjar  the  supposed  height  of  the  riser,  adopt  15,  then — 
•^Y-  —  7^g-  inches,  height  of  riser. 

For  this  particular  case,  assume  the  breadth  of  the  step  as  10  inches,  and 
the  length  at  3  feet,  a  very  usual  length,  seldom  exceeding  4  feet  in  the  stair- 
cases of  private  houses.  For  the  plan — lay  off  the  outside  of  the  stairs,  two 
parallel  lines  3  feet  apart,  and  space  off  from  the  point  of  beginning  14  treads 
of  10  inches  each,  and  draw  the  cross-parallel  lines.  To  construct  the  eleva- 


ARCHITECTURAL  CONSTRUCTION. 


581 


tion,  project  the  lines  of  the  steps  in  plan,  and  divide  the  height,  either  on  a 
perpendicular  or  by  an  inclined  line,  into  the  number  of  risers  (15),  and  draw 


FIG.  1409. 


FIG.  1-110. 


horizontal  lines  through  these  points;  or  the  same  points  maybe  determined  by 
intersection  of  the  projections  of  the  plan  with  a  single  inclined  line  drawn 
along  the^  nosing  of  top  and  bottom  steps.  The  number  of  treads  is  always  one 
less  than  the  number  of  risers,  the  reason  of  which  appears  in  the  elevation. 

For  the  framing  plan  the  drawing  of  the  elevation  of  stairs  is  in  general 
necessary,  to  determine  the  opening  to  be  framed  in  the  upper  floor,  to  secure 
proper  headway.  Thus  (Fig.  1410),  the  distance,  a,  between  the  nearest  stair 
and  the  ceiling  should  not  be  less  than  6  feet  6  inches ;  a  more  ample  space 
improves  the  look  of  the  stairway  ;  but  if  confined  in  our  limits,  this  deter- 
mines the  position  of  one  header ;  the  other  will  be  of  course  at  the  top  of  the 
stairs.  When  one  flight  is  placed  over  another,  the  space  required  for  timber 
and  plastering,  under  the  steps,  is  about  6  inches  for  ordinary  stairs. 

When  the  stairs  are  circular,  or  consist  in  part  of  winders  and  fliers,  as  in 
Fig.  1409,  the  width  of  the  tread  of  the  winders  should  be  measured  on  the 
central  line.  The  construction  of  the  elevation  is  similar  to  that  of  the  straight 
run  (Fig.  1410),  dividing  the  space  between  the  stories  by  a  number  of  parallel 
lines  equal  to  the  number  of  risers,  and  intersecting  the  parallels  by  projections 
from  the  plan.  The  objection  to  all  circular  stairs  of  this  form,  or  with  a  small 
well-hole  or  a  central  shaft,  is  that  there  is  too  much  difference  between  the 
width  of  the  tread,  but  a  small  portion  being  of  a  suitable  size.  The  hand- 
somest and  easiest  stairs  are  straight  runs,  divided  into  landings,  intermediate 
of  the  stories,  and  either  continuing  then  in  the  same  line,  or  making  a  full  re- 
turn at  right  angles.  It  is  at  times  fashionable  to  make  the  newel  a  prominent 
feature  in  the  hall,  often  occupying  valuable  space.  It  is  sufficient  that  it 


582 


ARCHITECTURAL  CONSTRUCTION. 


be  large  and  stiff  enough  for  a  support  to  the  hand-rail  and  may  be  equally 
ornamental. 

The  top  of  the  hand-rail  should,  in  general,  be  about  2'  8"  to  3'  above  the 
nosing,  and  should  follow  the  general  line  of  the  steps.  The  angles  of  the  hand- 
rail should  always  be  eased  off.  A  hand-rail,  affording  assistance  in  ascending 
or  descending,  should  not  be  wider  than  the  grasp  of  the  hand  (Fig.  1411) ;  but 
where,  for  architectural  effect,  a  more  massive  form  may  be  necessary,  it  is  very 
convenient  to  have  a  sort  of  double  form,  with  the  hand-rail  at  the  top  (Fig. 
1412),  or  as  in  Fig.  1413,  with  the  groove  outside. 

To  a  draughtsman  conversant  with  the  principles  of  projection  already  given, 
it  will  not  be  difficult  to  draw  in  the  hand-rail  of  stairs,  or  to  lay  off  the  mould 


FIG.  1411. 


Fio.  1412. 


FIG.  1413. 


for  its  construction.  It  will  follow  the  line  of  stair- nosing,  and  where  there  are 
changes  of  pitch  they  are  made  to  connect  by  curves  tangent  to  these  pitches, 
except  where  the  landings  are  square,  and  newels  set  at  the  head  of  the  land- 


Fro.  1414. 


ings,  the  rail  is  framed  into  the  newel.     At  the  bottom  the  rail  is  curved  to  the 
horizontal,  when  it  comes  into  or  upon  top  of  the  newel. 

Balusters  are  of  great  variety — usually  turned  forms — attached  to  the  treads 


ARCHITECTURAL  CONSTRUCTION. 


583 


by  dovetails,  covered  with  the  returned  nosing,  or  with  pin-ends  and  holes  in 
treads  and  under  side  of  caps.     Sometimes  (especially  in  iron-work)  the  baluster 


ELEVATION. 


PLAN. 


FIG.  1415. 


FIG.  1416. 


is  set  iii  a  bracket  from  the  face  of  the  string,  as  in  Fig.  1415  ;  or  the  balusters 
may  be  cast  with  the  bracket. 

Fig.  1414  is  the  side  elevation  of  a  stairs  with  wrought-iron  string  and  rail. 
The  string  is  made  of  wrought-iron  knees,  welded  together  continuously,  with 


a  flat  bottom-bar  riveted  across  the  lower  angle  of  the  knees,  usually  supported 
by  an  intermediate  round  bar-post.     Where  posts  can  not  be  put  in,  it  is  better 


ARCHITECTURAL  CONSTRUCTION. 


that  the  bottom  bar  should  be  a  carriage  or  beam  of  I  or  channel-iron,  with 
knees  or  cast-iron  angle-blocks  riveted  on  the  top  of  the  beam.  It  is  not  un- 
usual to  make  housed  strings  of  plate-iron,  with  angle-irons  riveted  on  to 
receive  the  treads  and  risers.  If  the  plate-iron  be  wide  enough  to  serve  in- 
stead of  balusters,  it  makes  a  very  strong  and  stiff  carriage. 

Figs.  1415  and  1416  are  the  plan  and  elevation  of  a  cast-iron  stairs,  with  a 
central  post  or  newel  (this  term  is  applied  also  to  the  first  post  of  any  stairs). 
The  newel-ring,  tread,  and  riser  of  each  step  are  cast  in  one  piece,  and  they  are 
put  together  by  placing  one  newel-ring  upon  that  below  and  bolting  the  outer 
extremity  of  the  riser  to  the  tread  below. 

Fig.  1417  is  a  form  of  cast-iron  stairs  with  a  well  instead  of  a  newel;  the 
step  and  riser  are  bolted  together  by  the  flanges.  It  will  be  seen  that  one  tread 
is  wider  than  the  others  ;  this  is  a  landing. 

Fireplaces. — Fireplaces  for  wood  are  made  with  flaring  jambs  of  the  form 
shown  in  plan  (Fig.  1418) ;  the  depth  from  1  foot  to  15  inches,  the  width  of 
opening  in  front  from  2  feet  6  inches 
to  4  feet,  according  to  the  size  of 
the  room  to  be  warmed ;  .height  2 


feet  3  inches  to  2  feet  9  inches,  the 
width  of  back  about  8  inches  less 

than  in  front ;  but  at  present  fire-  FIG  ]419 

places   for  wood  are   seldom    used, 

stoves  and  grates  having  superseded  the  fireplace.  The  space  requisite  for  the 
largest  grate  need  not  exceed  2  feet  in  width  by  8  inches  in  depth.  The  requi- 
site depth  is  given  by  the  projection  of  the  grate,  and  the  mantel-piece.  Eanges 
require  from  4  feet  4  inches  to  6  feet  4  inches  wide  X  12  inches  to  20  inches 
deep ;  jambs  8  inches  to  12  inches. 

Fig.  1419  represents  the  elevation  of  a  mantel-piece  of  very  usual  propor- 
tions. The  length  of  the  mantel  is  5  feet  5  inches,  the  width  at  base  4  feet  6 

inches,  the  height  of  opening  2  feet  7  inches, 
and  width  2  feet  9  inches.  A  portion  of  this 
opening  is  covered  by  the  iron  sides  or  architrave 
of  the  grate,  and  the  actual  open  space  would 
not  probably  exceed  18  inches  in  width  by  2  feet 
in  height.  In  brick  or  stone  houses  the  flues  are 
formed  in  the  thickness  of  the  wall,  but  when 
distinct  they  have  an  outside  shell  of  a  half-brick  or  4  inches,  and  sometimes 
8"  (Fig.  1420)  ;  the  witlis  or  division- walls  .always  4". 

The  size  of  house  flues  is  usually  8"  X  8",  but  some  are  4"  X  8^,  4"  X  12", 
and  8"  X  12".  The  flues  of  different  fireplaces  should  be  distinct.  Those  from 
the  lower  stories  pass  up  through  the  jambs  of  the  upper  fireplaces,  and,  keep- 
ing side  by  side  with  but  4-inch  brickwork  between  them,  are  topped  out  above 


Fio.  1420. 


ARCHITECTURAL  CONSTRUCTION. 


585 


the  roof,  sometimes  in  a  double  and  often  in  a  single  line  16  inches  wide  by  a 

breadth  required  by  the  number  of  flues,  as  in  Fig.  1420  or  in  Fig.  1421.     The 

._  .  latter   is   an  illustration  of   how   far 

flues  may  be  diverted  from  a  vertical 

.mi  ji  li  ll  Ij  jj{  line,  but  it  is  to  be  observed  that  the 

construction  must  be  stable,  as  any 
settling  or  cracks  not  only  injures  the 
draught  of  the  chimney,  but  impairs 


FIG.  1421. 


FIG.  1422. 


the  security  of  the  building  against  fire.  Changes  of  direction  of  flues  should 
never  be  abrupt.  The  back  of  the  fireplace  may  be  perpendicular  through  its 
whole  height,  but  it  is  usual  to  incline  the  upper  half  inwardly  toward  the  room, 
making  the  throat  to  the  flue  long  and  narrow.  It  is  very  common  to  form 
the  upper  3"  to  4"  of  the  inclined  back  by  an  iron  plate,  which  can  be  turned 
back  or  forward  to  increase  or  diminish  the  draught.  Fig.  1422  represents  the 
arrangement  of  frame  and  brick  arch  for  the  support  of  the  hearth.  The 
chimney  is  generally  capped  with  stone,  sometimes  with  tile  or  cement  pots. 
As  an  architectural  feature,  the  chimney  is  often  made  to  add  considerably  to 
the  effect  of  a  design. 

Roofs. — Framed  roofs  have  been  illustrated  (page  486),  City  roofs  are 
usually  flat,  and  timbered  similarly  to  floors,  but  not  so  strongly,  with  a  slight 
pitch  to  discharge  rainfall.  Eoofs  of  country  dwellings  are  usually  framed  like 
stud-partitions,  with  inclined  studs  somewhat  deeper  than  if  they  were  ver- 
tical, depending  on  the  inclination  from  the  vertical;  if  flat,  depth  like  that 
of  a  floor.  The  theory  of  the 
construction  of  the  gambrel  or 
Mansard  roof  (Fig.  1423),  a 


FIG.  1423. 


FIG.  1424. 


roof  with  two  kinds  of  pitch,  is  that  of  the  polygon  of  rods,  and  self-support- 
ing; but,  in  general,  they  have  central  support  from  partitions,  and  their 
outlines  are  much  varied  by  curves  in  the  lower  rafters  cut  from  plank. 


586 


ARCHITECTURAL  CONSTRUCTION. 


Fig.  1424  is  the  plan  of  a  roof  as  usually  drawn,  shaded  strongly  at  the 
ridges.  The  transept  roof  is  hipped  at  A  and  B. 

Gutters  are  generally  formed  in  the  cornice  (Fig.  1425) ;  sometimes  on  the 
roof  (Fig.  1426),  and  sometimes  by  raising  a  parapet  (Fig.  1427)  and  forming 
a  valley.  The  intersection  of  two  roofs  as  at  v  forms  a  valley. 


FIG.  14:25. 


FIG.  1426. 


FIG.  1427. 


Fig.  1425  represents  a  form  of  gutter  very  common  to  city  buildings,  the 
roof  boarding  extending  over  the  gutter;  but  it  is  preferable  to  make  the  roof 
pitch  from  both  rear  and  front  to  the  centre  of  the  building,  and  to  carry  the 
leader  down  in  the  interior,  where  it  may  serve  as  a  soil- 
pipe  for  the  water-closets,  basins,  and    baths,  affording 
ventilation  in  fair  weather  and  a  scour  in  rains. 


FIG.  1428. 


FIG.  1429. 


Fig.  1428  is  a  gutter  of  a  cottage  roof. 

Fig.  1429  is  the  section  of  a  Mansard  roof,  showing  the  side  elevation  of  a 
dormer-window,  with  the  gutter  below  its  sill. 

The  sheet-metal  forming  the  gutter  must  extend  well  up  or  back  beneath 
the  shingles  or  felt,  or  be  soldered  to  the  tin  of  the  roof,  to  prevent  water  find- 


ARCHITECTURAL  CONSTRUCTION. 


587 


ing  its  way  into  the  interior;  and  at  the 
sides  flashings  of  tin  must  extend  on  the 
walls  above  the  roof  and  into  the  joints  of 
the  brick. 

Sheet-metal  cornices,  at  their  first  intro- 
duction, were  put  up  on  wood  lookouts,  cut 
to  the  form  of  the  cornice,  but  it  is  now  the 
practice  to  use  metal  supports  and  fasten- 
ings to  the  entire  exclusion  of  wood — in 
many  cases  cheaper  and  always  safer  against 
fire  and  rotting,  but  the  iron  used  must  be 
protected  against  rust  by  galvanizing  or 
heavy  coats  of  paint  or  by  both.  Fig.  1430 
shows  a  section  of  a  galvanized  cornice  with 
bar-iron  frames  anchored  to  the  wall  and  FlG  1430 

roof  and  riveted  to  the  cornice ;  the  joints 

of  the  cornice  should  be  both  riveted  and  soldered.     The  pitch  of  the  gutter  is 
secured  by  variations  in  the  bend  of  the  roof  braces. 

Plastering. — To  prevent  damp  striking  through  the   plastering  of   outer 
walls,  and  cracks  in  ceilings,  it  is  usual  to  fur.  walls  and  beams;  that  is,  to  nail 


FIG.  1431. 


Fio.  1432. 


vertical  strips  of  wood  to  the  walls,  and  across  from  beam  to 
beam.  Furring-strips  are  from  1£"  to  2"  wide,  and  about  £•" 
thick,  nailed  at  distances  of  12"  or  16"  centres  (usually  the 
former),  adapted  to  the  length  of  the  laths,  which  are  4  feet 
long,  and  about  1|"  x  ±"  =  spaces  between  laths  £"  to  f".  The 
first  coat  of  mortar  is  the  scratch-coat,  which  is  forced  through 
the  interstices  between  the  laths,  to  make  a  lock  to  retain  it. 


FIG.  1434. 


FIG.  1435. 


FIG.  1436. 


This  coat  is  about  £"  thick.  The  next  or  brown  coat  is  about 
•£"  thick,  and  if  the  last  coat  is  a  sand-finish,  it  will  be  less  than 
•£"  thick ;  while,  if  the  last  coat  is  a  hard  finish,  its  thickness 
will  be  almost  imperceptible.  Figs.  1431  and  1433  are  sections 
of  furring  and  plastering. 


588  ARCHITECTURAL  CONSTRUCTION. 

The  brown  coat  is  usually  carried  down  to  the  floor.  Over  this  is  nailed 
the  base-board,  A  (Fig.  1433),  for  the  finish  around  the  bottom  of  the  walls  of 
the  room.  To  guard  against  the  crack  formed  between  the  floor  by  the  shrink- 
ing of  the  base,  a  teuon  is  formed  along  the  outer  edge  of  the  latter  with  a 
groove  for  its  reception  in  the  floor.  This  is  termed  dadoing.  Above  the  base 
is  a  moulding  forming  a  part  of  the  base ;  above  this,  there  may  be  a  moulded 
rail,  B,  called  the  chair-rail,  or  surbase,  and  between  a  panel,  termed  a  dado. 
The  walls  of  stores  are  generally  ceiled  up  as  high  as  the  surbase.  For  the 
finish  of  the  angle  of  the  wall  and  ceiling,  it  is  usual  in  the  better  rooms  to 
form  a  cornice  in  plaster.  The  cornices  are  mouldings  of  varied  forms,  with 
or  without  enrichments — that  is,  plaster  ornaments.  Figs.  1434,  1435,  and 
1436  are  sections  of  cornices.  If  the  rooms  are  low,  the  cornice  should  extend 
but  little  on  the  wall,  but  well  out  on  the  ceiling. 

In  all  architectural  finish  mouldings  are  a  necessity,  the  simpler  forms  of 
which  are  taken  from  Greek  or  Koman  examples. 

Greek  and  Roman  Mouldings. — The  regular  Greek  mouldings  are  eight  in 
number :  the  Fillet  or  Band,  Torus,  Astragal  or  Bead,  Ovolo,  Cavetto,  Cyma 
Ilec/ta  or  Ogee,  Cyma  Reversa  or  Talon,  and  Scotia. 

The  fillet  (a,  Fig.  1437)  is  a  small  rectangular  member,  on  a  flat  surface, 
whose  projection  is  usually  made  equal  to  its  height. 

The  torus  and  astragal  are  semicircles  in  form,  projecting  from  vertical 
diameters,  as  in  Fig.  1438.  The  astragal  is  distinguished  from  the  torus  in 
the  same  order  by  being  made  smaller.  The  torus  is  generally  employed  in  the 
bases  of  columns;  the  astragal,  in  both  the  base  and  capital. 


FIG.  1437.  FIG.  1433.  FIG.  1439. 

The  ovolo  is  a  member  strong  at  the  extremity,  and  intended  to  support. 
The  Roman  ovolo  consists  of  a  quadrant  or  a  less  portion  of  a  circle  (Fig.  1439). 
The  Greek  ovolo  is  elliptic. 

To  describe  the  Greek  ovolo  (Fig.  1440):  Draw  df  from  the  lower  end  of 
the  proposed  curve,  at  the  required  inclination ;  draw  the  vertical  g  efto  define 
the  projection,  the  point  e  being  the  extreme  point  of  the  curve.  Draw  e  li 
parallel  to  df,  and  draw  the  vertical  d  li  k,  such  that  d  li 
is  equal  to  hk.  Divide  eh  and  e f  into  the  same  number 
of  equal  parts ;  from  d  draw  straight  lines  to  the  points  of 
division  in  ef,  and  from  k  draw  lines  through  the  divi- 
sions in  e  h  to  meet  those  others  successively.  The  inter- 
sections so  found  are  points  in  the  curve,  which  may  be 
FIG.  1440.  traced  accordingly. 

The   cavetto  is  described  like  the  Roman  ovolo — by 

circular  arcs,  as  shown  in  Figs.  1441  and  1442.  Sometimes  it  is  composed  of 
two  circular  arcs  united  (Fig.  1443) ;  set  off  be,  two  thirds  of  the  projection, 
draw  the  vertical  b  d  equal  to  be,  and  on  d  describe  the  arc  b  i.  Join  e  d  and 
produce  it  top;  draw  i  n  perpendicular  to  e  d,  set  off  no  equal  to  ni,  and 


ARCHITECTURAL  CONSTRUCTION. 


589 


draw  the  horizontal  line  op  meeting  ep ;  on  p  describe  the  arc  io  to  complete 
the  curve. 

The  ogee,  or  cyma  recta  (Fig.  1444),  is  compounded  of  a  concave  and  a  con- 
vex surface.     Join  a  and  5,  the  extremities  of  the  curve,  and  bisect  a  b  at  c;  on 
a  and  c,  as  centres,  with  the  radius  a  c,  describe  arcs  cutting 
at  d ;  and  on  b  and  c,  describe  arcs  cutting  at  e.     On  d  and  e, 
t     \        as  centres,  describe  the  arcs  a  c,  cb,  composing  the  moulding. 

FIG.  1441. 


FIG.  1442. 


FIG.  1444. 


The  cyma  reversa,  or  talon  (Fig.  1445),  is  a  compound  curve,  distinguished 
from  the  ogee  by  having  the  convex  part  uppermost. 

If  the  curve  be  required  to  be  made  quicker,  a  shorter  radius  than  a  c  must 
be  employed.  The  projection  of  the  moulding  n  b  (Fig.  1444)  is  usually  equal 
to  the  height  a  n. 

To  describe  the  Greek  talon :  Join  the  extreme  points  a,  b  (Fig.  144G) ; 
bisect  a  b  at  c,  and  on  a  c  and  c  b,  describe  the  semicircles  b  d  c  and  c  a.  Draw 
perpendiculars  d  o,  etc.,  from  a  number  of  points  in  a  c  and 
c  b,  meeting  the  circumferences  ;  and  from  the  same  points  set 
off  horizontal  lines  equal  to  the  respective  perpendiculars  : 
o  n  equal  to  o  f/,  for  example.  The 
curve  line  b  n  a,  traced  through  the 
ends  of  the  lines,  will  be  the  contour 
of  the  moulding. 

To  describe  a  scotia :  Divide  the 
perpendicular  a  b  (Fig.  1447)  into  three 
equal  parts,  and  with  the  first,  a  e,  for 
radius,  on  e  as  a  centre,  describe  the  arc 
afh,  in  the  perpendicular  c  o  set  off  c  I  equal  a  e,  join  e  I,  and  bisect  it  by  the 
perpendicular  o  d,  meeting  c  o  at  o,  on  the  centre  0,  with  o  c  for  radius,  complete 
the  figure  by  the  arc  c  h. 

These  mouldings,  and  combinations  of  them,  are  stuck  in  wood,  and  are  to 
be  purchased  in  every  variety.  Fig.  1448  represents  some  of  the  common  forms 
always  to  be  had,  and  of  suitable  sizes. 

Proportions  and  Distribution  of  Rooms  and  Passages. — Rooms  of  dwell- 
ing-houses are  to  be  proportioned  and  arranged  according  to  the  necessities  of 
position  and  use,  the  space  that  can  be  occupied,  the  financial  means  available, 
and  of  ten  J;o  suit  the  peculiar  wishes  of  owners  or  occupants.  In  cities,  the 
limits  of  the  lot  restrict  the  arrangements  to  a  small  ground-space,  and  require 
an  increase  in  the  number  of  stories.  Use  has  established  certain  forms  often 
peculiar  to  different  cities,  beyond  which  there  is  little  change ;  but  in  the 
country,  where  there  is  plenty  of  ground-space,  and  where  many  stories  are 
usually  injurious  to  the*  aesthetic  effect,  and  where  there  are  few  canons  in  archi' 


FIG.  1447. 


590 


ARCHITECTURAL  CONSTRUCTION. 


FIG.  1448. 


ARCHITECTURAL   CONSTRUCTION.  591 

tecture  to  be  observed,  there  is  little  limit  to  the  variety  of  forms  and  arrange- 
ments of  country-houses. 

In  designing  a  country-house,  where  one  is  not  restricted  in  space,  it  is  often 
convenient  to  mark  out  the  rooms  of  the  desired  size  on  slips  of  paper,  accord- 
ing to  some  scale,  then  cut  them  out  and  arrange  them  in  as  convenient  an 
order  as  possible,  and  modify  the  arrangement  by  the  necessities  of  construction 
and  economy.  Thus,  the  greater  the  outside  surface  in  proportion  to  the  in- 
cluded area,  and  the  greater  the  number  of  chimneys  and  space  used  for  pas- 
sages, the  greater  the  cost.  The  kitchen  should  be  of  convenient  access  to  the 
dining-room,  both  should  have  large  and  commodious  pantries,  and  all  rooms 
should  have  an  access  from  an  entry,  without  being  compelled  to  pass  through 
other  rooms ;  this  is  particularly  applicable  to  the  communication  of  the  kitchen 
with  the  front  door.  Outside  doors  for  common  and  indiscriminate  access 
should  not  open  into  important  rooms.  All  rooms  to  be  occupied  as  living  or 
bedrooms  should  have  flues  opening  directly  or  indirectly  to  the  outer  air  for 
ventilation. 

As  to  the  size  of  the  different  rooms,  they  must  of  course  depend  on  the  pur- 
poses to  which  they  are  to  be  applied,  the  class  of  house,  and  the  number  of 
occupants.  The  kitchen  for  the  poorer  class  of  houses  is  also  used  as  an  eat- 
ing-room, and  should  therefore  be  of  considerable  size  to  answer  ooth  purposes; 
for  the  richer  houses,  size  is  necessary  for  the  convenience  of  the  work.  In  the 
older  New  York  private  houses  the  average  was  about  16  X  20  feet ;  for  me- 
dium houses  in  the  country  generally  less,  say  12  X  16.  A  back  kitchen,  scul- 
lery, or  laundry,  should  be  attached  to  the  kitchen,  and  may  serve  as  a  passage- 
way out. 

The  Dining  or  Eating  Rooms. — The  common  width  of  dining-tables  varies 
from  4  to  5  feet  6  inches ;  the  space  occupied  by  the  chair  and  person  sitting 
at  the  table  is  about  18  inches ;  the  table-space,  for  comfort,  should  be  not  less 
than  2  feet  for  each  person  at  the  sides  of  the  table,  and  considerable  more  at 
the  head  and  foot ;  hence  the  space  that  will  be  necessary  for  the  family  and 
its  visitors  at  the  table  may  be  calculated.  Allow  a  further  space  of  2  feet  at 
each  side  for  passages,  and  some  3  to  5  at  the  head  for  the  extra  tables  or  chairs, 
for  the  minimum  of  space  required  ;  but,  if  possible,  do  not  confine  the  dining- 
room  to  meagre  limits,  unless  for  very  small  families  ;  let  not  the  parties  be  lost 
in  the  extent  of  space,  nor  let  them  appear  crowded. 

TJie  parlours  should  be  made  according  to  the  rules  given  below,  not  square, 
but  the  length  about  once  and  a  half  the  width ;  if  much  longer  than  this,  break 
up  the  walls  by  transoms  or  projections.  As  to  the  particular  dimensions,  no 
rules  can  be  given;  they  must  depend  on  every  person's  taste  and  means; 
20  x  16  is  a  very  fair  size  for  a  regular  living-room  parlour,  not  a  drawing- 
room.  The  same  size  is  ample  for  a  sleeping-room.  The  usual  width  of  single 
beds  is  2'  8"  to  3'  6" ;  of  three-quarter,  4'  to  4'  6" ;  of  whole,  5  to  6  feet ;  the 
length,  6'  6"  ;  and  as  the  other  furniture  may  be  made  to  consist  of  but  very 
few  pieces,  if  adequate  means  of  ventilation  are  provided  parties  may  live 
snugly  in  small  quarters.  The  bed*should  not  stand  too  near  the  fire,  nor 
between  two  windows ;  its  most  convenient  position  is  head  against  an  interior 
wall,  with  a  space  on  each  side  of  at  least  2  feet.  To  the  important  bedrooms 
of  first-class  houses,  dressing  rooms  should  be  attached,  and,  if  there  is  water 


592 


ARCHITECTURAL  CONSTRUCTION. 


ARCHITECTURAL  CONSTRUCTION.  593 

and  sewer  service,  fitted  with  set  bowls  and  baths  and  water-closets.  If  pos- 
sible, there  should  be  windows  opening  to  the  outer  air,  but  always  with  flue- 
ventilation. 

Pantries.— Closets  for  crockery  should  not  be  less  than  14  inches  in  depth 
in  the  clear  ;  for  the  hanging  up  of  clothes,  not  less  than  18  inches,  and  should 
be  attached  to  every  bedroom.  For  medium  houses,  the  closets  of  large  sleep- 
ing-rooms should  be  at  least  3  feet  wide,  with  hanging-room,  and  drawers  and 
shelves.  There  should  also  be  blanket-closets,  for  the  storing  of  blankets  and 
linen ;  these  should  be  accessible  from  the  entries,  and  may  be  in  the  attic. 
Store-closets  should  also  be  arranged  for  groceries  and  sweetmeats. 

Passages.— Front,  entries  are  usually  6  feet  wide  in  the  clear ;  common  pas- 
sage-ways, 3  feet ;  these  are  what  are  required,  but  ample  passages  give  an  im- 
portant effect  to  the  appearance  of  the  house.  The  width  of  principal  stairs 
should  be  not  less  than  3  feet,  and  all  first-class  houses,  especially  those  not  pro- 
vided with  water-closets  and  slop-sinks  on  the  chamber-floor,  should  have  two 
pairs  of  stairs,  a  front  and  a  back  pair  ;  the  back  stairs  need  not  necessarily  be 
over  2  feet  6  inches  in  width. 

TJie  Height  of  Stories.— It  is  usual  to  make  the  height  of  all  the  rooms  on 
each  floor  equal ;  it  can  be  avoided  by  furring  down,  or  by  the  breaking  up  of 
the  stories,  by  the  introduction  of  a  mezzonine  or  intermediate  story  over  the 
smaller  rooms.  Both  remedies  are  objectionable. 

The  average  height  of  the  stories  for  common  city  dwellings  is  :  Cellar,  6 
feet  6  inches  ;  common  basement,  8  to  9  feet ;  English  basement,  9  to  10  feet ; 
principal  story,  12  to  35  feet ;  first  chamber  floor,  10  to  12  feet ;  other  chamber- 
floors,  8  to  10  feet — all  in  the  clear.  For  country-houses,  the  smaller  of  the 
dimensions  are  more  commonly  used.  Attic  stories  are  sometimes  but  a  trifle 
over  6  feet  in  height,  but  are  objectionable. 

Privies,  Water- Closets,  and  Out-Houses. — The  size  of  privies  must  depend 
greatly  on  the  uses  of  the  building  to  which  they  are  to  be  attached,  its  position, 
and  the  character  of  its  occupants.  Allowing  nothing  for  evaporation  and  ab- 
sorption, the  entire  space  necessary  for  the  excrementitious  deposits  of  each 
individual,  on  an  average,  will  be  about  seven  cubic  feet  for  six  months,  of 
which  seven  eighths  is  fluid.  In  the  country,  vaults  are  usually  constructed  of 
dry  rubble-stone,  and  the  fluid  matters  are  expected  to  be  filtered  through  the 
earth,  the  same  as  in  cesspool-waste ;  but  great  care  must  be  taken  that  they 
neither  vitiate  the  water-supply  nor  the  air  of  the  house.  A  brick  and  cement 
vault,  air  and  water  tight,  with  a  ventilating-pipe  into  a  hot  chimney-flue,  is 
the  best  preventive,  and  may  even  be  built  within  the  house.  In  all  other  cases 
there  should  be  free  air-space  between  the  house  and  privy.  In  the  city,  where 
there  is  adequate  water-supply  and  sewerage,  the  water-closet  should  be  adopted. 
The  water-closet,  or  privy,  with  a  single  seat,  should  occupy  a  space  not  less 
than  4'  x  2'  6".  The  rise  of  seat  should  be  about  17"  high  ;  and  the  hole  egg- 
shaped,  11"  x  8".  The  earth-closet,  when  properly  taken  care  of,  is  an  ex- 
tremely useful  appendage  to  a  country-house,  and  the  space  requisite  for  it  is 
the  same  as  that  of  a  water-closet. 

The  forms  of  modern  water  appliances,  and  the  means  to  get  rid  of  house- 
waste,  will  be  illustrated  hereafter,  under  the  heads  of  Ventilation  and 
Plumbing. 

39 


594:  ARCHITECTURAL   CONSTRUCTION. 

For  Wood  or  Coal  Sheds  or  Bins. — In  estimating  the  size  of  these  accesso- 
ries, it  may  only  be  necessary  to  state  that  a  cord  of  wood  contains  128  cubic 
feet,  and  a  ton  of  anthracite  egg  coal  occupies  a  space  of  about  40  cubic,  feet,  of 
bituminous  coal  about  45  cubic  feet,  of  coke  from  45  to  50  cubic  feet. 

On  the  Size  and  Proportion  of  Rooms  in  general. — "  Proportion  and  or- 
nament," according  to  Ferguson,  "  are  the  two  most  important  resources  at 
the  command  of  the  architect,  the  former  enabling  him  to  construct  ornamen- 
tally, the  latter  to  ornament  his  construction."  A  proportion  to  be  good  must 
be  modified  by  every  varying  exigence  of  a  design ;  it  is  of  course  impossible  to 
lay  down  any  general  rules  which  shall  hold  good  in  all  cases  ;  but  a  few  of  its 
principles  are  obvious  enough.  To  take  first  the  simplest  form  of  the  propo- 
sition, let  us  suppose  a  room  built,  which  shall  be  an  exact  cube — of  say  20  feet 
each  way — such  a  proportion  must  be  bad  and  inartistic ;  and,  besides,  the 
height  is  too  great  for  the  other  dimensions.  As  a  general  rule,  a  square  in 
plan  is  least  pleasing.  It  is  always  better  that  one  side  should  be  longer  than 
the  other,  so  as  to  give  a  little  variety  to  the  design.  Once  and  a  half  the 
width  has  been  often  recommended,  and  with  every  increase  of  length  an  in- 
crease of  height  is  not  only  allowable,  but  indispensable.  Some  such  rule  as 
the  following  meets  most  cases  :  "  The  height  of  the  room  ought  to  be  equal  to 
half  its  width  plus  the  square  root  of  its  length  "  ;  but  if  the  height  exceed  the 
width  the  effect  is  to  make  the  room  look  narrow.  Again,  by  increasing  the 
length  we  diminish,  apparently,  the  other  two  dimensions.  This,  however,5is 
merely  speaking  of  plain  rooms  with  plain  walls ;  it  is  evident  that  it  'will  be 
impossible,  in  any  house,  to  construct  all  the  rooms  and  passages  to  conform  to 
any  one  rule  of  proportion,  nor  is  it  necessary,  for  in  many  rooms  it  would  not 
add  to  their  convenience,  which  is  often  the  most  desirable  end  ;  and,  if  re- 
quired, the  unpleasing  dimensions  may  be  counteracted  by  the  art  of  the  archi- 
tect, for  it  is  easy  to  increase  the  apparent  height  by  strongly  marked  vertical 
lines,  or  bring  it  down  by  horizontal  ones.  Thus,  if  the  walls  of  two  rooms  of 
the  same  dimensions  be  covered  with  the  same  strongly  marked  striped  paper, 
in  one  case  the  stripes  being  vertical  and  in  the  other  horizontal,  the  apparent 
dimensions  will  be  altered  very  considerably.  So  also  a  deep,  bold  cornice 
diminishes  the  apparent  height  of  a  room.  If  the  room  is  too  long  for  its  other 
dimensions,  this  can  be  remedied  by  breaks  in  the  walls,  by  the  introduction 
of  pilasters,  etc.  So  also,  as  to  the  external  dimensions  of  a  wall,  if  the  length 
is  too  great  it  is  to  be  remedied  by  projections,  or  by  breaking  up  the  lengths 
into  divisions. 

Understanding  the  general  necessities  of  a  dwelling,  the  proportions  of 
rooms,  forms  of  construction,  and  space  to  be  occupied,  the  draughtsman  is 
prepared  to  undertake  designing,  and  for  this  purpose  cross-section  paper  will 
be  found  of  very  great  use.  Taking  the  side  of  a  small  square  as  a  unit — one 
foot,  for  instance — he  can  readily  pencil  in  rooms  and  passages,  and  alter  and 
modify  at  pleasure. 

Figs.  1445  to  1456  are  illustrations  of  this  form  of  designing.  Partitions 
are  to  be  as  much  as  possible  one  over  the  other,  and  the  posts  or  walls  ar- 
ranged in  the  cellar,  for  the  support  of  these  lines  of  partitions.  For  the 
sketch,  it  is  sufficient  to  make  door  and  window  openings  3  feet,  unless  for 
some  particular  purpose  double-fold  doors  or  bow  or  mullioned  windows  are 


ARCHITECT  ORAL  CONSTRUCTION. 


595 


required.     In  arranging  the  stairs,  the  whole  run  may  be  taken  as  !-£  time  the 
height  of  the  story  between  floor  and  floor ;  as  square  landings  have  one  riser, 


FIG.  1457. 


K 


FIG.  1458. 


FIG.  1459. 


p 

P 

=    = 

! 

P 

— 

-i    # 

i  1 

the  rise  will  be  equal  to  the  square  less  one  tread,  say,  for 
the  design  1  foot.  The  length  of  opening  in  the  frame, 
say  12  feet  for  a  straight  run. 

Figs.  1447  to  1472  are  plans  of  familiar  forms  of 
houses,  drawn   to  the  scale  of  32  feet  to  the  inch,  as 
illustrations  to  the  student  and  as  examples  to  be  copied 
on  a  larger  scale.     The  same  letters  of  reference  are  used 
on  all  the  plans.     Thus,  K  K  designate  kitchens,  cooking- 
rooms,  or  laundries ;   D  D   eating-rooms ;  S  S  sleeping- 
rooms;  PP  drawing-rooms,  parlours,  or  libraries;  pp  pantries,  china  or  store 
closets,  or  clothes-presses ;   c  c  water-closets  and  bath-rooms.      These  last  are 
not  shown  in  the  plans  of  country  houses,  but  are  recognised  as  a  necessity  in 
the  best  of  this  class.     The  space  occupied  by  them  is  given  on  page  593. 

Figs.  1457,  1458,  and  1460  are  first-story  plans  of  houses  of  square  out- 
line.    Fig.  1459  is  the  second  story  of  Fig.  1458. 


FIG.  1460. 


J) 


FIG.  1462. 


.   , 


FIG.  1461. 


FIG.  1463. 


FIG.  1464. 


This  form  of  house  has  the  greatest  interior  accommodations  for  the  outside 
cover,  and,  although  not  picturesque  in  its  elevation,  is  a  very  convenient 
and  economical  structure.  The  kitchen  (Fig.  1460)  is  in  the  basement,  and 
the  connection  with  the  dining-room  is  by  a  dumb-waiter  in  the  pantry  (p). 
In  Fig.  1461  the  plan  is  the  same  as  in  Fig.  1460,  but  the  kitchen  (K}  is 


596 


ARCHITECTURAL  CONSTRUCTION. 


in  an  L  attached  to  the  house;  there  is  a  small  opening  between  the  pantry 
(p)  and  kitchen,  through  which  dishes  are  passed  to  and  from  the  dining- 
room. 

Fig.  1462  is  the  plan  of  a  very  small  but  convenient  floor,  of  prettier  out- 
line than  the  square ;  V  is  a  portico  or  veranda.     No  chimney  is  shown  in  the 


.  .ML, 


I) 


i: 


i. 


K 


.>• 

s 

I 

~nt 

= 

_/''_L 

T 

s 

J" 

i_  - 

s 

s 

FIG.  1465. 


FIG.  1466. 


FIG.  1467. 


FIG.  1468. 


sleeping-room  S',  there  should  be  one  either  against  the  stairs  or  the  back 
wall. 

Figs.  1463  and  1464  are  first-story  plans  of  houses  still  more  extensive. 
All  of  the  above  are  adapted  to  the  country,  dependent  on  lights  on  all  sides, 
and  ample  spaces. 

In  the  cities,  houses  are  mostly  confined  to  one  form  in  their  general  out- 


iniiii  l 

|  r- 

FIT] 

1 

p 

| 

3 

__ 

\. 

T- 

—     • 

T- 

\ 

mm        m 

K 

1) 

FIG.  1469. 


FIG.  1470. 


FIG.  1471. 


s 


FIG.  1472. 


line — a  rectangle.  Figs.  1465  and  1469  may  be  taken  as  the  usual  type  of 
New  York  city  houses.  Figs.  1465,  1466,  and  1467  are  the  basement,  first  and 
second  floor  plans  of  a  three-rooms-deep,  high-stoop  house  as  the  first  floor  is 
reached  by  an  outside  flight  of  steps  about  6  feet  high.  There  is  usually  a 
cellar  beneath  the  basement,  but  in  some  cases  there  are  front  vaults,  entered 
beneath  the  steps  to  the  front  door ;  the  entrance  to  the  basement  itself  is  also 


ARCHITECTURAL  CONSTRUCTION. 


597 


LIBRARY          DINING.  RDDM 


FIR5T  5TDRY 


FIG.  1473. 


FIG.  1474 


598 


ARCHITECTURAL  CONSTRUCTION. 


FIG.  1475. 


FIG.  1476. 


ARCHITECTURAL  CONSTRUCTION.  599 

beneath  the  steps.  The  front  room  of  the  basement  may  be  used  as  an  eating- 
room,  for  the  servants'  sleeping-room,  billiards,  or  library.  The  usual  dining- 
room  is  on  the  first  floor,  a  dumb-waiter  being  placed  in  the  butler's  pantry,  p, 
for  convenience  in  transporting  dishes  to  and  from  the  kitchen.  The  objec- 
tion to  three-rooms-deep  houses  is  that  the  central  room  is  too  dark,  being 
lighted  by  sash  folding-doors  between  that  and  the  front  or  rear  rooms,  or  both. 
Fig.  1468  is  a  modification  to  avoid  this  objection,  the  dining-room,  or  tea- 
room, as  it  is  generally  called,  being  built  as  an  L,  so  that  there  is  at  least  one 
window  in  the  central  room  opening  directly  outdoors.  This  was  an  old 
fashion  here,  and  has  lately  been  revived. 

Figs.  1469  to  1470  are  plans  of  the  several  floors  of  an  English-basement 
house,  so  called,  distinguished  from  the  former  in  that  the  principal  floor  is  up 
one  flight  of  stairs.  The  first  story  or  basement  is  but  one  or  two  steps  above 
the  street,  and  contains  the  dining-room,  with  its  butler's  pantry  and  dumb- 
waiter, a  small  sitting-room,  with,  in  some  cases,  a  small  bedroom  in  the  space 
in  the  rear  of  it.  The  kitchen  is  situated  beneath  the  dining-room,  in  the  sub- 
basement.  The  grade  of  the  yard  is  in  general  some  few  steps  above  the  floor 
of  the  kitchen.  Vaults  for  coal  and  provisions  are  excavated  either  beneath 
the  pavement  in  front  or  beneath  the  yard.  The  advantages  of  this  form  of 
house  are  the  small  reception-room  on  the  first  floor,  which  in  small  families 
and  in  the  winter  months  is  the  most  frequently  occupied  as  a  sitting-room  of 
any  in  the  house ;  the  spaciousness  of  its  dining-room  and  parlours  in  propor- 
tion to  the  width  of  the  house,  which  is  often  but  16  feet  8  inches  in  width,  or 
three  houses  to  two  lots,  and  not  infrequently  of  even  a  less  width.  The  ob- 
jections to  the  house  are  the  stairs,  which  it  is  necessary  to  traverse  in  passing 
from  the  dining-rooms  or  kitchen  to  the  sleeping-rooms,  but  this  objection 
would,  of  course,  lie  against  any  house  of  narrow  dimensions,  where  floor-space 
is  supplied  by  height. 

In  New  York,  outside  access  to  the  kitchen  is  from  the  front,  as  there  is  no 
back  street  or  alley.  In  Philadelphia,  where  the  lots  are  deeper,  and  there  is 
a  street  in  the  rear,  the  kitchen  is  usually  in  a  rear  L,  on  the  level  of  the  first 
floor,  with  the  dining-room  above  it  on  a  mezzanine  or  half-story  between  the 
first  and  second  floors. 

Figs.  1477  to  1483  are  plans  and  elevations  of  a  country-house  in  the  Flem- 
ish or  Queen  Anne  style. 

Fig.  1486  is  the  front  elevation  of  a  high-stoop  house,  in  New  York  city,  of 
brown  stone,  a  comparatively  old  but  still  popular  design. 

To  accommodate  the  poor  and  people  of  small  means  in  all  cities,  it  was, 
and  to  some  extent  still  is,  the  custom  to  divide  houses  which  were  intended 
for  single  families  into  small  apartments  for  many,  or  to  let  rooms  singly  for  this 
purpose.  This  was  found  to  be  objectionable  to  both  occupants  and  owners, 
and  houses  have  been  constructed  especially  for  parties  of  limited  means. 
Virtually,  they  are  now  nearly  all  apartment-houses,  each  family  having  distinct 
rooms  or  suites  to  itself.  But  the  term  tenement-houses  is  applied  to  the  cheaper 
kind  of  apartments,  occupied  by  the  poorer  class,  and  situated  in  the  least  ex- 
pensive localities.  The  common  form  of  tenement-house  consists  of  two  build- 
ings, one  in  the  front  and  one  in  the  rear  of  the  lot,  with  an  outer  or  air  space 
between.  A  hall  leads  through  the  first  story  to  the  central  area ;  on  each  side 


600 


ARCHITECTURAL  CONSTRUCTION. 


PLAN  OF  FIKST  FLOOK.       - 
B 


ARCHITECTURAL  CONSTRUCTION. 


601 


PLAN  OF  SECOND  FLOOR. 


602 


ARCHITECTURAL  CONSTRUCTION. 


FKAMING-PLAN   OF  FIRST  FLOOR. 


FIG.  1479. 


ARCHITECTURAL  CONSTRUCTION. 


603 


604: 


ARCHITECTURAL  CONSTRUCTION. 


ELEVATION  OF  CHIMNEY  OF  DINING-KOOM. 


SECTION. 


FIG.  1481. 


FIG.  1482. 


J    FEET 


ARCHITECTURAL  CONSTRUCTION. 


605 


606 


ARCHITECTURAL  CONSTRUCTION. 


ENGLISH  KURAL  STYLE. 


FIG.  1484. 


ARCHITECTURAL  CONSTRUCTION. 
ITALIAN  VILLA,  BY   UPJOHN. 


607 


FIG.  1485. 


608 


ARCHITECTURAL  CONSTRUCTION. 


Flo.  1486. 


ARCHITECTURAL  CONSTRUCTION. 


609 


of  this  hall  there  may  be  small  stores  and  apartments.  Stairs  from  the  hall 
lead  to  the  apartments  above.  The  25  feet  is  divided  in  two,  making  two  liv- 
ing-rooms on  each  front ;  these  are  the  only  rooms  opening  directly  into  the 
outer  air.  Bedrooms  are  attached  to  each  of  these  rooms,  but  take  their  light 
and  air  from  the  staircases,  or  small  light-wells.  In  the  rear  houses  there  are 
two  tenements  to  each  story ;  they  take  their  light  and  air  from  the  central  and 
back  areas.  Water-closets  are  in  the  central  area.  These  tenements  are 
mostly  occupied  by  work-people,  largely  of  foreign  birth,  dependent  directly 
011  small  wages.  There  is  a  large  class,  of  limited  means,  to  whom  these 
accommodations  are  insufficient ;  parties  who  can  not  well  afford  an  entire 
house,  but  still  wish  for  the  privacy  of  one.  Within  the  limits  of  a  lot 
25'  X  100'  it  has  been  found  difficult  to  secure  all  the  necessaries  of  light  and 
ventilation,  with  the  number  of  suites  of  apartments  adapted  to  the  means  of 
the  occupants,  and  satisfactory  as  an  investment  to  the  owners.  Fig.  1487  is 
a  plan  of  one  of  the  best  of  these  designs.  It  provides  for  four  families 


FIG.  1487. 

on  each  story,  although  it  will  be  observed  by  the  plan  of  the  stairs  that 
the  front  and  rear  tenements  are  not  on  the  same  level ;  they  are  separated 
by  the  half  flight  of  stairs.  By  means  of  the  cross-shaped  court  between  the 
adjacent  houses,  every  room,  including  the  bath-room,  has  a  window  to  the 
open  air.  This  is  the  most  commendable  feature  of  the  plan.  It  is  remark- 
able, also,  however,  for  providing  more  conveniences  than  have  been  customary 
in  dwellings  of  this  class,  as,  for  instance,  a  small  bath-tub  as  well  as  a  water- 
closet  for  each  family,  and  two  wash-tubs  as  well  as  a  sink ;  also,  a  dumb- 
waiter (common  to  two  families  on  each  level)  for  bringing  up  fuel,  provisions, 
•etc.  The  large  rooms  have  recesses  for  beds,  which  provide  for  an  extra  bed- 
room, while  detracting  but  little  from  their  value  as  parlors,  as  the  recess  may 
be  curtained  off  in  the  daytime,  or  the  bed  turned  up.  The  dimensions  of  the 
rooms,  as  marked  on  the  plans,  are  the  average  length  and  breadth.  These 
suites  are  much  too  restricted  for  a  very  large  class,  but  apartment-houses  some- 
what on  this  model  are  constructed  in  desirable  localities,  where  the  accom- 
modations and  conveniences  are  equal  to  those  of  any  private  house,  and  not 
bounded  by  the  limits  of  a  single  lot  nor  single  story,  many  unsurpassed  in 
luxury  of  finish  and  appointments. 

The  larger  apartment-houses  are  often  designated  as  flats.     The  suites  should 
be  supplied  with  water,  gas,  and  steam  heat ;  should  be  entirely  distinct  in  their 
Tentilation  and  protected  against  fire ;  some  are  now  lighted  by  electric  light. 
40 


610 


ARCHITECTURAL  CONSTRUCTION. 


Fig.  1488  is  an  illustration  of  a  "  flat "  situated  on  the  corner  of  a  street, 
and  one  suite  takes  its  light  exteriorly  from  the  streets  while  the  other  depends 


in  a  measure  on  the  court,  with  a  ventilating  passage  from  the  rear  beneath 
the  fire-escape  grating.  Kitchens,  in  the  figure,  are  attached  to  the  suites ; 
the  laundries  are  in  the  upper  story.  Many  flats  are  without  kitchens  or  laun- 
dries, and  meals  are  furnished  either  from  without  or  from  restaurants  in  the 
building.  It  then  corresponds  very  nearly  to  a  hotel  without  transient  cus- 


ARCHITECTURAL  CONSTRUCTION. 


611 


SEDKWALK. 


Fia.  1489. 


FIG.  1490. 


612 


ARCHITECTURAL   CONSTRUCTION. 


torn,  with  ample  and  separate  suites.  It  would  seem  that  boarding-houses 
might  be  built  on  such  plans — less  extensive  in  their  arrangements  and  adapted 
to  small  families  of  moderate  means ;  but  boarding-houses  are  almost  invariably 
private  houses,  but  little  modified  for  the  more  public  use. 

Stores  and  Warehouses. — Fig.  1489  is  the  front  elevation  of  a  common  type 
of  New  York  city  store,  occupying  a  single  lot  of  25  feet  in  width.  It  will  be 
observed  that  there  are  two  stories  beneath  the  level  of  the  sidewalk,  the  base- 
ment and  sub-cellar,  and  this  construction  still  obtains  largely ;  but  deep  base- 
ments only  are  considered  preferable  by  some,  with  extra  stories  at  the  top 
rather  than  in  the  cellar.  Fig.  1490  is  a  section  of  the  front  wall,  showing 
heights  of  stories,  which  of  late  years  have  been  increased  over  former  practice, 
say  to  16'  for  the  first  story,  13'  for  the  second,  and  12'  and  11'  for  others,  the 
light  for  the  interior  being  taken  almost  universally  from  the  front  and  rear, 
and  sky  lights  done  away  with. 

Fig.  1491  is  a  plan  of  the  first-story  floor,  with  basement  in  front  dotted 
in ;  five  feet  of  this  space,  or  that  usually  allotted  for  areas,  is  covered  with 


B    |A 


FIG.  1491. 


illuminating  tile  (Fig.  1492),  that  is,  small  glass  lenses,  set  in  iron  frames,  the 
whole  water-tight ;  or  lenses  on  a  skeleton  frame  of  cast-iron  set  in  Portland 
cement.  In  the  extreme  rear  there  is  a  small  area,  A,  open  to  the  air,  of  about 


FIG.  1492. 

5  feet,  for  light  and  air  to  the  basement  and  cellar.  The  offices  of  the  first 
story  are  situated  at  B,  over  which  there  is  usually  a  curved  lean-to  of  illumi- 
nating tile.  The  main  wall  above  this  story  is  on  the  line  a  b— plain  brick — 
with  iron  shutters.  When  shutters  are  used  to  close  the  first-story  front  they 
are  mostly  rolling  shutters  of  sheet-steel.  The  hoist-way  to  the  upper  stories 
is  at  c,  a  position  somewhat  objectionable  as  interfering  with  the  use  of  the 


613 


ARCHITECTURAL  CONSTRUCTION 


H^ifW 


I...  11 


614 

stairs,  when  a  common  hoist-wheel  is  used ;  but  if  it  is  a  power-hoist,  then  it  is 
put  close  to  the  wall,  guarded  by  a  rail,  with  a  passage  round  to  the  stairs.  In 
50-feet-front  stores  the  hoist  is  put  on  the  opposite  corner  from  the  stairs,  as 


FIG.  1493. 

at  D,  but  this  cuts  off  considerable  light  from  the  first-story  front.  In  some 
the  arrangement  is  as  in  Fig.  1493,  in  which  the  hoists  c  c  are  in  the  rear  of 
the  stairs.  The  arrangement  for  offices  in  the  rear  of  the  first  story  is  in  a  T, 
with  spaces  at  the  sides  for  the  ventilation  and  light  of  the  lower  stories.  It 
will  be  observed  that  there  is  no  central  door,  as  in  the  elevation  (Fig.  1489), 
which  last  most  usually  obtains  for  wholesale  stores.  Formerly  illuminating 
tile  on  iron  quadrant  frames  over  rear  extensions  of  stores  were  common,  but 
were  objectionable  from  the  inside  condensation  and  drip.-  It  is  very  common 
to  leave  open  areas  at  the  sides,  inclosed  by  brick  walls  (Fig.  1493),  with  the 
windows  protected  by  iron  shutters.  For  deep  stores  the  area  should  be  at  one 
side  and  central,  say  from  30  to  40  feet  long  and  6  feet  wide,  which  may  be 
covered  in  the  first  story  with  glass.  If  this  recess  is  on  the  side  occupied  by 
the  staircases,  it  does  not  detract  from  the  inside  finish  of  the  stores. 

Hoists  now  in  large  stores  are  power-hoists — that  is,  worked  by  either 
steam,  water,  or  electricity.  The  platform  of  a  freight-hoist  is  usually  5  feet 
square ;  for  passenger-hoists,  in  wholesale  stores,  somewhat  less — 4'  X  5'.  For 
the  raising  of  goods  from  the  basement  or  sub-cellar  to  the  sidewalk  there  is 
a  hatch  in  the  front  light  platform,  opposite  some  window,  and  the  space  is 
like  that  of  freight-hoists,  5'  X  5' ;  these  may  be  power  or  hand  hoists.  For 
the  delivery  of  goods  into  these  lower  stories  there  is  often  a  slide  or  incline, 
iron-plated,  ending  at  the  bottom  with  an  easy  curve  to  the  horizontal,  down 
which  boxes  and  bales  are  slid. 

Fig.  1494  is  a  perspective  view  of  a  city  machine  and  blacksmith  shop.  It 
was  built  for  a  purpose,  and  to  express  the  purpose  constructionally  and  eco- 
nomically. As  regards  convenience  and  strength,  it  was  found  to  be,  on  occu- 
pation, all  that  could  be  wished.  Posts,  lintels,  window-frames,  sashes,  and 
ornamental  letters  were  of  iron,  and  painted  a  very  deep  green;  the  structure 
was  of  brick,  with  sills  and  bands  of  rubbed  Ulster  bluestone,  roof  of  Welsh 


ARCHITECTURAL  CONSTRUCTION. 


615 


ARCHITECTURAL  CONSTRUCTION. 

slate.  The  chimneys  shown  in  front,  although  not  dummies,  were  never  used. 
Power  and  heat  were  supplied  by  steam-boilers  in  the  front  vault,  with  a  long 
flue,  slightly  rising,  leading  to  a  chimney  at  the  centre  of  the  side  blank  wall. 
On  each  side  of  this  chimney,  and  separated  from  it  by  a  thin  with,  there  were 
flues.  Forges  occupied  all  the  exterior  walls  of  the  basement,  front  and  side 
areas,  and  the  draught  was  upward  and  then  down  into  the  nearly  horizontal 
flues  connected  with  the  central  flues,  and  the  draught  was  invariably  good. 
Care  was  taken  that  all  angles,  horizontal  and  vertical,  were  rounded. 

School- Houses. — Figs.  1495  and  1496  are  an  elevation  and  plan  of  a  country 
district  school-house,  with  seats  for  forty-eight  scholars.  There  are  two  en- 
trances, one  for  each  sex,  with  ample  accommodations  of  entry  or  lobby-room 
for  the  hanging  up  of  hats,  bonnets,  and  cloaks.  A  side  door  leads  from  each 
entry  into  distinct  yards,  and  an  inside  door  opens  into  the  school-room.  The 
desk,  T,  of  the  teacher,  is  central  between  the  doors,  on  a  platform,  P,  raised 
some  6"  or  8"  above  the  floor.  In  the  rear  of  the  teacher's  desk  is  a  closet  or 
small  room,  for  the  use  of  the  teacher.  The  seats  are  arranged  two  to  each 
desk,  with  two  alleys  of  18"  and  a  central  one  of  2'.  The  passages  around  the 
room  are  3'. 

Figs.  1497  and  1498  are  the  elevation  in  perspective  and  plan  of  an  English 
country  school-house,  introduced  as  suggestive — whether  a  one-story  plan  might 
not  be  better  suited,  and  of  more  beautiful  effect  in  our  own  country  towns, 
where  there  is  plenty  of  ground  space,  than  the  imitation  of  city  edifices  of 
many  stories. 

On  the  Requirements  of  a  School-House. — Every  scholar  should  have  room 
enough  to  sit  at  ease,  his  seat  should  be  of  easy  access,  so  that  he  may  go  to  and 
fro,  or  be  approached  by  the  teacher  without  disturbing  any  one  else.  The 
seat  and  desk  should  be  properly  proportioned  to  each  other  and  to  the  size  of 
the  scholar  for  whom  it  is  intended,  who  should  not  sit  in  a  cross-light,  the 
light  should  come  from  a  single  direction  as  near  as  possible  over  the  left  shoul- 
der. The  seats,  as  furnished  by  the  different  makers  of  school  furniture,  vary 
from  9"  to  14"  in  height ;  and  the  benches  from  17"  to  28" ;  measuring  on  the 
side  next  the  scholar.  The  average  width  of  the  desk  is  about  18",  and  it  is 
formed  with  a  slope  of  from  1£"  to  2-J-",  with  a  small 

i — p  I — p  I — p  P     horizontal  piece  of  from  2"  to  3"  at  top.     There  is  a 
—      —      — '  shelf  beneath  for  books,  but  it  should  not  come  within 

I — I      I — I      n     about  3"  of  the  front.     The  width  of  the  seat  varies 
p        p        from  10"  to  14",  with  a  sloping  back,  like  that  of  a 
chair ;    it  should,  in  fact,  be  a  comfortable  chair.     In 


a 


QQ] 


the  figure,  two  scholars  occupy  one  bench.     Fig.  1499 
represents  another  arrangement,  in  which  each  scholar 
has  a  distinct  bench ;  this  is  more  desirable,  but  not 
quite  so  economical  in  room.     In  primary  schools  desks 
— '  [1     are  not  necessary;   and  in  many  of  the  intermediate 
"FIG.  i499~  schools   the  seat  of  one  bench  is  formed   against  the 

back  of  the  next  bench  ;  but  seats  distinct  are  preferable. 

The  teacher's  seat  is  invariably  on  a  raised  platform,  and  had  better  be  against 
a  dead  wall  than  where  there  are  windows.  Blackboards  and  maps  should  be 
placed  along  the  walls.  Care  should  be  taken  in  the  warming  and  ventilation ; 


I 1 


ARCHITECTURAL  CONSTRUCTION. 


017 


warm  air  should  be  introduced  in  proportion  to  the  number  of  scholars,  and 
ventiducts  should  be  formed  to  carry  off  the  impure  air. 


FIG.  1498. 


In  cities  and  large  towns  it  is  almost  indispensable  to  build  school-houses 
many  stories  in  height,  dividing  the  rooms  in  each  story  according  to  the  neces- 


618 


ARCHITECTURAL   CONSTRUCTION. 


ARCHITECTURAL  CONSTRUCTION. 


619 


sities  of  their  occupancy.  The  management  of  schools  differs  in  different  locali- 
ties. This  will  be  seen  in  the  illustrations  given  below,  showing  the  arrange- 
ments of  school-houses  in  the  city  of  New  York  and  of  Cleveland,  Ohio. 

Fig.  1500  is  an  elevation  in  perspective  of  one  of  the  largest  of  the  New 
York  city  schools,  showing  the  yards  around  it.     Fig.  1501  is  the  plan  of  the 


FIG.  1501. 

grammar-department  floors  of  this  house ;  and  Fig.  1502  the  plan  of  the  same 
floors  of  another  house  of  a  different  outline. 

Figs.  1503  to  1506  are  plans  of  school-houses,  built  at  Cleveland,  Ohio,  a 
type  inaugurated  under  the  supervision  of  the  then  superintendent,  Mr.  A.  J. 
Kickoff.  Figs.  1503,  1504,  and  1505  are  plans  of  the  High-School  house.  Fig. 
1503  is  the  plan  of  the  third  story ;  Figs.  1504  and  1505  of  those  portions  of 
the  second  and  first  stories  which  differ  from  that  of  the  third.  There  is  a  rear 
vestibule  in  the  first  story  to  correspond  with  the  one  in  front,  shown  in  the 
figure.  In  the  whole  building  there  are  14  session-rooms,  each  37'  X  30'  X 
16' ;  each  having  its  connecting  cloak-room ;  one  general  assembly-room,  94'  X 
56'  X  38'  high,  with  a  seating  capacity  for  at  least  1,000  persons ;  one  lecture- 
room,  with  seats  for  100,  with  an  apparatus- room ;  one  room  for  drawing,  30'  x 
55',  with  a  room  for  models,  drawing-boards,  etc. ;  two  rooms  for  the  principal 
and  reception-room ;  five  rooms  for  library  and  recitation-rooms. 


620 


ARCHITECTURAL  CONSTRUCTION. 


Fig.  1506,  a  plan  of  one  half  of  one  story  of  the  Walton  Avenue  School,  on 
a  larger  scale,  explains  more  fully  the  arrangement  of  seats  and  the  ventilation. 
Four  ventilating  educts,  of  8  square  feet  of  section  each,  may  be  heated  to  any 
required  temperature  for  the  purposes  of  circulation  by  four  upright  2"  steam- 
pipes  ;  six  ducts  of  1  square  foot  section  lead  from  different  points  in  the  floor 


OW)a]:C:D:G:D:D:DSH]:D:[tO: 


Fio.  1502 

of  each  session-room  (as  shown  in  dotted  lines  in  the  figure)  into  the  ventilating 
educts.  There  are  besides  other  registers  opening  directly  into  the  educts. 
The  building  is  heated  by  steam  coils  or  radiators  placed  under  the  windows  of 
the  rooms,  with  provision  for  the  admission  of  fresh  air  under  the  stone  sills 
behind  the  radiators.  The  main  light  of  every  room  is  admitted  at  the  left 
hand  of  the  pupil,  so  that  in  writing  the  shadow  of  the  hand  does  not  fall  on 
the  space  to  be  written  on.  There  are  none  of  the  cross-lights  that  so  seriously 
impair  the  vision.  The  wall  facing  the  pupil  and  behind  the  teacher  is  un- 
broken by  windows,  affording  large  and  convenient  spaces  for  blackboards. 

Churches,  Theatres,  Lecture- Roomx,  Munic  and  Lcyixlative  Halls. — To  the 
proper  construction  of  rooms  or  edifices  adapted  for  these  purposes  some  knowl- 
edge of  the  general  principles  of  acoustics,  and  their  practical  application,  is 
necessary.  In  the  case  of  lecture-rooms  and  churches,  the  positions  of  the 
speaker  and  the  audience  are  fixed ;  in  theatres,  one  portion  of  the  inclosed 
space  is  devoted  to  numerous  speakers  and  the  other  to  the  audience;  in  legis- 
lative halls,  the  speakers  are  scattered  over  the  greater  part  of  the  space,  and 
also  form  the  audience. 


ARCHITECTURAL  CONSTRUCTION. 


621 


622 


ARCHITECTURAL  CONSTRUCTION. 


-fHJ  )- 


[ipa  aaaa l|p 
jo  a  p.-  a  a  D  iji  ja 
la  a  a  a  a  a  q  ja 

to  D  D  D  a  D  d  p 

itpDDDDOdjD 

|p  a  D  D  a  D  nip 
a  a  a  a  D  a  DJD 


'•'•'  i  i  i  i  i  FEET 


ARCHITECTURAL  CONSTRUCTION.  623 

The  transmission  of  sound  is  by  vibrations,  illustrated  by  the  waves  formed 
by  a  stone  thrown  into  still  water;  but  direction  may  be  given  to  sound,  so  that 
the  transmission  is  not  equally  strong  in  every  direction ;  thus,  Saunders  found 
that  a  person  reading  at  the  centre  of  a  circle  of  100 
feet  in  diameter,  in  an  open  meadow,  was  heard  most  dis-  ,.-  '      ~  --x 

tinctly  in  front,  not  as  well  at  the  sides,  but  scarcely  at 
all  behind.  Fig.  1507  shows  the  extreme  distance  every 
way  at  which  the  voice  could  be  distinctly  heard :  92  feet 
in  front,  75  feet  on  each  side,  and  31  feet  in  the  rear. 
The  waves  of  sound  are  subject  to  the  same  laws  as  those 
of  light,  the  angles  of  reflection  are  equal  to  those  of  in- 
cidence ;  therefore,  in  every  inclosed  space  there  are  re- 
fleeted  sounds,  more  or  less  distinct,  according  to  the  po- 
sition of  the  hearer,  and  to  the  form  and  condition  of  the  surfaces  against 
which  the  waves  of  sound  impinge.  Thus,  of  all  the  sounds  entering  a  para- 
bolic sphere,  the  reflected  sounds  are  collected  at  the  focus.  Solid  bodies 
reflect  sound,  but  draperies  absorb  it.  As,  in  all  rooms,  the  audience  can  never 
be  concentrated  at  focal  points,  nor  is  it  possible  in  any  construction  to  make 
calculation  for  all  positions,  it  is  in  general  best  to  depend  on  nothing  but  the 
direct  force  of  the  voice,  and  not  to  construct  larger  than  can  be  heard  directly 
without  aid  from  reflected  sounds. 

There  is  great  difference  in  the  strength  of  voice  of  different  speakers ;  the 
limits  as  given  in  the  figure  are  for  ordinary  reading  in  an  open  space.  In  in- 
closed spaces,  owing  to  the  reflected  sounds  or  some  other  cause,  there  are  cer- 
tain pitches  or  keys  peculiar  to  every  room,  and  to  speak  with  ease  the  speaker 
must  adapt  his  tone  to  those  keys.  The  larger  the  room,  the  slower  and  more 
distinct  should  be  the  articulation. 

It  has  been  observed  that  the  direction  of  the  sound  influences  the  extent  to 
which  it  may  be  heard.  The  direction  of  the  currents  of  air  through  which 
the  sound  passes  affects  the  transmission  of  the  sound,  and  this  may  be  made 
useful  when  the  rooms  are  heated  by  hot  air,  by  introducing  the  air  near  the 
speaker  and  placing  the  ventilators  or  educts  at  the  outside  of  the.  rooms,  and 
by  placing  their  apertures  rather  nearer  the  bottom  of  the  room  than  at  the 
top.  It  would  seem  much  better  and  easier  to  make  a  current  of  air  a  vehicle 
of  sound  rather  than  depend  on  reflection. 

In  the  "  Baltimore  Academy  of  Music,"  designed  by  Mr.  J.  Crawford  Neil- 
son,  architect,  the  ventilation  was  arranged  to  obstruct  the  formation  of  air- 
currents  of  unequal  density.  The  whole  supply  of  fresh  air  is  admitted  at  the 
back  of  the  stage,  is  there  warmed,  crosses  the  stage  horizontally,  and  passes 
through  the  proscenium  and  then,  somewhat  diagonally  toward  the  roof,  across 
the  auditorium  in  one  grand  volume  and  with  gentle  motion  so  as  to  almost 
entirely  prevent  the  formation  of  minor  air- currents.  It  is  exhausted  partly 
by  an  outlet  in  the  roof  and  partly  by  numerous  registers  in  the  ceilings  of 
the  galleries.  From  this  central  outlet  and  from  the  large  flues  of  the  reg- 
isters the  air  passes  into  the  ventilating-tower  over  the  great  chandelier,  which 
supplies,  in  its  heat,  a  part  of  the  motive  power  of  the  circulation.  It  is 
further  expelled  from  the  tower  by  means  of  large  valves,  offering  no  obstacle 
to  the  egress  of  air,  but  completely  cutting  off"  its  entrance. 


624: 


ARCHITECTURAL  CONSTRUCTION. 


FIG.  1508. 


FIG.  1509. 


The  direction  of  the  air-currents  within  the  house  was  determined  by  thistle 
balls,  and  the  quantity,  as  found  by  anemometers,  was  about  15,000  cubic  feet 
per  minute.  This  amount,  sufficient  to  ventilate  the  house,  is  that  required  to 
impress  the  proper  movement  on  its  atmosphere.  It  is  amply  sufficient  for 
ventilation,  as  is  shown  by  the  fact  that  the  thermometers  of  the  upper  circle  do 
not  vary  perceptibly  from  those  of  the  orchestra  circle.  The  seating  capacity 
of  the  house  is  about  sixteen  hundred  persons.  The  acoustics  are  satisfactory. 
On  the  Space  occupied  by  Seats  in  general. — A  convenient  arm-chair  occu- 
pies about  20"  X  20",  the  seat  itself  being  about  18"  in  depth,  and  the  slope  of 

the  back  2"  ;  18"  more  affords  am- 
ple space  for  passage  in  front  of 
the  sitter.  In  churches  the  seats 
are  arranged  by  pews  or  stalls,  the 
width  of  each  pew  in  general  being 
about  2'  10".  In  the  arrangement 
of  theatre  seats  the  bottom  turns 
up  (Figs.  1508  and  1509),  and  29" 
only  is  allowed  for  both  seat  and 
passage-way,  and  18"  for  the  width 
of  seat,  which  may  be  taken  as  the 
average  allowance  in  width  to  each 
sitter  in  comfortable  public  rooms. 
In  lecture-rooms,  benches  and  set- 
tees are  often  used,  the  space  there  occupied  by  seat  and  passage  being  about 
2'  6". 

In  the  earlier  churches,  ceremonies  and  rites  formed  a  very  large  part  of  the 
worship,  the  sight  was  appealed  to  rather  than  the  hearing,  and  for  this  pur- 
pose churches  were  constructed  of  immense  size,  and  with  all  the  appliances 
of  ornament  and  construction,  with  pillars,  vaults,  groins,  and  traceried  win- 
dows. In  the  churches  of  this  country,  the  great  controlling  principle  in  the 
construction  of  a  church  is  its  adaptation  to  the  comfortable  hearing  and  seeing 
the  preacher.  In  this  view  alone,  the  church  is  but  a  lecture-room ;  the  ceiling 
should  be  low,  and  pillars  and  transoms  should  be  little  used ;  but  since  even 
the  character  of  the  building  may  tend  to  devotional  feelings  in  the  audience, 
and  since  certain  styles  and  forms  of  architecture  have  long  been  used  for 
church  edifices,  it  has  been  the  custom  to  follow  these  time-honoured  examples, 
adapting  them  to  modern  requirements  of  church  worship,  with  adequate  means 
of  heating  and  ventilation. 

Fig.  1511  is  a  plan  of  an  ancient  basilicon  or  Romanesque  church.  Fig. 
1510  is  a  sectional  elevation  of  the  same.  Fig.  1512  is  a  plan  of  a  Gothic 
church,  in  which  C  is  the  chancel,  usually  at  the  eastern  extremity,  T  T  the 
transept,  and  N  the  nave.  In  general  elevation  the  Gothic  and  Eomanesque 
agree :  a  high  central  nave  and  low  side  aisles.  In  the  later  Eomanesque  the 
transept  is  also  added. 

The  basilicas  aggregated  within  themselves  all  the  offices  of  the  Romish 
church.  The  circular  end  or  apse,  with  the  raised  platform,  or  dais,  in  front 
appropriated  to  the  altar ;  in  the  rear  the  confessional  and  the  sacristy ;  beneath 
was  the  crypt,  where  were  placed  the  bodies  of  the  saints  and  martyrs,  and  pul- 


ARCHITECTURAL  CONSTRUCTION. 


625 


pits  were  placed  in  the  nave,  from  which  the  services  were  said  or  sung  by  the 
inferior  order  of  clergy. 

The  plan  (Fig.  1512)  is  that  of  the  original  Latin  cross,  the  eastern  limb 
or  chancel  being  the  shortest,  and  the  nave  the  longest.    Sometimes  the  eastern 


FIG.  1510. 


Fui.  1511. 


limb  was  made  equal  to  that  of  the  transept,  sometimes  even  longer,  but  never 
to  exceed  that  of  the  nave.  In  the  Greek  cross  all  the  limbs  are  equal.  In 
most  of  the  French  Gothic  churches  the  eastern  end  is  made  semicircular,  often 
inclosed  by  three  or  more  apsidal  chapels,  that  is,  semi-cylinders,  surmounted 
by  semi-domes. 

The  Byzantine  ohurch  consisted  internally  of  a  large  square  or  rectan- 
gular chamber,  surmounted  in  the  centre  by  a  dome,  which  rested  upon 
massive  piers  ;  an  apse  was  formed  at  the  eastern  end.  Circular  churches 
were  built  in  the  earlier  ages  for  baptisteries,  and  for  the  tombs  of  saints  and 
emperors. 

The  Greek,  Roman,  and  English  churches  conform  in  their  cathedrals  and 
larger  edifices  nearly  to  the  Komanesque  or  Gothic  models.  But  as  the  general 
requirements  for  church  services  now  are  those  of  a  lecture-room,  modern 
churches  are  constructed  adapted  to  these  purposes,  and,  in  cities,  to  the  size 
and  form  of  the  lots,  with  some  ecclesiastical  accessories  of  towers  and  steeples, 
windows  and  doors  and  interior  finish. 

Fig.  1513  is  the  plan  of  the  English  church  at  The  Hague. 


FIG.  1513. 


Fig  1514  is  the  plan  of  a  Wesleyan  chapel  in  London ;  the  requirements  of 
the  service  have  been  well  adapted  to  the  necessities  of  the  lot. 
41 


626 


ARCHITECTURAL  CONSTRUCTION. 


Fig.  1515  is  the  cross-section  of  a  common  form  of  small  country  church, 
with  nave  w,  aisles  a  a,  and  clear-story  c.     The  effect,  both  inside  and  out,  is 


FIG.  1514. 


good,  but  there  are  objections  to  large  or  masonry-columns,  which  cut  off  the 
view  of  the  desk  and  the  altar  from  many  sitters,  and  to  the  windows  of  the 


FIG.  1515. 


ARCHITECTURAL  CONSTRUCTION. 


627 


clear-story,  which  in  winter  act  as  coolers  to  the  air  descending  in  draughts 
upon  the  heads  of  the  congregation  beneath  them.  Neither  columns  nor  clear- 
story are  constructively  necessa- 
ry ;  the  span  can  readily  be  met 
by  a  single  roof,  and  sufficient 
light  can  be  obtained  from  the 
sides. 

Figs.  1516,  1517,  and  1518 
are  examples  of  open- timbered 
Gothic  roofs  of  churches. 

The  technical  names  (Fig. 
1516)  are:  1,  Principals ;  2,  Pur- 
lines;  3,  Collars;  4,  Braces;  5, 
Wall-pieces  ;  6,  Wall-plates  ;  7, 
Struts;  8,  Rafters.  4  and  5  are 
shown  in  section. 

The  length  of  pews  is  vari- 
ous, being  of  two  sizes,  adapted 
to  either  small  or  large  families, 
say  from  7'  6"  to  12'  6",  18"  be- 
ing allowed  for  each  sitter.  In 
arrangement  it  is  always  consid- 
ered desirable  that  there  should 
be  a  central  aisle,  and  if  but 
four  rows  of  pews  (often  of  two 
sizes  in  the  same  church),  an 
aisle  against  each  wall ;  if  six 
rows,  one  row  on  each  side  will 
be  wall-pews.  Formerly  it  was 
the  universal  practice  to  con- 
struct pews  with  doors,  but  of 
late  it  is  more  customary  to  omit 
the  doors,  making  the  pews  open 
stalls. 

Few  churches  are  now  with- 
out an  organ ;  its  dimensions 
should  of  course  depend  on  the 
size  of  the  church.  In  form  it 
may  be  adapted  somewhat  to  the 
place  which  may  be  appropriated 
to  it — either  in  a  gallery  over 
the  main  entrance  or  above  the 
pulpit  or  at  the  side  of  the  chan- 
cel, as  in  Fig.  1513.  Sometimes 
there  are  two,  one  at  each  ex- 
tremity of  the  church,  one  organist  playing  on  both  by  electric  connection.  In 
general,  it  is  oblong  in  form,  the  longer  side  being  with  the  keys.  The  di- 
mensions suited  to  a  medium-sized  church  are  about  9'  X  15',  and  12'  in  height. 


FIG.  1518. 


f,28  ARCHITECTURAL  CONSTRUCTION. 

The  vestry-room,  if  used  for  the  purposes  of  its  meetings,  should  be  adapted 
in  size  to  the  purpose ;  but  if  only  for  a  withdrawing  or  robing  room  for  the 
clergyman,  it  may  be  of  very  small  dimensions,  and  should  be  accessible  from 
without.  The  Sunday-school  room,  in  general,  requires  in  plan  about  half 
the  area  of  the  church.  From  motives  of  economy  it  is  usually  placed  in  the 
basement  of  the  church ;  but,  in  the  country  especially,  it  is  better  that  it 
should  be  a  separate  building,  and  form  one  of  the  group  of  church,  parson- 
age, and  Sunday-school  house. 

In  elevation,  city  churches  are  generally  Romanesque  and  Gothic,  occasion- 
ally Byzantine.  The  Greek  have  no  tower,  but  often  a  spire  above  the  portico ; 
the  Romanesque  and  Gothic  generally  one  tower,  over  the  central  door  of  en- 
trance, or  at  one  corner ;  sometimes  two,  one  at  each  side  of  the  principal  door, 
almost  invariably  surmounted  by  spires,  high  and  tapering,  usually  of  wood,  but 
in  some  instances  of  stone. 

Theatres. — In  theatres  and  opera-houses  it  is  not  only  necessary  that  the 
audience  should  have  a  good  position  for  hearing  and  seeing  the  performance 
upon  the  stage,  but  also  to  see  each  other.  The  most  approved  form,  now,  for 
the  body  of  a  dramatic  theatre  is  a  circular  plan,  the  opening  for  the  stage 
occupying  from  one  fourth  to  one  fifth  of  the  circumference,  the  sides  of  the 
proscenium  being  short  tangents;  but  for  a  lyric  theatre,  where  music  only -is 
performed,  and  where,  consequently,  hearing  is  easier,  the  curve  is  elongated 
into  an  ellipse,  with  its  major  axis  toward  the  stage. 

In  the  general  position  of  the  stage,  proscenium,  orchestra,  orchestra  seats, 
parquette,  and  boxes,  but  one  plan  is  followed.  The  line  of  the  front  of  the 
stage,  at  the  footlights,  is  generally  slightly  curved,  with  a  sweep,  say,  equal  to 
the  depth  of  the  stage,  and  the  orchestra  and  parquette  seats  are  arranged  in 
circles  concentric  with  it :  of  the  space  occupied  by  seats  we  have  already 
spoken.  The  entrance  to  the  parquette  may  be  through  the  boxes,  near  the 
proscenium,  and  centrally,  but  better  at  the  sides,  dividing  the  boxes  into  three 
equal  benches ;  the  seats  in  the  boxes  are  usually  concentric  with  the  walls,  and 
more  roomy  than  those  of  the  parquette.  The  orchestra  seats  are  of  a  height 
to  bring  the  shoulders  of  the  sitter  level  with  the  floor  of  the  stage,  and  the 
floor  of  the  parquette  rises  to  the  outside,  1  in  15  to  18.  The  floor  of  the  first 
row  of  boxes  is  some  2  to  3  feet  above  the  floor  of  the  parquette  at  the  front 
centre,  and  rises,  by  steps  at  each  row,  some  4  inches ;  in  the  next  tier  of  boxes 
the  steps  are  considerably  more  in  height,  and  so  on  in  the  boxes  above.  In 
general,  three  rows  of  boxes  are  all  that  is  necessary ;  in  front,  above  the  sec- 
ond, the  view  of  the  stage  is  almost  a  bird's-eye  view.  The  floor  of  the  stage 
descends  to  the  footlights  at  the  rate  of  about  1  in  50.  In  large  theatres  it  is 
of  the  utmost  importance  that  all  the  lobbies  or  entries  should  be  spacious,  and 
the  means  of  exit  numerous  and  ample — the  staircases  broad,  in  short  flights 
and  square  landings,  and  not  circular,  as,  in  case  of  fright,  the  pressure  of 
persons  behind  may  precipitate  those  in  front  the  whole  length  of  the  flight. 
Ladies'  drawing-rooms  should  be  placed  convenient  to  the  lobbies,  of  a  size 
adapted  to  that  of  the  theatre,  also  rooms  for  the  reception  of  gentlemen's 
canes  and  umbrellas,  both  with  usual  water  arrangements.  The  box-office 
should  be  near  the  entrance  and  arranged  to  interfere  as  little  as  possible  with 
the  approach  to  the  doors  of  the  house.  At  the  entrance  there  should  be  a 


ARCHITECTURAL  CONSTRUCTION. 


629 


FIG.  1519. 


very  spacious  lobby,  or  hall,  so  that  the  audience  may  wait  sheltered  from  the 
weather ;  if  possible,  there  should  be  a  long  portico  over  the  sidewalk,  to  cover 
the  approach  to  the  carriages.  Only  single 
entrances  are  necessary  to  distinct  parts  of 
the  house,  but  the  greater  the  number  of, 
and  the  more  ample  places  for  exit  at  the 
conclusion  of  the  piece,  or  for  the  contin- 
gency of  fire,  the  better. 

Fig.  1519  is  a  plan  suggested  by  Fer- 
guson of  keeping  the  centre  of  the  bal- 
conies perpendicular  over  one  another,  and 
then,  by  throwing  back  the  sides  of  each 
balcony  till  the  last  is  a  semicircle,  the 
whole  audience  would  sit  more  directly 
facing  the  stage,  would  look  at  it  at  a  bet- 
ter angle,  and  the  volume  of  sound  be  con- 
siderably increased  by  its  freer  expansion 
immediately  on  leaving  the  stage. 

Figs.  1520  and  1521  are  a  plan  and  section  of  Wagner's  theatre. 
In  cities,  the  auditoria  of  dramatic  theatres  conforming  to  the  shape  of  the 
lots  are  rectangular  in  their  outline,  and  seldom  exceed  a  seating  capacity  of 

1,500.     Lyric  theatres  are 

PLAN-  much  larger,  both  in  seat- 

ing and  scenic  capacity. 
Lecture-rooms  are  usually 
arranged  with  the  au- 
dience-floor flat,  room  rec- 
tangular, with  reading-desk 
or  platform  raised,  and 
with  or  without  galleries. 
The  same  form  usually  ob- 
tains for  music-halls,  only 
they  are  much  greater  in 
extent,  the  first  being  capa- 
ble of  containing  from  500 
to  1,000  persons  ;  whereas 
some  music-halls  will  con- 
tain 2,500,  and  Ferguson 
thinks  that  a  music-hall 
might  be  arranged  so  that 
even  10,000  might  hear  as 
well  as  in  those  of  present 
construction.  The  lecture 
and  music  halls  are  seldom 
devoted  to  a  single  purpose, 
but  are  used  for  political 
meetings,  for  fairs,  and  dances,  and  the  constructon  must  be  such  as  to  serve 
these  other  purposes. 


FIG.  1520. 


SECTION. 


FIG.  1521. 


630  ARCHITECTURAL  CONSTRUCTION. 

COMPARATIVE   TABLE   OP  THE   DIMENSIONS   OP   A   PEW  THEATRES. 


DISTANCE,   IN  FEET. 

HEIGHT,  IN  FEET. 

•a 

1 

cS 

|4 

to 

ll 

'$  !? 

•~   03 

9 

a 
9 

rj 

|| 

ft 

*M    V 
°    0 

ll 

NAME  AND  LOCATION. 

O  bo 

Ou 

«*s 

£« 

O 

"SS 

o'o 

"o  S 

§^ 

*c  " 

S-g 

_Q  -FH 

O 

^8 

0® 

$"§ 

£,3 

s 

•O 

•T3  1. 
S  « 

So 

1C  g 

•J 

&  c3 

4J 

"S 

• 

s  ^ 

0" 

S  c3 

«g 

E 

W  fl 

—  -!_> 

E 

£  g 

03 

« 

oj 

o 

n 

«» 

' 

£° 

Alexandre,  St.  Petersburg  

65 

11 

84 

58 

56 

75 

53 

58 

Berlin  .                 .... 

62 

16 

76 

51 

41 

92 

43 

47 

La  Scala,  Milan    

77 

18 

78 

71 

49 

86 

60 

64 

San  Carlo  Naples          

77 

18 

74 

74 

52 

66 

81 

83 

Grand  Theatre,  Bordeaux  

46 

10 

69 

47 

37 

80 

50 

57 

Salle  Lepelletier,  Paris  

67 

9 

82 

66 

43 

78 

52 

66 

Covent  Garden,  London  

66* 

55 

51 

32 

86 

54 

Drury  Lane,  London  

64* 

80 

56 

32 

48 

60 

Boston,  Boston  

53 

18 

68 

46 

87 

554 

58 

Academy  of  Music,  New  York.  .  .  . 

74 

13 

71 

62 

48 

83 

74 

Grand  Opera-House,  New  York.  .  . 

54 

84 

634 

48 

44 

76 

52 

67 

Opera-House,  Philadelphia  

61 

17 

72 

66 

48 

90 

644 

74 

*  These  dimensions  include  the  distance  between  the  footlights  and  curtain. 

Legislative  Halls. — Although  much  has  been  written  about  their  construc- 
tion in  relation  to  acoustic  principles,  there  is  great  disagreement  in  practical 
examples,  and  in  the  deductions  of  scientific  men.  The  Chamber  of  French 
Deputies  was  constructed,  after  a  report  of  most  celebrated  architects,  in  a 
semicircular  form,  surmounted  by  a  flat  dome,  but  as  the  member  invariably 
addresses  the  house  from  the  tribune,  at  the  centre,  in  its  requirements  it  is  but 
a  lecture-room.  Mr.  Mills,  architect,  of  Philadelphia,  recommends  for  legisla- 
tive or  forensic  debate  a  room  circular  in  its  plan,  with  a  very  slightly  concave 
ceiling.  Dr.  Reid,  on  the  contrary,  in  reference  to  the  Houses  of  Parliament, 
gave  preference  to  the  square  form,  with  a  low,  arched  ceiling.  The  Hall  of 
Representatives  at  Washington  is  139  feet  long  by  93  feet  wide,  and  about  36 
feet  high,  with  a  spacious  retiring  gallery  on  three  sides,  and  a  reporters'  gal- 
lery behind  the  Speaker's  chair.  The  members'  desks  are  arranged  in  a  semi- 
circular form.  The  ceiling  is  flat,  with  deep-sunk  panels,  openings  for  ventila- 
tion, and  glazed  apertures  for  the  admission  of  light.  The  ventilation  is 
intended,  in  a  measure,  to  assist  the  phonetic  capacity  of  the  hall,  the  air 
being  forced  in  at  the  ceiling  and  drawn  out  at  the  bottom. 

In  reviewing  the  general  principles  of  acoustics,  it  will  be  found  that  those 
rooms  are  the  best  for  hearing  in  which  the  sound  arrives  directly  to  the  ear, 
without  reflection ;  that  the  sides  of  the  room  should  neither  be  reflectors  nor 
sounding-boards,  and  that  surfaces  absorbing  sound  are  less  injurious  than 
those  that  reflect.  Slight  projections,  such  as  ornaments  of  the  cornices  and 
shallow  pilasters,  tend  to  destroy  sound,  but  deep  alcoves  and  recessed  rooms 
produce  echoes.  Let  the  ceiling  be  as  low  as  possible,  and  slightly  arched  or 
domed ;  all  large  external  openings  should  be  closed ;  as  M.  Meynedier  ex- 
presses it,  in  his  description  of  an  opera-house,  "  Let  the  hall  devour  the  sound  ; 
as  it  is  born  there,  let  it  die  there." 

Hospitals. — In  large  cities,  hospitals,  by  necessity,  are  confined  to  narrow 
spaces,  but  they  should  be  placed,  if  possible,  on  river  fronts  or  on  open  parks, 


ARCHITECTURAL  CONSTRUCTION.  631 

to  secure  as  much  open-air  ventilation  as  possible.  They  are  usually  many 
stories  in  height,  with  large  warils  one  above  the  other.  Sir  J.  T.  Simpson 
alleges  a  very  high  rate  of  mortality  in  hospitals  after  surgical  operations  as 
compared  with  the  mortality  after  the  same  operations  when  performed  at  the 
homes  of  the  patients,  and  asserts  that  the  mortality  after  operations  performed 
in  hospitals  containing  more  than  300  beds  is  in  excess  of  that  in  hospitals  con- 
taining less;  that  great  hospitals  are  great  evils  in  exact  proportion  to  their 
magnitude,  and  suggests  the  construction  of  smaller  hospitals. 

Figs.  1522  and  1523  are  an  elevation  and  plan  of  an  English  country  hos- 
pital. 

Stables. — Under  this  general  name  are  included  the  barn,  or  the  receptacle 
of  hay  and  fodder,  the  carriage-house,  and  the  stable  proper,  or  lodging-house 
for  horses  and  cows.  The  first  two  may  be  included  under  one  roof,  the  car- 
riages on  the  first  floor,  and  hay  in  the  loft ;  but  the  lodging-place  should  be 
distinct,  in  a  wing  attached  to  the  barn,  that  the  odours  from  the  animals  may 
not  impregnate  their  food,  or  the  cloth-work  of  the  carriages,  or  the  ammonia 
tarnish  their  mountings. 

Hay  in  bulk,  in  the  mow,  occupies  about  340  cubic  feet  per  ton ;  bales  aver- 
age 2'  4"  X  2'  6"  X  4',  and  weigh  from  220  to  320  pounds.  The  door-space  for 
a  load  of  hay  in  the  bulk  should  be  from  12  to  13  feet  high  and  12  feet  wide. 
The  floor  beneath  the  hay  should  be  tight,  so  that  dust  and  seed  may  not  drop 
on  the  carriage.  A  door  for  carriages  should  be  10  feet  6  inches  high  by  9  feet 
wide. 

The  horse  is  to  be  treated  with  greater  care  than  any  other  domestic  animal. 
His  stable  is  to  be  carefully  ventilated,  that  he  may  have  fresh  air  without 
being  subject  to  cross-draughts.  Preferably  the  floor  should  be  on  the  ground, 
that  there  may  be  no  cold  from  beneath.  He  should  stand  as  near  as  possible 
level ;  and  for  this  purpose  a  grated  removable  floor,  with  small  interstices, 
should  be  laid  over  a  concrete  bottom,  with  a  drip  toward  the  rear  of  the  stall, 
and  the  urine  should  be  collected  in  a  drain  and  discharged  into  a  trapped 
manure-tank  outside  the  stable.  In  Fig.  1524  the  pitch  of  bottom  of  stalls  is 
to  the  centre  and  outward.  The  manure  should  never  be  deposited  beneath 
the  stable,  but  should  be  wheeled  out  and  deposited  in  a  manure-yard  or  tank 
daily.  It  is  as  essential  that  all  excrements  should  be  removed  entirely  from 
the  stable  as  that  the  privy  should  be  placed  outside  the  house. 

The  breadth  of  stalls  should  be  from  4  feet  6  inches  to  5  feet  in  the  clear; 
the  length,  7  feet  6  inches  to  8  feet ;  the  rack  and  feed-box  require  two  feet  in 
addition,  to  which  access  is  given  in  the  best  stables  by  a  passage  in  front. 
Rack  and  feed-boxes  are  often  made  of  iron,  and  the  upper  part  of  stalls  fitted 
with  wrought-iron  guards.  Box-stalls,  in  which  horses  are  shut  up  but  not 
tied  in  cases  of  sickness  or  foaling,  are  about  10  feet  square. 

In  large  stables  in  cities  the  first  floors  are  often  occupied  by  the  carriages, 
while  the  horse-stalls  are  in  the  basement  or  upper  stories,  with  inclined  ways 
of  access.  In  the  basement  provision  must  be  made  for  light  and  ventilation. 
In  the  upper  stories  these  may  be  secured  more  readily,  but  the  floors  must  be 
made  tight  and  deafened,  that  the  urine  may  not  leak  through,  nor  the  cold 
come  through  from  below  to  make  too  cool  a  bed  for  the  horse. 

Fig.  1524  is  an  elevation  in  perspective  of  two  first-class  stalls,  a  box  shown 


632 


ARCHITECTURAL  CONSTRUCTION. 


FIG.  152*. 
GROUND  PLAN. 


iCALC      OF      FE.E7 


FIG.  1523. 


ARCHITECTURAL  CONSTRUCTION. 


633 


with  the  door  open,  and  a  single  stall.     The  lower  part  of  the  inclosures  is  of 
plank,  with  wrought-iron  guards  and  ramp  above.     The  posts  are  of  oak,  and 


FIG.  1524. 

the  hay-boxes  or  mangers  of  cast-iron ;  the  hay-rack  in  the  box-stall  is  of 
wrought-iron.  These  are  of  common  manufacture,  and  are  of  varied  patterns ; 
but  in  the  country  they  are  usually  made  of  wood,  and  connected  with 
the  stall. 

Fig.  1525  is  the  plan  of  a  small  country  stable,  showing  the  desirable  pas- 


Open      Shed 


0 

0 

0 

o 

Box    Sfall. 

Carriage    House 


FIG.  1525. 

sages  around  the  stalls  and  exterior  windows  in  front  of  each  stall,  that  the 
horses  may  not  only  have  light  and  air,  but  can  see  out. 

Cow-houses,  for  cows  giving  milk,  should  be  constructed  with  care  for  ven- 
tilation, light,  and  cleanliness.  Other  cattle  are  usually  left  out,  with  sheds 
under  which  they  can  go  for  shelter.  For  those  housed,  the  spaces  occupied 
should  be  about  the  same  per  head  as  the  single  horse-stall.  The  manger 
should  be  on  the  floor,  12"  to  18"  high,  and  about  18"  wide.  It  is  not  usual  to 


634 


ARCHITECTURAL  CONSTRUCTION. 


have  partitions,  but  there  ought  to  be  between  every  pair,  reaching  from  the 
manger  half-way  to  the  gutter  behind.  The  floor  should  be  level,  grated,  with 
a  drip  beneath,  and  cleansed  by  washing  out.  The  partition  and 
mangers  are  often  of  cast-iron,  and  on  sale,  but  for  large  stables  and 
in  the  country  they  are  commonly  of  wood. 

Greenhouses. — Fig.   1526  is  the   section   of   a  greenhouse, 
with  shelves  for  plants.      The  floor  is  of  concrete   and 
the  walls  are  of  masonry ;  the  northern  exposure  is 
a  blank  wall. 

Fig.  1527  is  the  details  of  windows. 
The  sides  are  box-sash,  hung  with 
weights    (w,  w,  Fig.    1528). 
The  lower  roof  sash  is 
firmly  fixed,  but 
the    upper 


FIG.  1526. 


FEET 


one  can  be  slid  down ;  it  is  usually  retained  in  place  by  a  cord  attached  to  the 
lower  part  of  the  sash,  passing  over  a  pulley  on  the  upper  bar  of  the  frame, 
with  the  loose  end  within  reach  of  the  gardener,  who  can  fasten  it  to  a  cleat. 

Ventilation  and  Warming. — The  purposes  of  ventilation  are  not  changes  of 
air  merely,  but  the  removal  of  foul  and  vitiated  air,  and  the  substitution  there- 
for of  pure  air ;  and  this  air  may  be  warm  or  cool  according  to  the  necessities 
of  the  season  and  personal  requirements.  Open  space  is  not  necessarily  well 
ventilated;  there  must  be  circulation,  outward  and  inward — the  latter  from 


ARCHITECTURAL   CONSTRUCTION. 


635 


purer  sources  than  the  former.     With  an  equal  discharge  and  sup- 
ply of  pure  air,  the  smaller  the  room,  the  more  frequent  the  change 
of  air,  the  better  its  distribution  and  the  better  the  ventilation. 
But  if  the  means  of  removal,  supply,  and  distribution  of 
air  be  proportioned  to  the  size  of  the  room,  then 
the  larger  the  room  the  better.     Apertures 
do  not  necessarily  mean  circulation 
flue   may  draw  or  it  may  not 
draw,  it  may  be  inert,  or 
the  air   may  come 


j  FEET. 


FIG.  1527. 


636  ARCHITECTURAL  CONSTRUCTION. 

down ;  a  window  may  be  open,  with  little  or  no  inward  or  outward  movement 
of  air.  In  a  house  exposed  to  a  fresh  breeze,  on  the  windward  side  there  is  an 
air-pressure,  on  the  leeward  side  there  is  an  eddy  or  vacuum.  Air  is  forced  in 
on  the  first  through  every  crack  of  door  and  window — often  down  chimney- 
flues — and  drawn  out  on  the  other  side.  This  often  happens  even  with  fires  in 
the  chimneys,  and  with  insufficient  heat  in  ventilating  educts.  If  one  will 
make  an  experiment  in  cold  weather,  when  the  windows  are  closed  and  there 
are  fires  in  some  rooms,  he  will  often  find  that  there  is  cold  air  coming  down 
the  unused  flues,  and  will  feel  the  cold  current  flowing  down  the  stairs  and 
along  the  floors  to  the  fires.  Architects  have  placed  kitchens  in  the  basement 
and  in  the  attic,  and  the  smell  of  cooking,  rises  through  the  house  from  the 
former,  and  usually  descends  from  the  latter  when  the  air  is  light  and  muggy. 

Every  room  should  have  its  distinct  flue ;  if  the  current  is  not  upward  it 
will  probably  be  downward,  affording  a  fresh  supply  of  air  for  ventilation  if 
there  is  an  escape  elsewhere.  A  chimney-flue  may  be  too  large  for  the  purposes 
of  a  fire;  for  most  fires  a  flue  8"  X  8"  is  amply  sufficient,  and  will  serve  for 
ventilation  in  the  common  occupation  of  a  house.  If  the  throat  of  the  chim- 
ney be  made  with  rounded  corners  and  a  diverging  sectional  area,  or  a 
damper  hinged  at  the  bottom,  for  like  effect,  it  should  increase  upward,  and 
prevent  back  draught. 

Small  circular  flues  of  from  6"  to  8"  diameter,  or  of  equivalent  rectangular 
section,  are  now  made  in  concrete  or  stoneware,  which,  as  they  are  smoother 
and  with  less  joints  than  brickwork,  give  greater  velocities  of  current  with  less 
section,  and,  laid  with  care,  changes  in  direction  afford  but  little  obstruction. 
In  an  ordinary  chimney  with  natural  draught  the  velocity  of  ascending  current 
is  about  six  feet  per  second. 

It  is  usual  to  depend  largely  on  windows  for  ventilation,  but  the  space  on 
which  they  open  may  be  too  circumscribed  to  afford  the  requisite  change  of  air, 
or  the  outer  air  itself  may  be  too  hot,  or  too  cold,  or  too  malarial  or  offensive, 
to  make  the  change  of  air  sanitary  or  pleasant.  In  tenement  or  apartment 
houses  care  should  especially  be  taken  that  the  inner  windows  on  different  flats 
open  into  as  large  air-shafts  as  possible,  and  that  these  shafts  should  have  free 
opening  to  the  outer  air  below  and  at  the  top,  without  skylights ;  and  that  the 
floors  should  be  tight,  so  that  the  smells  may  not  pass  from  one  flat  to  another. 
Nothing  more  surely  shows  faults  in  ventilation  than  the  diffusion  of  kitchen 
smells  or  tobacco  smoke.  Distinct  flues  should  be  constructed  for  each  room, 
extending  independently  well  above  the  roof;  and  not  into  an  attic  with  a 
ventilating  louvre,  as  the  air  may  ascend  one  flue  and  descend  another,  and 
not  out  of  the  louvre.  Pipe  flues  may  lead  into  a  single  stack  if  each  branch  is 
given  the  direction  of  the  main  current  at  its  connection,  without  obstructing 
its  flow,  as  in  sewer  branches. 

The  quantity  of  air  taken  into  and  expired  from  the  lungs  by  a  single  indi- 
vidual is  quite  small,  probably  about  14  cubic  feet  on  an  average  per  hour. 
The  usual  gas-burner  delivers  from  4  to  6  cubic  feet  per  hour,  under  a  pressure 
of  1"  and  2"  of  water.  It  will  be  seen,  therefore,  how  small  apertures  are  neces- 
sary to  supply  the  lungs  of  a  person,  if  it  could  be  provided  directly  to  him  and 
taken  away  without  vitiating  other  air.  But,  in  addition,  air  is  vitiated  by 
personal  emanations  and  consumed  by  lights.  These  last  can  readily  be  ar- 


ARCHITECTURAL  CONSTRUCTION. 


637 


ranged  in  connection  with  flues,  not  only  to  remove  all  their  products  of  com- 
bustion, but  also  improve  the  ventilation  of  the  room. 

All  systems  of  ventilation  are  based  on  the  idea  that  so  many  individuals 
within  a  room  and  so  many  lights  burning  vitiate  so  much  air,  and  that  conse- 
quently a  very  large  quantity  of  outer  air  must  be  introduced  to  reduce  the 
percentage  of  vitiation,  and  generally  with  very  little  consideration  as  to  the 
distribution  of  this  air,  although  it  is  in  every  one's  experience  that  the  air  in 
some  portions  may  be  fresh,  in  others  stifling ;  that  in  hospital  wards  there  are 
often  dead  ends  where  the  air  does  not  circulate,  and  where  patients  do  not  as 
a  rule  recover.  The  system  is  to  provide,  somewhere  in  a  room,  air  enough  and 
trust  to  chance  for  its  distribution. 

Some  architects  make  the  educts  at  the  ceiling,  some  at  the  floor,  some  at 
both,  with  registers  to  control  the  openings.  For  sleeping  apartments,  if  there 
is  a  fireplace  this  is  all  that  will  be  necessary ;  if  the  air  goes  up  or  comes  down 
it  does  not  make  draughts  about  the  heads  of  the  occupants. 

To  make  flues  draw,  various  forms  of  chimney-tops  or  cowls  are  adopted. 
The  best  and  simplest  are  the  Emerson  (Fig.  1529)  and  a  modification  of  the 
same  (Fig.  1530) ;  there  are  also  various  forms  . 

of  self-acting  flaps,  turn-cowls,  etc.,  the  prin- 
ciple being  to  take  advantage  of  the  wind  to 
make  a  draught.  With  the  wind  blowing 
across  the  top  of  a  chimney,  a  bit  of  square- 
ended  iron  pipe  extending  above  the  chimney 
will  answer  as  an  expirator,  but  without  a 
wind  the  draught  must  depend  on  circum- 
stances within  the  dwelling  and  artificial 

draught.  When  sufficient  circulation  can  not  be  obtained  from  natural  differ- 
ences of  temperature  in  the  atmosphere,  or  from  winds,  it  is  usual  to  have 
recourse  to  fans  to  force  air  into  or  draw  it  from  a  building,  or  by  heat  applied 
to  the  air  in  flues,  ducts,  or  chambers  in  the  hot-air  furnaces.  Both  the  air 
and  the  heat  are  necessary. 

"  No  systematic  ventilation,  however  well  devised  and  constructed,  however 
extensive  its  supply  of  fresh  air,  however  regularly  or  judiciously  operated,  can 
afford  to  dispense  with  the  repeated  displacement  of  the  air  of  rooms  and  sub- 
stitution of  entirely  fresh  air  through  open  windows  and  doors,  at  times,  during 
all  seasons  of  the  year"  (Briggs). 

Methods  of  Heating. — The  open  fireplace  grate  heats  by  radiation,  com- 
municating heat  to  objects,  which  by  contact  transfer  it  to  the  air.  Persons 
coming  in  contact  with  rays  are  themselves  heated,  while  the  air  around  them 
is  cool  and  invigorating  for  breathing;  the  bright  glow  has  a  cheering  and  ani- 
mating effect  upon  the  system,  somewhat  like  that  of  sunlight.  As  a  ventilator, 
an  open  fire  is  one  of  the  most  important,  drawing  in  air  not  only  for  the  sup- 
port of  combustion,  but  also,  by  the  heat  of  the  fire  and  flue,  making  a  very 
considerable  current  through  the  throat  of  the  chimney  above  the  fire.  From 
this  cause,  although  there  is  a  constant  change  of  air,  yet  there  arises  one  great 
inconvenience  of  disagreeable  draughts,  especially  along  the  floor,  if  the  air- 
supply  be  drawn  directly  from  the  outer  cold  air;  but  in  connection  with  prop- 
erly regulated  furnaces  or  stoves,  the  open  fireplace  becomes  the  most  perfect 


FIG.  1529. 


Fio.  1530. 


638 


ARCHITECTURAL  CONSTRUCTION. 


FIG.  1531. 


means  of  heating  and  ventilation.  As  a  heater  merely,  the  open  grate  in  very 
cold  weather  is  not  satisfactory ;  its  influence  is  only  felt  in  its  immediate 
vicinity,  and  but  from  10  to  15  per  cent,  of  the  heat  of  the  fuel  is  rendered 
available. 

Fig.  1531  represents  an  old  form  of  open  fire  used  in  a  tavern  bar-room  and 
office,  which  answered  admirably  for  heating  and  ventilation,  and  admitted  of 

access  to  many  persons.  It  con- 
sisted of  a  circular  grate  at  the 
level  of  the  floor  in  the  centre  of 
the  room.  In  the  cellar  beneath 
was  an  ash-pit,  a,  in  brickwork, 
with  an  opening,  o,  to  supply  air 
for  the  combustion  of  the  fuel. 
Above  the  grate  was  a  counter- 
weighted  sheet-iron  hood,  7i,  con- 
nected by  a  pipe  with  the  chimney, 
which  could  be  raised  or  lowered 
to  suit  the  required  draught. 
Around  the  grate  was  a  ring-guard 
to  rest  the  feet  on,  and  the  cus- 
tomers ranged  themselves  in  a  circle 
round  the  fire. 

Stoves. — Open  stoves  heat  by  direct  radiation,  and  by  heating  the  air  in  con- 
tact with  them,  and  close  stoves  by  the  latter  way  only ;  as  economical  means 
of  heating  the  latter  are  the  best,  and,  when  properly  arranged,  give  both  a  com- 
fortable and  wholesome  atmosphere.  There  should  be  some  dish  of  water  upon 
them  to  supply  a  constant  evaporation,  sufficient  to  compensate  for  increased 
capacity  of  the  air  for  moisture  due  to  its  increased  heat.  In  the  hall  there  will 
be  no  objection  to  a  close  stove,  letting  it  draw  its  supply  of  air  as  it  best  can ; 
but  in  close  rooms  the  open  stove  is  best,  on  the  plan  of  the  old  Franklin  stove, 
or,  if  a  close  stove,  somewhat  on  the  plan  of  a  furnace,  with  an  outer  air-supply 
for  combustion  and  ventilation. 

Stoves  are  made  of  sizes  adapted  to  large  and  small  rooms,  in  every  style  and 
with  all  possible  appliances  for  comfort,  convenience,  and  economy :  self-feed- 
ers, in  which  the  coal  is  furnished  to  the  fire  in  a  close  chute  from  the  top 
downward  and  in  proportion  to  the  coal  consumption  below ;  base-burners,  in 
which  the  draught  is  reversed  so  that  the  base  becomes  a  portion  of  the  heating 
surface ;  doors  with  mica  panels  around  the  circumference,  by  which  the  fire 
is  seen  with  the  advantage  of  radiant  heat  and  easy  'access  to  the  fire-pot. 
Stoves  are  usually  coal-burners,  but  plain  box-stoves  in  cast  or  sheet  iron  are 
well  adapted  for  wood-burners  and  for  holding  fire  and  retaining  heat.  They 
have  appliances  for  controlling  draught  by  dampers  or  by  opening  the  smoke- 
pipe  or  flue  to  the  room,  thereby  reducing  the  velocity  of  draught,  but  not 
throwing  the  products  of  combustion  outward  into  the  room,  as  is  done  by 
dampers. 

Hot-air  furnaces  are  close  cast-iron  stoves,  inclosed  in  air-chambers  of  brick 
or  metal,  into  which  external  air  is  introduced,  heated,  and  distributed  by  metal 
pipes  to  the  different  rooms  of  a  house.  Furnaces  have  been  of  late  very  much 


ARCHITECTURAL   CONSTRUCTION.  639 

decried,  but  under  proper  regulation  they  are  a  very  cheap,  economical,  and 
even  healthful  means  of  ventilation,  and  warming.  The  heating  surface  should 
be  very  large,  the  pot  thick,  or  even  incased  with  fire-brick,  that  it  may  not  be- 
come too  hot ;  there  should  be  a  plentiful  supply  of  water  in  the  chamber  for 
evaporation,  perhaps  also  beneath  the  opening  of  each  register ;  the  air  supply 
should  always  be  drawn  from  the  outer  air  and  unobjectionable  sources,  through 
ample  and  tight  ducts,  without  any  chance  of  draught  from  the  cellar ;  the  pot 
and  all  joints  in  the  radiator  should  be  perfectly  gas-tight  so  that  nothing  may 
escape  from  the  combustion  into  the  air-chamber.  With  these  provisions  on  a 
sufficient  scale,  and  proper  means  for  distribution  of  the  heated  air  and  escape 
of  foul  air,  almost  any  edifice  may  be  very  well  heated  and  ventilated.  The  air 
should  be  delivered  through  the  floor  or  the  base-board  of  the  room,  and  at  the 
opposite  side  from  the  flue  for  the  escape  of  foul  air,  making  as  thorough  a 
current  as  possible  across  the  room,  and  putting  the  whole  air  in  motion.  In 
dwelling-houses  the  fireplace  will  serve  the  best  means  of  exit ;  in  public  rooms 
distinct  flues  will  have  to  be  made  for  this  purpose,  and  they  should  be  of 
ample  dimensions  and  well  distributed,  with  openings  at  the  floor  and  ceiling 
with  registers,  and  means  should  be  provided  for  heating  the  flues.  An  archi- 
tect, in  laying  out  flues  for  heating  and  ventilation,  should,  both  in  plan  and 
elevation,  fix  the  position  of  hot  and  foul  air  flues,  and  trace  in  the  current  of 
air,  always  keeping  in  mind  that  the  tendency  of  hot  air  is  to  rise ;  he  will  then 
see  that,  if  the  exit-opening  be  directly  above  the  entrance-flue,  the  hot  air  will 
pass  out,  warming  the  room  but  little ;  if  the  exit-opening  be  across  the  room 
and  near  the  ceiling,  the  current  will  be  diagonal,  with  a  cold  corner  beneath, 
where  there  will  be  very  little  circulation  or  warmth.  To  heat  the  exit-flue,  a 
very  simple  way  is  to  make  the  furnace-flue  of  iron,  and  let  it  pass  up  centrally 
through  the  exit-flue ;  but  the  current  may  be  obstructed  by  a  high  wind. 

Fig.  1532  is  one  of  the  many  forms  of  furnaces  which  consist  of  the  most 
approved  stoves,  with  a  large  heating-chamber  above — in  the  figure  of  cast-iron, 
and  composed  of  numerous  flues,  but  very  often  a  drum  of  wrought-iron.  The 
whole  is  inclosed  in  a  brick  chamber ;  in  those  denominated  portable  furnaces 
the  case  is  of  galvanized  iron.  The  figure  contains  the  usual  appliances  for 
feeding  and  clearing  fires,  with  a  check  draught  opening  from  outside  into  the 
smoke  flue,  and  dust  damper  and  flue  so  arranged  that  when  the  grate  is  shaken 
no  ashes  or  dust  comes  into  the  hot-air  chamber.  The  air  is  introduced  at  the 
bottom  of  the  case,  passes  up  and  around  the  stove,  and  out  through  the  ducts 
to  different  parts  of  the  building.  The  water-pan  is  indispensable  to  the  hot- 
air  furnace,  and  should  be  of  capacity  enough  for  a  day's  supply,  or  have  auto- 
matic means  of  keeping  up  the  supply. 

Air  in  winter  is  very  dry,  but  as  its  volume  is  enlarged  by  heat  it  draws  a 
supply  of  moisture  from  everything  with  which  it  comes  in  contact — from  the 
skin  and  lungs,  creating  that  parched  and  feverish  condition  experienced  in 
many  furnace-heated  houses ;  from  furniture  and  woodwork,  snapping  joints 
and  making  unseemly  cracks.  Thus,  taking  the  air  at  10°  and  heating  it  to 
70°,  the  ordinary  temperature  of  our  rooms  requires  about  nine  times  the  mois- 
ture contained  in  the  original  external  atmosphere,  and,  if  heated  to  100°,  as 
most  of  our  hot-air  furnaces  heat  the  air,  it  would  require  about  twenty-three 
times. 


640 


ARCHITECTURAL  CONSTRUCTION. 


The  portable  furnace  is  not  so  economical  as  the  furnace  set  in  brickwork, 
as  more  heat  escapes  through  the  metallic  case.     The  former  are  usually  made 


Fio    1532. 


from  12"  to  36"  diameter  of  pot,  from  2'  to  6'  outside  diameter,  and  5'  to  6' 
height  of  case.  The  brick-set  furnaces  are  from  20"  to  32"  pot,  outside  brick- 
work from  5'  to  6'  square,  walls  4"  thick,  height  6'  to  7'.  It  is  difficult  to  give 
any  rule  for  the  heating  capacity.  A  22"  pot  should  be  adequate  for  the  heat- 
ing of  a  common  25'  X  60'  city  house,  and  the  higher  the  air-duct  the  less  its 
diameter. 

The  total  sectional  area  of  the  hot-air  educts  should  be  equal  to  that  of  the 
fire-pot ;  that  to  the  first  floor  should  be  larger  than  to  the  other  floors,  since 
the  column  of  hot  air  is  shorter  it  will  have  less  velocity.  Air  ducts  that  have 
outlets  at  the  same  level  under  the  same  conditions  should  have  greater  area  if 
the  horizontal  pipes  are  longer.  The  cold-air  duct  should  have  about  the  same 
area  as  the  grate,  and  the  inlet  should  be  above  the  level  of  the  street  or  back 
area  to  avoid  dust.  If  air  ducts  lead  from  both  sides  of  the  building  to  the 
furnace-chamber,  the  current  can  be  controlled  according  to  the  wind,  and  the 
hot  air  distributed  more  equably  through  the  building. 


ARCHITECTURAL  CONSTRUCTION. 


641 


The  Baltimore  heater  (Fig.  1533)  was  the 
earliest  union  of  the  stove  with  tire  furnace. 
A  stove  is  set  in  the  fireplace  of  a  room  in  a 
lower  story,  of  which  the  exterior  or  orna- 
mental half  is  exposed  for  the  heating  of 
this  room,  while  the  inner  half  acts  as  a  fur- 
nace for  the  upper  rooms.  The  smoke-pipe 
passes  up  into  a  chimney  above,  and  is  in- 
closed by  an  air  pipe  or  jacket  to  which  heat 
is  communicated  and  distributed  by  dram 
pipes  and  registers  to  upper  stories. 

Steam  and  hot-water  circulation  are  ap- 
plied to  the  heating  of  buildings  by  means 
of  wrought-  or  cast-iron  pipes  connected 
with  boilers.  In  the  simplest  form,  as  com- 
mon in  workshops  and  factories,  steam  is 
made  to  give  warmth  without  ventilation  by 
direct  radiation  from  wrought-iron  pipes. 
The  general  arrangement  is  by  rows  of  1"  to 
1£"  pipe  hung  against  the  walls  of  the  room, 
or  suspended  from  the  ceilings,  3'  of  1"  pipe 
being  considered  adequate  to  heat  200  cubic 
feet  of  space ;  if  there  are  many  windows  in 
the  room,  or  the  building  is  very  much  ex- 
posed, more  length  should  be  allowed. 

Steam,  as  a  means  of  heating,  is  the  most 
convenient  and  surest  in  its  application  to 
extensive  buildings  and  works.  From  boilers, 
located  at  some  central  point,  steam  can  be 
conveyed  to  points  so  remote  that  in  many 
cities  it  is  a  matter  of  sale  both  for  heating 
and  power  purposes.  The  limits  of  the  ex- 
tension of  steam-pipes  economically  have  not 
yet  been  determined,  but  within  the  range  of 
the  buildings  occupied  by  any  single  textile 
manufacturing  industry  steam-heating  has 
proved  satisfactory,  and  is  almost  universally 
adopted.  For  stores,  warehouses,  large  build- 
ings of  all  sorts,  where  there  are  extensive  or 
numerous  rooms  to  be  heated,  steam  has  been 
long  used,  and  the  appliances  for  its  use  can 
be  as  readily  obtained  in  all  our  cities  and 
large  towns  as  stoves  or  grates.  Steam  is 
used  for  heating  at  either  high  or  low  pres- 
sures ;  tinder  5  or  6  pounds  would  be  consid- 
ered low  pressure.  A  low-pressure  apparatus 
may  draw  direct  from  a  boiler,  or  be  supplied 
from  the  exhaust  of  a  steam-engine ;  if  from 
42 


FIG.  1533. 


642  ARCHITECTURAL  CONSTRUCTION. 

the  latter,  a  certain  amount  of  back  pressure  must  be  put  on  the  engine  to  es- 
tablish a  circulation  in  the  steam-heating  pipes.  But  the  loss  in  power  is  more 
than  repaid  by  the  utilization  of  the  heat  in  the  steam.  If  the  heating-pipes 
are  ample,  they  may  be  arranged  to  act  as  condensers,  reducing  the  back 
pressure  below  atmosphere  and  supplying  low  steam  for  heating. 

In  the  operation  of  heating  by  steam,  the  steam,  in  giving  off  its  latent 
heat  through  the  pipes  to  the  air  of  the  room,  returns  to  water ;  the  apparatus 
would  then  be  nothing  but  pipes  to  convey  the  steam  to  radiators  to  condense 
it,  and  pipes  to  return  the  water  to  the  boiler,  were  it  not  for  air  invariably  in 
water  and  steam.  This  necessitates  a  more  complicated  circulation;  there 
should  be  a  regular  flow  outward  of  steam  from  the  boiler,  and  inward  of  water 
and  steam  to  it,  which  must  be  provided  for  in  the  design  and  by  care  in  con- 
struction that  there  are  no  corners  or  angles  forming  eddies  where  air  can 
lodge,  and  with  provision  for  its  continuous  movement. 

When  hot  water  is  used  for  heating,  there  must  be  circulation  throughout 
the  system ;  the  water  flows  out  from  the  top  of  the  boiler,  gives  out  its  heat, 
and  returns,  practically  of  the  same  bulk,  cold  to  the  bottom  of  the  boiler,  and 
any  radiator  out  of  the  line  of  this  current  is  of  no  use. 

Both  steam  and  water  are  used  for  heating  rooms  either  directly  or  indirectly. 
Direct  heating  is  like  that  of  common  stoves,  without  any  considerations  for 
ventilation ;  indirect  heating,  like  that  of  hot-air  furnaces.  Radiators  are  in- 
closed in  a  box  or  chamber,  into  which  air  is  drawn  or  forced,  and  the.n  dis- 
tributed by  ducts  to  the  rooms  to  be  warmed  and  ventilated.  With  steam  or 
hot-water  heating,  the  metallic  surfaces  brought  in  contact  with  the  air  usually 
range  from  212°  to  250°,  while  the  pot  of  the  air-furnace  is  often  from  900° 
to  1000°.  In  a  sanitary  point  of  view  hot-water  or  low-steam  coils  in  air- 
chambers  are  a  more  surely  healthy  means  of  warming  and  ventilation ;  the 
greatest  objection  is  their  expense,  the  care  requisite  in  attending  them,  and 
the  danger  of  freezing  and  bursting  the  pipes  if  worked  intermittently  in  win- 
ter. In  the  arrangement  it  is  usual  in  dwelling-houses  to  place  the  coils  at 
different  points  in  the  cellar,  as  near  as  possible  beneath  the  rooms  to  be  heated. 
In  public  buildings  frequently  a  very  large  space  in  the  cellar  is  occupied  by 
the  coils,  into  which  the  air  is  forced  by  a  fan,  and  then  distributed  by  flues  or 
ducts  throughout  the  building. 

All  inlet  or  outlet  ventilating  flues  should  be  provided  with  dampers  or 
registers  to  control  the  supply  or  discharge  of  air,  cutting  it  off  when  suffi- 
cient heat  is  secured,  or  retaining  the  warmth  when  ventilation  is  not  re- 
quired. 

Fig.  1534  is  an  elevation  showing  the  usual  arrangement  of  mains,  s  s,  and 
returns,  r  r,  when  the  horizontal  distance  from  the  boiler  is  small  and  the 
risers  few.  The  inclination  of  the  mains  is  toward  the  boiler,  and  their  con- 
densed water  returns  by  them  to  the  boiler. 

Fig.  1535  is  the  better  practice,  and  necessary  if  the  steam  is  higli  pressure, 
the  mains  extended,  and  the  branches  numerous.  The  inclination  of  the  mains, 
s  s,  is  from  the  boiler,  and  the  condensed  water  flows  down  to  the  lowest  angle, 
where  it  is  connected  with  the  return,  r,  and  is  by  this  brought  back  to  the 
boiler. 

The  size  of  the  boiler  for  a  steam-heating  apparatus  is  based  on  the  amount 


ARCHITECTURAL  CONSTRUCTION. 


643 


of  radiating  surface,  which  must  include  that  of  the  steam- mains  and  of  the 
returns. 

In  Fig.  1535  the  steam  riser,  s,  descends  from  the  boiler  to  the  last  riser, 
which  is  connected  at  this  point  with  the  return,  and  this  should  obtain  in  all 
forms  of  steam-heating,  keeping  the  flow  of  condensed  water  as  far  as  possible 
in  the  direction  of  the  flow  of 
the    steam,    and    removing    it 
from  the  steam-pipes. 

Figs.  1536  to  1538  are  com- 
mon forms  of  distributing  steam 
and  return  pipes  of  different 
systems  of  heating. 

In  Fig.  1536  the  riser  pro- 
ceeds from  the  boiler  and  leads 
directly  to  the  highest  point  of 

service.     Provision  is  made  for  the  condensation  in  the  pipe  by  a  direct  con- 
nection. 

In  Fig.  1537  the  risers  are  as  in  Fig.  1536,  but  there  are  separate  returns 
for  each  radiator. 

In  Fig.  1538  the  main  riser  is  carried  directly  to  the  highest  story  to  be 
warmed,  and  the  distributing  mains  are  led  from  it  with  a  pitch  from  the  riser, 
and  the  descending  pipes  conveying  the  steam  to  the  different  radiators  and 
the  condensed  water  to  the  hot  well  and  boiler.  This  should  be  the  quietest  cir- 


Fio.  1534. 


FIG.  1535. 


culation,  as  the  steam,  except  in  the  main  riser,  does  not  interfere  with  the  flow 
of  the  condensed  water. 

Valves  are  introduced  in  the  mains  or  returns  where  necessity  or  conven- 
ience may  require  the  shutting  off  of  any  of  the  radiators  or  mains,  and  air- 
cocks  to  relieve  stagnation  in  angles  or  pockets  where  circulation  must  be 
established  before  the  whole  of  the  heating  surface  can  be  utilized. 

The  amount  of  radiating  surface  depends  on  the  cubic  feet  of  air  to  be 
heated  and  the  number  of  degrees  to  which  it  is  to  be  heated.  These  are  de- 
termined from  the  outer  exposure  of  the  building  or  room,  its  plan,  material, 
and  construction,  whether  there  is  more  or  less  window  surface,  and  its  occu- 
pancy ;  whether  for  living  rooms  or  for  business,  sedentary  or  active ;  in  the 
store  the  bookkeeper  needs  much  more  heat  than  the  salesman. 

On  an  average,  100  to  150  cubic  feet  of  room  space  can  be  heated  from  0° 
to  70°  by  1  square  foot  of  radiating  surface — say  3'  of  I"  pipe.  This  covers  an 
average  glass  exposure  which  may  be  taken,  according  to  Mr.  Briggs,  at  100 
cubic  feet  of  space  to  each  square  foot  of  glass. 

The  effect  of  glass  under  air  exposure  is  to  be  noticed  in  the  different  con- 


644 


ARCHITECTURAL  CONSTRUCTION. 


FIG.  1536. 


FIG.  1538. 


ARCHITECTURAL  CONSTRUCTION. 


645 


ditions  experienced  in  cars  while  in  motion  and  when  stopped  in  cold  weather, 
and  the  advantages  of  double  windows  in  these  conveyances. 

Proportions  of  mains  to  radiating  surface :  one  of  1"  diameter  will  serve  for 
75  feet  of  radiating  surface,  including  that  of  the  mains.  One  and  a  half  inch 
diameter  for  250  square  feet,  2"  diameter  for  500  square  feet,  3"  diameter  for 
1,250  square  feet,  4"  diameter  for  2,500  square  feet. 

For  the  returns,  one  size  less  than  that  of  the  steam  mains  is  the  rule ;  thus, 
a  f  "  return  for  a  1"  pipe,  but  no  pipe  of  less  diameter  than  f  "  is  used ;  for  a 
2£"  steam  a  2"  return,  and  a  larger  than  2"  is  seldom  used.  It  may  not  be 
always  practicable  to  return  the  condensed  water,  as  shown  in  the  figures 
above,  by  gravitation,  but  there  are  various  forms  of  receivers  or  traps  in  which 
the  water  is  collected  and  returned  by  hand  or  automatically  pumping  to  the 
boiler. 

Fig.  1539  is  a  float  trap,  in  which p  is  the  pot  with  a  tight  cover, /an  open 
float  sliding  on  the  stem,  s,  at  the  foot  of  which  is  a  valve,  v ;  the  condensed 
water  flows  in  through  the  inlet,  i,  raises 
the  float,  /,  and  closes  the  valve,  v ;  event- 
ually the  condensed  water  overflows  into/ 
till  it  sinks  and  opens  the  valve,  v,  and  the 
condensed  water  flows  out  through  the 
valve,  v,  under  the  pressure  of  steam  at  the 
inlet ;  when  blown  out,  /  rises  and  v  closes 
for  another  charge.  The  condensed  water 
is  either  wasted  or  returned  to  the  boiler  by 
a  pump.  The  hand  valve,  A,  is  an  inde- 
pendent relief  to  the  trap. 

There  are  traps  which  return  the  con- 
densed water  directly  to  the  boiler,  in 
which  the  condensed  water  is  forced  into 
a  chamber  above  the  level  of  the  water  in  the  boiler  and  the  steam  pressure 
then  brought  upon  the  chamber,  and  the  water  flows  down  from  it  into  the 
boiler. 

Heating  by  indirect  radiation  is  like  that  by  hot-air  heaters ;  the  heaters 
are  inclosed  in  chambers  to  which  cold  air  is  introduced  and  the  heated  air 
conveyed  into  different  rooms  by  pipes.  It  is  usual  to  place  the  hot-air  cham- 
bers in  the  cellar  and  basement,  as  directly  beneath  the  room  to  be  heated  as 
possible,  and  extending  the  cold-air  duct  to  the  hot  chamber.  The  chamber  is 
usually  made  of  galvanized  iron  in  a  wooden  box,  and  often  suspended  from 
the  ceiling  of  the  cellar.  Where  the  heating  is  indirect,  as  there  are  more  cubic 
feet  of  air  to  be  heated,  the  radiating  surface  is  to  be  increased,  usually  to  about 
three  times  that  of  the  direct  heating. 

Heating  by  Hot  Water. — The  principle  of  it  is  based  on  the  fact  that  water 
when  heated  becomes  of  greater  volume  and  less  density,  and  rises;  coming  in 
contact  with  cooler  surfaces,  it  loses  its  heat  and  descends ;  the  water  circulates 
by  the  addition  and  reduction  of  heat.  The  possibility  of  a  rapid  and  thorough 
circulation  gives  efficiency  to  the  apparatus.  One  of  its  greatest  advantages  is, 
that  when  necessary  the  circulation  will  continue  with  a  water  temperature  at 
an  extremely  low  point,  say  110°,  and  a  proportionate  consumption  of  coal. 


FIG.  1539. 


646 


ARCHITECTURAL  CONSTRUCTION. 


Fig.  1540  exhibits  the  application  of  hot  water  to  the  heating  of  a  building. 
The  boiler  shown  will  serve  as  an  illustration  of  the  water  circulation ;  it  is  of 

cast-iron,  of  which  there  are  numerous 
forms  in  this  material,  as  well  as  wrought- 
iron. 

The  main  rises  directly  to  the  top, 
where  there  must  be  an  expansion  cham- 
ber, C,  in  connection  with  it,  to  provide 
for  the  increase  of  volume  in  the  water 
due  to  the  heat.  It  is  usual  to  have  this 
chamber  open  at  the  top,  and  water  may 
be  poured  down  through  the  funnel  noz- 
zle. A  glass  at  the  side  shows  the  level 
of  the  water. 

The  mains  are  of  a  little  larger  diame- 
ter than  in  steam,  and  reduced  in  size  as 
the  current  is  distributed  into  the  radia- 
tors on  which  valves  are  placed  to  control 
the  current ;  these  valves  should  be  gates, 
to  provide  for  full  water-way.  The  re- 
turns are  to  be  of  the  same  diameter  as 
the  rising  mains.  The  surface  of  the  ra- 
diator should  be  greater  than  for  steam, 
as  the  temperature  of  the  water  is  less. 
When  the  radiators  are  vertical,  as  shown 
in  the  first  and  second  story,  there  must 
be  air-cocks,  a,  as  shown,  for  air  effectu- 
ally cuts  off  circulation.  Hot-water  cir- 
culation can  be  used  for  direct  or  indi- 
rect heating  with  like  appliances  as  for 
steam. 

Boilers  are  of  such  varied  forms  and 
proportions  to  the  area  of  grate  that  it  is 
impossible  to  determine  the  value  of  the 
heating  surface  except  by  actual  test.  As 
a  unit  it  is  better  to  refer  to  the  area  of 
grate  as  a  measure  of  the  capacity  of  the 
boiler,  the  evaporation  of  water  by  the 
combustion  of  pounds  of  coal  being  the 
standard  of  efficiency. 

Under  the  head  of  chimneys  it  is 
stated  that  two  square  inches  of  flue  is 
sufficient  for  the  combustion  of  each 
pound  of  coal  per  hour.  This  has  been 

FIG.  1540. 

found  in  excess  for  a  5-foot  diam.  chimney, 

where  provision  has  been  made  for  avoiding  eddies  by  the  rounding  of  corners, 
and  where  there  is  a  good  natural  draught,  but  there  must  be  a  factor  of  safety 
when  care  has  not  been  taken  in  the  location  and  construction.  For  the  small 


ARCHITECTURAL  CONSTRUCTION. 


647 


flues  connected  with  the  heating  of  common  buildings  this  rule  will  not  obtain ; 
flues  for  this  purpose  should  be  at  least  8"  X  12".  But  as  a  large  area  of  chim- 
ney flue  does  not  interfere  with  the  draught,  and  as  the  necessities  of  chimneys  usu- 
ally increase  by  the  extension 
of  works,  it  is  safer  to  make 
the  flue  larger,  but  without 
omitting  care  in  construc- 
tion. 

The  combustion  of  coal 
on  small  grates  may  be  taken 
at  4  to  6  pounds  of  anthra- 
cite coal  per  square  foot  of 
surface ;  on  grates  4'  X  4',  8 
pounds ;  on  grates  of  larger  area,  10  pounds,  which  would  be  a  fair  average  of 
this  class,  and  the  vents  of  large  chimneys  may  be  calculated  on  this  data, 
although  the  draught  under  equal  conditions  is  in  favour  of  the  chimneys  of 
large  diameter. 

With  forced  draught  by  fans,  ejectors,  or,  as  in  locomotives,  by  the  exhaust, 
very  large  quantities  of  coal  can  be  consumed  on  grates. 

The  air-ducts  from  boiler»and  heaters  for  smaller  and  private  dwellings  have 
a  natural  draught ;  but  for  schoolhouses,  churches,  and  other  public  edifices  a 
forced  draught'  is  usual,  is  under  surer  control,  and  with  adequate  indirect 
heaters  the  quantity  of  air  can  be  readily  furnished.  It  is  common  to  intro- 
duce local  fans  driven  by  electric  motors  to  supply  air  at  varied  points  and  in 
quantities  suited  to  the  needs  of  the  position.  By  the  use  of  dampers  or  valves 
air  of  any  temperature,  from  that  of  the  outside  to  that  of  the  radiator,  may  be 
distributed. 

In  Figs.  1536,  1537, 1538,  and  1540  illustrations  are  given  of  the  usual  radi- 
ators:  the  wall  coil  with  return  bends,  which  may  be  more  or  less  open  (with 
branch  Ts  and  multiple  coils  they  are  called  box  coils),  wall  coils  with  branch 


FIG.  1542. 


FIG.  1543. 


648 


ARCHITECTURAL  CONSTRUCTION. 


Ts,  vertical  tube  radiators  with  box  bases  of  effective  heating  surface,  cast-iron 

radiators  of  similar  design,  ornamented  and  of  great  variety.  Indirect  radia- 
tors, Fig.  1541,  in  cast-iron  with 
pin  or  iron  projections,  and 
wrought-iron  pipes  covered  with 
compound  coils  of  wrought-iron 
ribbons,  increase  heating  surface. 
In  measuring  the  surface  of  cir- 
culating coils  include  the  lengths 
of  angles  and  all  fittings ;  in  the 
vertical  radiators  include  the  base. 
Figs.  1542  and  1543  are  the 
end  and  side  elevation  of  a  radia- 
tor for  live  or  exhaust  steam,  in- 
closed in  a  case  for  indirect  heat- 
ing. Air  is  forced  through  the 
case  into  the  building  by  a  fan. 

By  the  location  of  the  radia- 

FIQ  1544  tors  in  an   independent   chamber 

and  ft  valve,  Fig.  1544,  the  air  may 

be  forced  through  it  hot,  or  mixed  with  cold  air  or  without  connection  with  the 

chamber  cold. 


FIG.  1545. 


ARCHITECTURAL  CONSTRUCTION. 


649 


Fig.  1545  is  the  plan  of  a  portion  of  a  large  building  heated  by  steam.  B  B 
are  two  boilers,  either  of  which  would  be  sufficient  for  the  purpose ;  the  steam 
mains  are  shown  by  black  lines  following  those  of  the  building,  with  the  sizes 
marked  upon  them ;  the  risers  by  inclined  lines,  with  the  square  foot  of  radiat- 
ing surface  on  each  story  marked.  This  is  a  very  convenient  form  of  drawing, 
explanatory  of  the  system.  It  is  usual  to  draw  the  steam  mains  and  risers  in 
red  and  the  returns  in  blue,  with  the  diameters  on  each. 

Plumbing. — The  conveniences  for  comfort  in  modern  buildings  require  the 
introduction  of  water  and  its  removal.  Most  cities  have  water-supplies  and  a 
system  of  sewers,  and  the  plumber  makes  the  connections  with  both.  In  the 
country,  where  there  are  not  these  public  conveniences,  their  places  are  largely 
supplied  by  pumps  and  elevated  tanks  and  by  cesspools.  The  quantity  used  in 
each  household  varies  with  the  wants  and  habits  of  the  occupants.  An  average 
bath  will  take  25  gallons ;  each  use  of  a  water-closet  from  1  to  3  gallons.  A 
wash-tub  will  hold  from  10  to  20  gallons.  If  the  water  is  to  be  pumped  by 
hand,  from  7  to  10  gallons  may  be  reckoned  as  the  daily  use  by  each  person ;  if 
from  aqueduct,  30  to  50  gallons  is  ample.  With  the  popular  style  of  water- 
closets  the  use  of  water  has  been  largely  increased,  and  by  carelessness  in  the 
selection  and  use  of  fixtures  the  waste  has  become  greater. 

The  regulation  size  of  taps  for  city  mains  is  from  •£"  to  1",  and  the  pipes 


FIG.  1546. 


650 


ARCHITECTURAL  CONSTRUCTION. 


leading  into  the  house  from  f "  to  1"  diameter.  The  pipes  are  usually  of  lead, 
as  most  waters  are  not  affected  sensibly  by  lead,  if  the  pipes  are  always  kept 
full,  but  water  which  has  stood  for  some  time  in  the  pipe  should  not  be  used 
for  drinking,  and  lead-lined  tanks  should  be  coated  with  asphalt  varnish.  In 
some  cases  block-tin  pipes  are  used ;  or  iron,  galvanized,  or  coated  with  some 
preparation  of  asphalt,  or  glass-lined. 

The  soil  or  house-sewer  pipe  connections  with  the  main  sewer  or  cesspool 
are  usually  vitrified  stoneware  pipe,  from  4"  to  6"  diameter,  the  large  size  is 
for  the  discharge  of  the  sewage,  and  the  rainfall  from  the  roof.  Within  the 
house  the  pipe  is  either  of  stoneware  or  cast-iron ;  invariably  of  the  latter  if 
the  pipe  is  exposed.  The  rising  pipe  to  the  roof  is  here,  also,  usually  of  cast- 
iron,  and  4"  diameter  may  be  considered  ample  for  a  common  house ;  branches 
as  small  as  2"  are  usually  of  lead. 

Fig.  1546  is  the  perspective  of  a  kitchen-range  boiler  and  sink :  c  is  the 
cold-water  pipe  leading  to  the  sink  and  to  the  boiler ;  it  enters  the  top  of  the 
boiler,  and  is  led  down  nearly  to  the  bottom.  The  hot  water  is  drawn  from 
the  top,  through  the  pipe  A,  is  led  down  to  the  sink  and  up 
for  distribution  through  the  house.  The  water  is  heated  in* 
the  boiler  by  the  water-back,  which  consists  of  a  closed-box 
casting,  forming  the  back  of  the  range,  r,  with  two  connec- 
tions with  the  boiler,  the  one  at  the  bottom  introducing  cold 
water,  and  \the  one  at  the  extreme  top  discharging  it  heated 
into  the  boiler  above,  the  circulation  taking  place  as  in  hot- 
water  heating ;  the  water  flows  through  the  pipe,  I,  is  con- 
nected with  the  lower  part  of  the  water-back,  and  returns  by 
the  pipe,  w,  from  the  top  of  the  water-back  to  a  higher  point 
in  the  boiler;  b  is  the  blow-off  pipe.  Stoves  are  arranged 
with  water-backs. 

The  pipes,  a  a,  are  carried  above  the  draw-cocks  over  the 
sink,  forming  air-chambers,  to  cushion  the  blow  of  the  water- 
hammer  when  the  cocks  are  shut  quickly.  Beneath  the  sink 
there  is  a  trapped  connection  with  the  sewer-pipe. 

Fig.  1547  is  the  elevation  of  a  galvanized-iron  boiler,  but 
those  in  general  use  here  are  of  copper. 

Fig.  1548  is  the  perspective  drawing  of  a  cast-iron  sink, 


B; 

Fiu.  1547. 


FIG.  1548. 


of  the  usual  form  and  material.  They  are  to  be  obtained  of  all  suitable  dimen- 
sions, rectangular,  from  16"  X  12"  X  5"  deep,  to  96"  X  24"  X  10"  deep;  also, 
half-circle  and  corner  sinks,  and  deep  and  slop  sinks. 


ARCHITECTURAL  CONSTRUCTION. 


651 


In  the  kitchen,  or  a  laundry^room  adjacent,  tubs  are  set  for  washing,  with 
hot  and  cold  water  service.  The  water-pipe  connections  are  usually  £",  the 
waste  connections  2''.  The  tubs  themselves  are  mostly  of  wood,  but  there  are 
many  of  cast-iron  (Fig.  1549),  galvanized  or  enamelled,  of  slate,  of  earthen- 
ware, and  of  soapstone. 

In  the  butler's  pantry  there  is  usually  a  sink  of  planished  tinned-copper, 
with  hot  and  cold  water  connections.  In  the  chambers  and  dressing-rooms 


FIG.  1549. 

wash-basins,  usually  of  porcelain  or  porcelain-lined  cast-iron,  are  set  with  like 
connections.  The  sizes  of  basins  vary  from  12"  to  18"  outside  diameters. 

Fig.  looO  shows  the  usual  form  of  setting  of  a  wash-basin  in  a  countersunk 
marble  slab,  with  a  back  of  the  same  material ;  swing  faucets  for  the  supply  of 
hot  and  cold  water;  self-closing  faucets  prevent  waste,  and  compression 
cocks  are  best  suited  for  high  pressures.  The  waste  is  closed  by  a  metal  or 
rubber  plug,  attached  to  a 
chain,  with  the  other  end 
fastened  to  a  pin  in  the 
marble  slab.  The  sides 
are  inclosed  with  wood, 
forming  a  closet  beneath 
the  basin,  with  usually 
small  drawers  for  towels 
at  each  side  of  the  closet. 
It  is  cleaner  and  neater 
to  support  the  slabs  and 

basins  by  a  metal  frame  and  posts  or  brackets,  with  the  traps  and  pipes  ex- 
posed. A  later  form  of  wash-basin  is  an  oval  (largest  size  19"  X  15",  outside 
measure),  which  admits  of  the  washing  of  the  head  and  shoulders,  with  a 
standard  waste  or  hollow  pipe  overflow,  preventing  offence  in  the  oxidation  of 
the  soapy  waste  which  obtains  from  pipes,  formed  on  the  basin,  and  which  can 


FIG.  1550. 


652 


ARCHITECTURAL  CONSTRUCTION. 


not  be  readily  cleaned.  Fig.  1551  is  a  plan,  and  Fig.  1552  a  section,  of  a  cast- 
iron  bath-tub  porcelain-lined  ;  there  are  cocks  for  hot  and  cold  water ;  for  the 
discharge  there  is  a  standard  waste,  which  can  be  taken  out  entirely,  but  there 
is  often  a  common  plug  and  an  overflow  by  an  independent  pipe. 

The  dimensions  of  tubs  are  varied  to  suit  the  rooms  in  which  they  are  to 
be  placed  ;  the  largest  are  6'  X  24",  18"  and  19"  deep.  They  may  be  reduced 
to  3'  6"  in  length,  but  should  then  be  made  deeper.  Tubs  of  porcelain  are  set 
up  on  blocks ;  porcelain-lined,  on  cast-iron  legs,  about  6"  in  height.  •  Bath- 
tubs are  more  generally  made  of  planished  tinned-copper  in  a  wooden  box  for 
support,  and  inclosed  by  wooden  panels.  In  most  bath-rooms  there  are  basin 


FIG.  1552. 


FIG.  1551. 


and  water-closet — often  a  foot-bath  and  bidet-pan — but  it  is  preferable  to  make 
the  water-closet  a  separate  room,  distinct,  with  its  own  water  and  sewer-service 
and  means  of  ventilation. 

The  construction  of  one  form  of  water-closet,  with  all  the  modern  appli- 
ances for  the  removal  of  soil  and  for  ventilation,  will  be  understood  from  the 
section  (Fig.  1553).  The  seat  is  not  shown,  but  is  just  above  the  basin,  B, 
which  contains  some  water  to  receive  the  defecations,  to  prevent  the  soil  attach- 
ing to  the  side  of  the  basin,  and  in  a  measure  to  check  its  offensive  smell.  T 
is  the  trap  or  water-seal  which  prevents  the  smell  from  the  soil-pipe  S  passing 
up  through  the  basin.  The  water-discharge  from  the  pipe  W  is  through  a  rim- 
flush  around  the  edge  of  the  basin.  The  sudden  discharge  washes  out  the  basin 
B  into  the  trap  T,  which  is  also  cleaned  by  the  rush  of  water.  The  soil-pipe  S 
extends  up  through  the  roof,  and  may  or  may  not  also  serve  as  a  rain-leader. 
A  sudden  flow  of  water  down  the  soil-pipe  often  acts  as  an  ejector  to  draw  the 
water  out  of  the  trap  T,  and  break  the  water-seal ;  to  prevent  this  there  is  a 
back-air  connection,  A,  leading  also  to  the  top  of  the  house.  But  as  the  offence 
of  a  water-closet  is  largely  due  to  its  recent  use,  and  as  smell  once  getting  into 
the  room  is  with  difficulty  removed,  but  generally  diffused,  there  is  a  ventilat- 
ing-pipe,  V,  connecting  the  basin  B  with  a  ventilating-flue ;  this  is  the  most 
important  part  of  the  apparatus ;  connected  with  a  chamber  commode,  it  would 
remove  all  smell,  and  if  there  were  no  trap  to  the  soil-pipe,  or  were  the  water- 
seal  broken,  it  would  still  prevent  any  offensive  smell  from  penetrating  the 
house.  If  the  soil-pipe  be  made  also  a  ventilating-pipe,  as  is  frequently  done 
by  its  connection  with  the  hot-air  flue,  then  the  trap  and  pipes  A  and  V  are 
unnecessary. 

Many  sanitary  engineers  object  to  the  back-air  pipe  as  imperfect  in  its 


ARCHITECTURAL  CONSTRUCTION. 


653 


action  (a  sudden  suction  will  draw  the  water  out  of  the  trap  before  the  suction 
can  be  relieved  through  a  back-air  pipe),  that  it  is  expensive,  and  that  there  are 
many  better  ways  of  protecting  the  seats  by  anti-siphon  traps  or  diverging  Y- 


FIG.  1553. 


FIG.  1554. 


W 


branches.  In  Fig.  1554  is  shown  a  branch  by  which  the  flow  from  the  up- 
per pipe  dripping  into  the  .lower  trap  preserves  the  water  seal.  As  the  water- 
closet  must  be  ventilated,  it  is  better  to  have  a  regular  flue  in  the  wall  with 
an  induced  ventilation  by  heat  in  some  form,  or  electric  fans,  and  air  supplied 
from  outer  rooms  or  windows. 

Fig.  1555  is  an  elevation  of  the  simplest 
form  of  closet — the  hopper-closet — and  in  many 
respects  the  best.  A  standard  waste  in  the  cis- 
tern c  will  serve  both  for  the  disk- valve  and  the 
overflow.  A  rim-flush  is  supplied  through  the 
pipe  W,  controlled  by  a  plain  cock  or  by  a  han- 
dle A,  as  in  Fig.  1556,  lifts  the  disk  valve,  clos- 
ing automatically ;  or  by  cock  connecting  with 
the  seat,  which,  when  down  for  occupancy, 
opens  the  flush,  and,  as  the  sitter  rises,  the 
counterbalanced  lid  rises  and  closes  the  cock. 

The  service  box  beneath  the  cistern  continues  a  temporary  flow  after  the  valve 
is  dropped.  V  is  a  ventilator  branch. 

Fig.  1557  is  the  section  of  a  pan-closet,  for  many  years  the  most  popular 


FIG.  1555. 


654: 


ARCHITECTURAL  CONSTRUCTION. 


closet.     The  copper  pan,  when  shut,  cuts  off  the  view  of  the  trap  below  and 
any  odour  from  it ;  with  a  small  flow  of  water  the  basin  is  readily  kept  clean, 

but  soil  is  apt  to  lodge  in  the  iron  re- 
ceiver, and  the  odour  to  arise  from  it 
when  the  pan  is  down.  There  is  an 
annular  ventilating-tube  beneath  the 
seat,  with  an  air-shaft  attached,  but  of 


FIG.  1556. 


FIG.  1558. 


SIPHON  JET  CLOSE.T. 


altogether  inadequate  dimension  for  the  purpose,  as  may  be  said  of  all  such 
vents  attached  to  water-closets.  There  is  also  the  air- vent  to  prevent  the  water 
being  drawn  from  the  trap.  No  water  connections  are  shown  in  the  figure. 

If  the  2"  vent  be  removed,  and  the'  air- 
draught  pipe  be  enlarged  and  connected 
with  a  positive  draught-flue,  all  offence 
from  either  recent  or  former  use  of  the 
closet  will  be  cut  off. 

Fig.  1558  is  the  section  of  a  flap-closet, 
in  which  a  flap-valve  supplies  the  place  of 
a  pan. 

Fig.  1559  is  the  section  of  a  siphon-jet 
closet.  In  addition  to  the  fan  flush,  /, 
into  the  basin,  it  has  a  jet-pipe,  /,  at  its 

bottom,  inducing  a  current  in  the  direction  of  the  inclined  leg  of  the  trap,  and 
by  flush  and  jet  the  water  is  siphoned  from  the  basin. 


FlG.  1559. 


ARCHITECTURAL   CONSTRUCTION. 


655 


Traps  are  varied  in  their  form,  but  all  to  cut  off  the  air-connection  of  the 
soil-pipe  with  the  room  in  whicli  the  appliance  is  placed.  The  smaller  traps 
are  invariably  lead,  the  larger  cast-iron. 

Figs.  1560  to  1567  represent  the  usual  forms  of  lead  traps.  There  are 
screw-plugs  at  the  bottom  of  the  traps,  which  can  be  taken  out  to  remove 


s. 


SHORT  BEND.      LONG  BEND. 


Fia.  1560. 


Fia.  1561.    FIG.  1562. 


FIG.  1563. 


FIG.  1564. 


FIG.  1565. 


FIG.  156 


FIG.  1567. 


any  obstruction.  As  the  water  may  be  drawn  out  of  any  trap  by  the  passage 
of  water  down  the  pipe  with  which  it  is  connected,  air-vents,  as  already  de- 
scribed, in  the  water-closet  trap,  are  put  on  these  small  traps.  But  if  upper 
waste  pipes  be  inserted,  as  in  Figs.  1560  and  1561,  at  a  a,  and  shown  in  sec- 
tion (Fig.  1554,  p.  653),  loss  of  seal  is  cut  off. 

Figs.  1568  and  1569  are  cast-iron  traps,  with  a  cap  that  may  be  removed  to 
clean  the  trap,  or  the  aperture  may  be  used  for  air- vent  connection. 

Fig.  1570  is  the  section  of  a  bell-trap,  used  on  sinks,  with  a  strainer,  S, 
above  it. 

Fig.  1571  is  a  plate  with  plug,  for  the  bottom  of  basins  and  bath-tubs. 


S-TRAP. 


TRAP  WITH  SIDE  OUTLET. 


FIG.  1568. 


FIG.  1569. 


FIG.  ISI'O. 


FIG  1571. 


Figs.  1572  to  1577  are  common  cast-iron  bends  or  angles. 

Figs.  1578  to  1583  are  cast-iron  branches.  The  T-branch  and  cross 
are  objectionable,  as  the  flows  from  the  branches  and  mains  are  at  right  angles, 
and  mutually  obstructive ;  whereas  in  the  Y,  especially  in  the  full  Y,  the  flows 
are  at  acute  angles  with  each  other,  and  the  currents  converge.  Similar  fittings 
are  used  for  water,  but  they  are  much  heavier. 


QUARTER 
BEND. 


DOUBLE  HUB, 
QUARTER  BEND. 


FIG.  1572. 


SIXTH 
BEND. 


FIG.  1573. 


FIG.  1574. 


FIG.  1575. 


FIG.  1576. 


FIG.  1577. 


Most  water-closet  basins  are  inclosed  by  a  lidded  seat  and  riser,  but  the  less 
wood-work  about  a  basin  the  better.  The  seat  is  generally  hung  with  hinges 
of  brass  or  composition,  so  that  it  can  be  raised,  and  the  basin  makes  the 


656 


ARCHITECTURAL  CONSTRUCTION. 


T-BBANCH. 


CROSS-HEAD. 


HALF 
Y-BRANCH.        Y-BRANOH. 


DOUBLE  DOUBLE  HALF 

Y-BRANCH.  Y-BRANCU. 


FIG.  1578. 


FIG.  1579. 


FIG.  1580. 


FIG.  1581. 


FIG.  1582. 


FIG.  1583. 


FIG.  1584. 


best  urinal  for  men,  the  upper  edge  of  the  basin  being  covered  with  an  earthen- 
ware tray,  sloping  toward  the  basin.     Instead  of  the  tray,  if  the  rim  of  the 

basin  be  made  square,  of  sufficient  width  to 
support  the  seat,  sloping  to  the  basin,  and 
overhanging,  it  will  make  the  better  urinal, 
and  afford  space  for  an  adequate  ventilating 
pipe. 

Urinals,  of  which  one  form  for  males  is 
shown  (Fig.  1584),  are  often  used  in  public 
buildings,  and  in  open  stalls.  Although  they 
have  water  connections,  w,  and  a  rim  flush, 
it  is  almost  impossible  to  keep  them  sweet ;  a 
cake  of  carbolic  soap  is  often  put  in  the  ba- 
sin, but  the  most  effectual  means  adopted  on 
many  railway-cars  is  a  piece  of  ice. 

As  direct  supply  from  the  service  is  uncer- 
tain if  there  is  a  draught  in  another  quarter, 
it  is  now  common  to  have  small  cisterns  for 
closets,  shown  in  Fig.  1556.  The  water  from 
the  service  pipe  is  discharged  well  below  the 

surface  overflow,  generally  through  a  pipe  attached  to  the  goose-neck  on  the 
ball-valve  pipe,  to  avoid  the  noise  of  running  water. 

Lighting  is  one  of  the  present  necessities  of  civilization,  and  for  a  great 
many  years  gas  has  been  used  for  lighting  in  domestic  and  industrial  buildings. 
Gas  fittings  are  in  all  forms — brackets  and  pendants,  wide  branches  with 
fixed,  swing,  and  slide  joints ;  and  burners  in  great  variety — bat  wings,  fish- 
tail tips,  and  Argand  burners,  and  many  patents  for  increased  light  and  econ- 
omy of  consumption. 

Service  mains  are  seldom  placed  in  buildings  less  than  f "  diameter  for  10 
burners  and  100  feet  of  pipe,  to  If"  and  200  feet  length. 

Electric  lighting,  although  not  superseding  gas  for  common  use,  is  now 
largely  employed  in  industrial  operations,  and  for  all  shows  and  brilliant  illu- 
minations. 

The  three  accompanying  drawings  (Fig.  1584,  A,  B,  C)  illustrate  three 
methods  of  wiring  for  electric  lighting. 

Fig.  A  is  a  series  installation.  The  lamps  are  in  series  and  dynamo  series 
wound.  The  wires  may  be  led  in  any  direction,  care  being  taken  to  insulate 
them  properly  and  avoid  proximity  to  inflammable  substances.  The  current 
leaves  the  dynamo  at  +,  passes  through  each  lamp,  and  returns  to  the  dynamo 


ARCHITECTURAL  CONSTRUCTION. 


657 


at  — .  This  current  is  maintained  at  a  constant  strength  required  by  the  con- 
struction of  each  style  of  lamp,  and  determined  by  the  E.  M.  F.  of  the  dynamo, 
and  the  full  resistance  of  the  entire  circuit,  including  the  dynamo,  the  lamps, 
and  the  conducting  wires.  The  strength  of  the  current  required  varies  greatly, 
ranging  from  ten  to  twenty  amperes  for  series  installations  in  the  various  lead- 
ing arc-light  systems  for  which  this  method  is  used. 

Fig.  B. — One  method  of  wiring  is  shown  for  incandescent  electric  lighting, 
and  is  known  as  the  multiple-series  installation.  Between  two  main  conductors 
extending  from  the  dynamo  are  placed,  in  parallel,  several  short  lines  connect- 


rn r 


FIG.  1584. 


ing  with  the  lamps,  the  current  being  thus  divided  among  the  lamps  in  pro- 
portion to  their  number  and  resistance,  while  in  the  series  system  the  entire 
current  passes  through  every  lamp.  This  method  is  common  to  both  the 
direct  and  alternating  current  system,  and  is  convenient  for  lighting  a  large 
room  or  hall  where  many  lamps  are  required  at  one  time.  A  simpler  and 
better  arrangement  for  most  purposes  is  the  parallel  system,  in  which  two 
mains  are  led  from  the  dynamo,  and  each  lamp  is  placed  on  a  separate  branch 
between  the  mains,  so  that  it  can  be  lighted  or  extinguished  without  inter- 
fering with  the  remaining  lamps. 

Fig.  C  shows  the  Edison  three-wire  system  for  incandescent  lighting.  Two 
dynamos  are  joined  in  series  as  shown.  Each  lamp  has  the  same  advantage  of 
independent  connection  with  the  dynamo  as  in  the  two- wire  system,  shown  at 
B.  If  an  equal  number  of  lamps  are  burning  simultaneously  in  each  row  the 
current  will  flow  through  the  parallel  branches  from  one  dynamo  to  the  other, 
the  central  wire  remaining  neutral ;  but  if  the  number  is  varied  by  the  extin- 
guishing of  lamps  or  otherwise,  the  third  wire  furnishes  a  path  for  the  surplus 
current  required  by  the  row  having  the  greater  number  lighted,  which  will  flow 
to  that  side  in  consequence  of  the  reduced  resistance  resulting  from  the  greater 
number  of  branches  open  through  the  lighted  lamps. 

The  chief  advantage  of  this  system  is  in  the  reduced  amount  of  copper  used 
for  conductors,  three  wires  instead  of  four  being  used,  and  each  only  one  half 
the  area,  a  saving  of  five  eighths  being  thereby  effected. 

A  diagram  in  the  Appendix  illustrates  a  graphic  method  for  obtaining  the 
size  of  wire  to  be  used  in  electric  lighting. 
43 


ARCHITECTURAL  CONSTRUCTION. 


GREEK    AND   ROMAN    ORDERS    OF   ARCHITECTURE, 

as  examples  of  proportions  of  graceful  curves  and  outlines,  are  useful  as 
studies  and  manual  practice  for  the  draughtsman. 

The  Tuscan,  Doric,  Ionic,  Corinthian,  and  Composite  orders  are  systems  or 
assemblages  of  parts  subject  to  certain  uniform  established  proportions,  regu- 
lated by  the  office  each  part  has  to  perform,  consisting  of  two  essential  parts, 
a  column  and  entablature,  subdivided  into  three  parts  each  :  the  first  into  the 
base,  the  shaft,  and  the  capital;  the  second  into  the  architrave,  or  chief  beam, 
C  (Fig.  1585),  which  stands  immediately  on  the  column  ;  the  frieze,  B,  which 
lies  on  the  architrave  ;  and  the  cornice,  A,  which  is  the  crowning  or  uppermost 
member  of  an  order.  In  the  subdivisions  certain  horizontal  members  or  mould- 
ings are  used  :  thus,  the  ogee  (a),  the  corona  (i),  the  ovolo  (c),  the  cavetto  (d), 
with  the  fillets,  compose  the  cornice;  the  fasciae  (//),  the  architrave;  the 
abacus  (#),  the  ovolo  (c),  the  astragal  (ii),  and  the  neck  (7i),  are  the  capital  of 
the  column  ;  the  torus  (&)  and  the  plinth  (/)  (Fig.  1587)  are  the  base.  The 
character  of  an  order  is  displayed  not  only  in  its  column,  but  in  its  general 
forms  and  details,  whereof  the  column  is,  as  it  were,  the  regulator  ;  the  expres- 
sion being  of  strength,  grace,  elegance,  lightness,  or  richness.  Though  a  build- 
ing be  without  columns,  it  is  nevertheless  said  to  be  of  an  order,  if  its  details  be 
regulated  according  to  the  method  prescribed  for  such  order. 

In  all  the  orders  a  similar  unit  of  reference  is  adopted  for  the  construction 
of  their  various  parts.  Thus,  the  lower  diameter  of  the  column  is  taken  as 
the  proportional  measure  for  all  other  parts  .and  members,  for  which  purpose 
it  is  subdivided  into  sixty  parts,  called  minutes,  or  into  two  modules  of  thirty 
minutes  each.  Being  proportional  measures,  modules  and  minutes  are  not  fixed 
ones  like  feet  and  inches,  but  are  variable  as  to  the  actual  dimensions  which 
they  express  —  larger  or  smaller,  according  to  the  actual  size  of  the  diameter  of 
the  column.  For  instance,  if  the  diameter  be  just  five  feet,  a  minute,  being 
one  sixtieth,  will  be  exactly  one  inch.  To  draw  an  elevation  of  any  one  of  the 
orders,  determine  the  diameter  of  the  column,  and  from  that  form  a  scale  of 
equal  parts  by  sixty  divisions,  and  then  lay  off  the  widths  and  heights  of  the 
different  members  according  to  the  proportions  of  the  required  order,  as  marked 
in  the  body  or  on  the  sides  of  the  figures. 

Figs.  1585  to  1589  are  illustrations  of  the  Tuscan  order  :  <?,  in  the  frieze 
corresponding  to  the  Doric  triglyph,  may  or  may  not  be  introduced.  Fig.  1585 
is  an  elevation  of  the  capital  and  entablature  ;  Fig.  1587  of  the  base  ;  and  Fig. 
1586  of  another  capital. 

A  slightly  convex  curvature,  or  entasis,  is  given  in  execution  to  the  outline 
of  the  shaft  of  a  column,  by  classic  architects,  to  counteract  a  fancied  appear- 
ance of  concave  curvature,  which  might  cause  the  middle  of  the  shaft  to  ap- 
pear thinner  than  it  really  is. 

Fig.  1588  represents  the  form  of  a  half-column  from  the  Pantheon  at 
Home.  In  Fig.  1589,  another  example,  the  lower  third  of  the  shaft  is  uni- 
formly cylindrical.  The  entasis  of  the  two  thirds  is  constructed  by  dividing 
the  arc,  a  i,  into  equal  parts,  and  the  columns  into  the  same  number,  and  pro- 
jecting the  divisions  of  the  arc  on  to  those  of  the  column.  The  upper  diame- 
ter of  column  or  chord  at  b  is  52  minutes. 


ARCHITECTURAL   CONSTRUCTION. 


659 


o 


feft 


S 


J/  V 


FIG.  1585. 


ci 


FIG.  1586. 


f 

.g.... 


7 


30  .....  — 


rt 


1JT 


at- - 


—4 


9 
-0 


<%..... 


.......... 


FIG.  1588. 


FIG.  1589. 


-i 


iM 


ARCHITECTURAL   CONSTRUCTION. 

Figs.  1590  to  1594  exhibit  an  example  of  the  Doric  order,  from  the  Temple 
of  Minerva,  in  the  Island  of  Egina.  Fig.  1590  is  an  elevation  of  the  capital 
and  the  entablature;  Fig.  1591  of  the  base;  Fig.  1592  shows  the  forms  of 
the  flutes  at  the  top  of  the  shaft,  and  Fig.  1593  at  the  base ;  Fig.  1594  the 
outline  of  the  capital  on  an  enlarged  scale. 

The  mutules,  a  a,  the  triglyphs,  b  b,  the  guttse  or  drops,  d  d,  of  the  entabla- 
ture, the  echinus,/,  and  the  annulets,  g g,  of  the  capital,  may  be  considered 
characteristic  of  the  Doric.  The  triglyph  is  placed  over  every  column,  and 
one  or  more  intermediately  over  every  intercolumn  (or  span  between  two  col- 
umns), at  such  a  distance  from  each  other  that  the  metopes,  c,  or  spaces  between 
the  triglyphs,  are  square. 

In  the  best  Greek  examples  of  the  order  there  is  only  a  single  triglyph  over 
each  intercolumn.  The  end  triglyphs  are  placed  quite  up  to  the  edge  or  outer 
angle  of  the  frieze.  The  mutules  are  thin  plates  attached  to  the  under  side  or 
soffit  of  the  corona,  over  each  triglyph  and  each  metope,  with  the  former  of 
which  they  correspond  in  breadth,  and  their  soffits  or  under  surfaces  are 
wrought  into  three  rows  of  guttae  or  drops,  conical  or  otherwise  shaped,  each 
row  consisting  of  six  guttae,  or  the  same  number  as  those  beneath  each  triglyph. 
The  shaft  of  the  Doric  column  was  generally  fluted ;  the  number  of  channels 
is  either  sixteen  or  twenty,  afterward  increased  in  the  other  orders  to  twenty- 
four,  a  centre  flute  on  each  side  of  the  column. 

Figs.  1595  to  1598  exhibit  an  example  of  the  Ionic  order,  taken  from  the 
Temple  of  Minerva  Polias,  at  Athens.  Fig.  1595  is  an  elevation  of  the  capital 
and  entablature ;  Fig.  1596,  of  the  base ;  Fig.  1597  is  a  sectional  half  of  the 
plan  of  the  column  at  the  base  and  the  top;  Fig.  1598  an  elevation  of  the  bal- 
uster side  of  the  capital.  It  differs  from  the  Doric  in  the  more  slender  pro- 
portions of  its  shaft,  and  the  addition  of  a  base ;  but  the  capital  is  the  indi- 
cial  mark  of  the  order. 

When  a  colonnade  was  continued  in  front  and  along  the  flanks  of  the 
building,  this  form  of  capital  in  the  end  column  occasioned  an  offensive 
irregularity;  for  while  all  the  other  columns  on  the  flanks  showed  the  volutes, 
the  end  one  showed  the  baluster  side.  It  was  necessary  that  the  end  column 
should,  therefore,  have  two  adjoining  volute  faces,  which  was  effected  by  plac- 
ing the  volute  at  the  angle  diagonally. 

Figs.  1599  and  1600  represent  an  example  of  the  Corinthian  order,  from 
the  Arch  of  Hadrian,  at  Athens.  This  order  is  distinguished  from  the  Ionic 
more  by  its  deep  and  foliaged  capital  than  by  its  proportions.  The  capital  is 
considerably  more  than  a  diameter  in  height,  varying  in  different  examples 
from  one  to  one  and  a  half  diameter,  upon  the  average  about  a  diameter  and  a 
quarter,  and  has  two  rows  of  leaves,  eight  in  each  row,  so  disposed  that  of  the 
taller  ones,  composing  the  upper  row,  one  comes  in  the  middle,  beneath  each 
face  of  the  abacus,  and  the  lower  leaves  alternate  with  the  upper  ones,  coming 
between  the  stems  of  the  latter ;  so  that  in  the  first  or  lower  tier  of  leaves  there 
is  in  the  middle  of  each  face  a  space  between  two  leaves  occupied  by  the  stem 
of  the  central  leaf  above  them.  Over  these  two  rows  is  a  third  series  of  eight 
leaves,  turned  so  as  to  support  the  small  volutes  which,  in  turn,  support  the 
angles  of  the  abacus.  Besides  these  outer  volutes,  invariably  turned  diagonally, 
there  are  two  other  smaller  ones,  termed  catilicoli,  which  meet  each  other  be- 


ARCHITECTURAL    CONSTRUCTION. 


661 


M 
I    11  \ 


662 


ARCHITECTURAL   CONSTRUCTION. 


ARCHITECTURAL   CONSTRUCTION. 


663 


I 


664 


ARCHITECTURAL  CONSTRUCTION. 


FIG.  1001. 


neath  a  flower  on  the  face  of  the  abacus.  The  sides  of  the  abacus  are  concave 
in  plan,  being  curved  outward  so  as  to  produce  a  sharp  point  at  each  corner, 
which  is  usually  cut  off. 

Fig.  1601  represents  one  of  the  capitals  of  the  Tower  of  the  "Winds,  showing 
the  earliest  formation  of  the  Corinthian  capital.  In  this  example  the  abacus 

is  square,  and  the  upper  row  of  leaves,  of  the  kind 

i  ~7    called  water-leaves,  are  broad  and  flat,  and  merely 

carved  upon  the  vase  or  body  of  the  capital. 

The  shaft  is,  in  general,  fluted,  similarly  to  that 
of  the  Ionic  column,  but  sometimes  the  flutes  are 
called ;  that  is,  the  channels  are  hollowed  out  for 
only  about  two  thirds  of  the  upper  part  of  the 
shaft,  and  the  remainder  cut  so  that  each  channel 
has  the  appearance  of  being  partly  filled  up  by  a 
round  staff  or  piece  of  rope. 

The  cornice  is  very  much  larger  than  in  the 
other  orders,  in  height  and  in  projection,  consisting 
of  a  greater  number  of  mouldings  beneath  the  corona,  for  that  and  the  cymati- 
um  over  it  are  invariably  the  crowning  members.  In  Fig.  1599  square  blocks 
or  dentels  are  introduced,  but  often  to  the  dentels  is  added  a  row  of  modillions 
(Fig.  1719),  immediately  beneath,  and  supporting  the  corona ;  and  between 
them  and  the  dentels,  and  also  below  the  latter,  are  other  mouldings,' some- 
times cut,  at  others  left  plain. 

The  Composite  Order  is  a  union  of  the  Ionic  and  Corinthian  orders.  Its 
capital  consists  of  a  Roman  Ionic  one,  superimposed  upon  a  Corinthian  foli- 
aged  base,  in  which  the  leaves  are  without  stalks,  placed  directly  upon  the  body 
of  the  base. 

The  spacing  between  the  columns,  or  intercolumn,  is  from  one  to  one  and 
one  half  diameters,  but  modern  architects  have  coupled  the  columns,  making 
a  wide  intercolumn  between  every  pair  of  columns,  so  that  as  regards  the 
average  proportion  between  solids  and  voids,  that  disposition  does  not  differ 
from  what  it  would  be  were  the  columns  placed  singly.  Supercolumniation, 

or  the  system  of  piling  up  orders,  or  different    

stages  of  columns  one  above  another,  was  em- 
ployed for  such  structures  merely  as  were  upon 
too  large  a  scale  to  admit  of  the  application  of 
columns  at  all  as  their  decoration,  otherwise 
than  by  disposing  them  in  tiers. 

The  Greeks  seldom  employed  human  figures 
to  support  entablatures  or  beams ;  the  female 
figures,  or  Caryatides,  are  almost  uniformly  rep- 
resented in  an  erect  attitude,  without  any  ap- 
parent effort  to  sustain  any  load  ;  while  the 
male  figures,  Telamones  or  Atlantes,  display 
strength  and  muscular  action.  Besides  entire 
figures,  either  Hermes  pillars  or  Termini  are 
occasionally  used  as  substitutes  for  columns  of  the  usual  form,  on  a  moderate 
scale.  The  first  mentioned  consist  of  a  square  shaft  with  a  bust  or  human  head 


ARCHITECTURAL   CONSTRUCTION. 


665 


for  its  capital ;  the  latter  of  a  -half-length  figure  rising  out  of,  or  terminating 
in,  a  square  shaft  tapering  downward.  Hermes  pillars  are  frequently  employed 
by  modern  architects  for  the  decoration  of  window  architraves. 

The  Romans  introduced  circular  forms  and  curves,  not  only  in  elevation 
and  section,  but  in  plan.     The  true  Roman  order  consists,  not  in  any  of  the 
columnar  ordinances,  but  in  an  arrangement  of  two  pillars  (Fig.  1602)  placed 
at  a  distance  from  one  an- 
other nearly  equal  to  their 
own  height,  and  having  a 
very      long      entablature, 
which,  in  consequence,  re- 
quired to  be  supported  in 
the    centre    by    an    arch 
springing  from  piers. 

Figs.  1603,  1604,  and 
1605,  from  the  Palace  of 
Diocletian  at  Spalatro,  are 
illustrations  of  the  differ- 
ent modes  of  treatment  of 
the  arch  and  entablature. 

Perhaps  the  most  sat- 
isfactory works  of  the  Ro- 
mans are  those  which  we 
consider  as  belonging  to 
civil  engineering  rather 
than  to  architecture — 
their  aqueducts  and  via- 
ducts, all  of  which,  admi- 
rably conceived  and  exe- 
cuted, have  furnished 
practical  examples  for 
modern  constructions,  of 
which  High  Bridge  across 
Harlem  River  may  be  tak- 
en as  an  illustration. 

The  history  of  Roman 
architecture  is  that  of  a 
style  in  course  of  transi- 
tion, beginning  with  purely  pagan  or  Grecian,  and  passing  into  a  style  almost 
wholly  Christian.     The  first  form  of  Christian  art  was  the  Romanesque,  which 
afterward  branched  off  into  the  Byzantine  and  the  Gothic. 

The  Romanesque  and  Byzantine,  as  far  as  regards  the  architectural  features, 
are  almost  synonymous ;  in  the  earlier  centuries  there  is  an  ornamental  distinc- 
tion. In  its  widest  signification,  the  Romanesque  is  applied  to  all  the  earlier 
round-arch  developments,  in  contradistinction  to  the  Gothic  or  later  pointed 
arch  varieties  of  the  North.  In  this  view  the  Norman  is  included  in  the  Ro- 
manesque. 

The  general  characteristics  of  the  Gothic  are  its  essentially  pointed  or  ver- 


MiVMyvAwrv  Y^ 


FIG.  1604. 


666 


ARCHITECTURAL  CONSTRUCTION. 


FIG.  1606. 


FIG.  1607. 


FIG.  1608. 


FIG.  1609. 


FIG.  1611. 


FIG.  1612. 


FIG.  1613. 


FIG.  1615. 


FIG.  1617. 


FIG. 

1618. 

ARCHITECTURAL  CONSTRUCTION. 


667 


tical  tendency,  its  geometrical 'details,  its  window-tracery,  its  openings,  its 
cluster  of  shafts  and  bases,  its  suits  of  mouldings,  the  universal  absence  of  the 
dome,  and  the  substitution  of  the  pointed  for  the  round  arch. 

The  Romanesque  pillars  are  mostly  round  or  square,  and,  if  square,  gener- 
ally set  evenly,  while  the  Gothic  square  pillar  is  set  diagonally. 

Figs.  1606  to  1610  represent  sections  of  Gothic  pillars.  Fig.  1611  is  half 
of  one  of  the  great  western  piers  of  the  Cathedral  of  Bourges,  measuring  8  feet 
on  each  side.  Figs.  1612  and  1613  are  elevations  of  capitals  and  bases,  and  sec- 
tions of  Gothic  pillars ;  one  from  Salisbury,  the  other  from  Lincoln  Cathedral. 

Figs.  1614,  1615,  and  1616  are  examples  of  Byzantine  capitals;  Fig.  1617 
a  Norman  one,  from  Winchester  Cathedral ;  and  Fig.  1618  a  Gothic  capital 
and  base,  from  Lincoln  Cathedral. 

Arches  are  generally  divided  into  the  triangular-headed  arch,  the  round- 
headed  arch,  and  the  pointed  arch.  Of  the  round-headed  arch,  there  are 
semicircular,  segmental,  stilted  (Fig.  1619),  and  horseshoe  (Fig.  1620).  Of 


FIG.  1619. 


FIG.  1620. 


FIG  1621. 


the  two-centred  pointed,  the  equilateral  (Fig.  1621),  the  lancet,  and  the  ob- 
tuse. Of  the  first,  the  radii  of  the  segments  forming  the  arch  are  equal  to  the 
breadth  of  the  arch,  of  those  of  the  lancet  longer,  and  of  the  obtuse  shorter. 

Of  the  complex  arches,  there  are  the  ogee  (Fig.  1622)  and  the  Tudor  (Fig. 
1623).  The  Tudor  arch  is  described  from  four  centres,  two  on  a  level  with  the 
spring  and  two  below  it. 

Of  foiled  arches,  there  are  the  round-headed  trefoil  (Fig.  1624),  the  pointed 


FIG.  1622. 


FIG.  1623. 


FIG.  1624. 


FIG.  1625. 


FIG.  1626. 


trefoil  (Fig.  1625),  and  the  square-headed  trefoil  (Fig.  1626).  The  points  c  are 
termed  cusps. 

The  semicircular  arch  is  the  Roman  Byzantine  and  Norman  arch ;  the  ogee 
and  horseshoe  are  the  profiles  of  many  Turkish  and  Moorish  domes ;  the  pointed 
and  foliated  arches  are  Gothic. 

Domes  and  Vaults. — The  Greek  vaulting  consisted  wholly  of  spherical  sur- 
faces, the  Roman  of  cylindrical  ones.  Figs.  1627  and  1628  illustrate  this  dis- 
tinction, Fig.  1627  being  the  elevation  of  a  Roman  cylindrical  cross-vault,  and 
Fig.  1G28  the  elevation  of  the  roof  of  the  church  of  St.  Sophia  at  Constantino- 
ple ;  and  the  sprouting  of  domes  out  of  domes  continues  to  characterize  the 


668 


ARCHITECTURAL  CONSTRUCTION. 


Byzantine  style.    As  a  constructive  expedient  the  cross- vault  is  to  be  preferred, 
as  the  whole  pressure  and  thrust  are  collected  in  four  definite  resultants,  ap- 


FIG.  1627. 


KIG.  1C28. 


plied  at  the  angles  only,  so  that  it  might  be  supported  by  four  flying  buttresses, 
placed  in  the  direction  of  the  resultants,  and  strong  enough  to  resist  the 
pressure. 

Fig.  1629  represents  a  compartment  of  the  simplest  Gothic  vaulting — a,  a, 
groin  ribs ;  #,  5,  #,  side  ribs. 

The  Romans  introduced  side  ribs,  appearing  on  the  inside  as  flat  bands,  and 
harmonizing  with  the  similar  form  of  pilasters  in  the  walls,  but  they  never  used 
groin  ribs ;  the  Gothic  builders  introduced  these,  and  deepened  the  Roman 
ribs.     The  impenetration  of  vaults,  either  round  or  pointed,  produces  elliptical 
groin  lines,  or  else  lines  of  double  curvature ;  yet  the  early  Gothic  architects 
made  their  groin  ribs  usually  simple  pointed  arches  of  circular  curvature, 
thrown  diagonally  across  the  space  to  be  groined,  and 
the  four  side  arches  were  equally  simple,  the  only  care 
being  that  all  the  arches  should  have  their  vertices  at 
the  same  level.     The  strength  depended  on  the  ribs, 
and  the  shell  was  made  quite  light,  often  not  more 
than   six  inches,  while   Roman  vaults   of   the    same 
span  would  have  been  three  or  four  feet.     The  Ro- 
mans made  their  vault  surfaces  geometrically  regu- 
lar, and  left  the  groins  to  take  their  chance ;  while  the 
early  Gothic  architects  made  their  groins  geometri- 
cally regular,  and  let  the  intermediate  surfaces  take  their  chance. 

In  the  next  step  the  groin  ribs  were  elliptical,  and  when  intermediate  ribs 
or  tiercerons  were  inserted,  these  ribs  had  also  elliptical  or  cylindrical  curva- 
tures, different  from  the  groins,  and  the  ribs  were  placed  near  each  other,  in 
order  that  the  portion  of  the  vault  between  each  pair  might  practically  be 
almost  cylindrical.  In  the  formation  of  the  compound  circular  ribs  three  con- 
ditions were  to  be  observed :  1.  That  the  two  arcs  should  have  a  common  tan- 
gent at  the  point  of  meeting.  2.  That  the  feet  of  all  the  ribs  should  have  the 
same  radius,  up  to  the  level  at  which  they  completely  separate  from  each  other. 
3.  That  from  this  point  upward  their  curvature  should  be  so  adjusted  as  to 
make  them  all  meet  their  fellows  on  the  same  horizontal  plane,  so  that  all  the 
ridges  of  the  vaults  may  be  on  one  level. 

The  geometrical  difficulty  of  such  works  led  to  what  is  called  fan-tracery 
vaulting.  If  similar  arches  spring  from  each  side  of  the  pillars  (Fig.  1629), 
the  portion  of  vault  springing  from  each  pillar  would  have  the  form  of  an  in- 
verted concave-sided  pyramid,  its  horizontal  section  at  every  level  being  square. 


Flo.  1629. 


ARCHITECTURAL  CONSTRUCTION. 


669 


FIG.  1630. 


The  later  architects,  by  converting  this  section  into  a  circle,  the  four-sided 

pyramid  became  a  conoid,  and  all  the  ribs  forming  the  conoidal  surface  became 

alike  in  curvature,  so  that  they  all  might  be  made  simple  circular  arcs ;  these 

ribs  are  continued  with  unaltered  curvature  till  they  meet  and  form  the  ridge ; 

but  in  this  case  the  ridges  are  not  level,  but 

gradually  descend  every  way  from  the  centre 

point  (Fig.  1630). 

In  the  figure  this  is  not  fully  carried  out, 

for  no  rib  is  continued  higher  than  those  over 

the  longer  sides  of  the  compartment,  so  that  a 

small  lozenge  is  still  left,  with  a  boss  at  its 

centre.     When  the  span  of  the  main  arch  ba 

was  large  in  proportion  to  that  of  b  (c,  the  arch 

b  c  became  a  very  acute  lancet  arch,  scarcely 

admitting  windows  of  an  elegant  or  sufficient 

size.      To   obviate  this,   the   compound   curve 

was  again  introduced. 

The  four-centred  arch  is  not  necessarily  flat  or  depressed ;  it  can  be  made 

of  any  proportion,  high  or  low,  and  always  with  a  decided  angle  at  the  vertex. 

In  general,  the  angular  extent  of  the  lower  curve  is  not  more  than  65°,  nor  less 

than  45°.     The  radius  of  the  upper  curve  varies  from  twice  to  more  than  six 

times  the  radius  of  the  lower.     The  projecting  points  of  the  trefoil  arch,  or 

cusps,  are  often  introduced  for  ornament  merely,  but  serve  constructively,  both 
in  vaults  and  arches,  as  a  load  for  the  sides,  to  prevent 
them  rising  from  the  pressure  on  the  crown. 

As  vaultings,  in  general,  were  contrived  to  collect  the 
whole  pressure  of  each  compartment  into  four  single  re- 
sultants, at  the  points  of  springing,  leaving  the  walls  so 
completely  unloaded  that  they  are  required  only  as  in- 
closures  or  screens,  they  might  be  entirely  omitted  or  re- 
placed by  windows.  Indeed,  the  real  supporting  walls 
are  broken  into  narrow  strips,  placed  at  right  angles  to 
the  outline  of  the  building,  and  called  buttresses,  and 
the  inclosing  walls  may  be  placed  either  at  the  outer  or 
inner  edge  of  the  buttresses.  The  first,  that  adopted  by 
the  French  architects,  gave  deep  recesses  to  the  interiors, 
while  the  other,  or  English  method,  served  to  produce 
external  play  of  light  and  shade. 

The  Norman  buttress  (Fig.  1631)  resembles  a  flat 
pilaster,  being  a  mass  of  masonry  with  a  broad  face, 
slightly  projecting  from  the  wall.  They  are,  generally, 
of  but  one  stage,  rising  no  higher  than  the  cornice,  under 
which  they  often,  but  not  always,  finished  with  a  slope. 
Sometimes  they  are  carried  up  to,  and  terminate  in,  the 
corbel  table. 

Fig.  1632  represents  a  buttress  in  two  stages,  with  slopes  as  set-offs. 
Fig.  1633  is  a  buttress  of  the  early  English  style,  having  a  plain  triangular 

or  pedimental  head.     The  angles  were  sometimes  chamfered  off,  and  sometimes 


670 


ARCHITECTURAL  CONSTRUCTION. 


ornamented  with  slender  shafts.  In  buttresses  of  different 
stages,  the  triangular  head  or  gable  is  used  as  a  finish  for  the 
intermediate  stages. 

In  the  Decorated  style,  the  outer  surfaces  of  the  buttresses 
are  ornamented  with  niches,  as  in  Fig.  1634.  In  the  Perpen- 
dicular style  the  outer  surface  is  often  partially  or  wholly  cov- 
ered with  panel-work  tracery  (Fig.  1635). 

The  buttress  was  a  constructive  expedient  to  resist  the 
thrust  of  vaulting;  but  to  resist  the  thrust  of  the  principal 
vault,  or  that  over  the  nave  or  central  part  of  the  church,  but- 
tresses of  the  requisite  depth  would  have  filled  up  the  side 
aisles  entirely.  To  obviate  this,  the  system  of  flying  but- 


FIQ.  1632. 


Fio.  1633. 


FIG.  1634. 


FIG.  1635. 


FIG.  1636. 


Fio.  1637. 


tresses  was  adopted  ;  that  is,  the  connection  of  the  interior  with 
the  outer  buttress,  by  an  arch  or  system  of  arches,  as  shown  in 
Fig.  1636.  The  outer  piers  were  surmounted  by  pinnacles,  to 
render  them  a  sufficiently  steady  abutment  to  the  flying  arches. 
The  earlier  towers  of  the  Romanesque  style  were  con- 
structed without  spires.  All  are  square  in  plan,  and  extremely 
similar  in  design.  Fig.  1637  is  an  elevation  of  the  tower  at- 
tached to  the  church  of  Sta.  Maria,  in  Cosmedin,  and  is  one  of 
the  best  and  most  complete  examples  of  this  style.  It  is  15  feet 
broad  and  110  feet  high.  These  towers  are  the  types  of  the 
later  Italian  campaniles,  generally  attached  to  some  angle  of 
churches ;  if  detached,  so  placed  that  they  still  form  a  part  of 
the  church  design.  Sometimes  they  are  but  civic  constructions, 
_as  belfries,  or  towers  of  defence.  The  campanile  is  square, 
carried  up  without  break  or  offset  to  two  thirds,  at  least,  of  its 


ARCHITECTURAL  CONSTRUCTION. 


671 


B 


intended  height ;  it  is  generally  solid  to  a  consid- 
erable height,  or  with  only  such  openings  as  serve 
to  admit  light  to  the  staircases.  Above  this  solid 
part  one  round  window  is  introduced  in  each 
face ;  in  the  next  story,  two ;  in  the  one  above 
this,  three ;  then  four,  and  lastly  five ;  the  lights 
being  separated  by  slight  piers,  so  that  the  upper 
story  is  virtually  an  open  loggia. 

The  Gothic  towers  have  projecting  buttresses, 
frequent  offsets,  lofty  spires,  and  a  general  pyra- 
midal form.  Fig.  1638  is  the  front  elevation  of 
a  simple  English  Gothic  tower;  here  the  plain 
pyramidal  roof,  rising  at  an  equal  slope  on  each 
of  the  four  sides,  is  intersected  by  an  octagonal 
spire  of  steep  pitch.  The  first  spires  were  simple 
quadrangular  pyramids  ;  afterward  the  angles 
were  cut  off,  and  they  became  octagonal,  and  this 


FIG.  1C38. 


Fio.  1639. 

is  the  general  Gothic  form  of  spire.  Often,  in- 
stead of  intersecting  the  square  roof,  as  in  the 
figure,  the  octagonal  spire  rests  upon  a  square 
base,  and  the  angles  of  the  tower  are  carried  up 
by  pinnacles,  or  the  sides  by  battlements,  or  by 
both,  as  in  Fig.  1639,  to  soften  the  transition  be- 
tween the  perpendicular  and  sloping  part. 

In  general  the  spires  of  English  churches  are 
more  lofty  than  those  on  the  Continent,* the  an- 
gle at  the  apex  in  the  former  being  about  10°, 
and  in  the  latter  about  15°.  The  apex  angle  of 
the  spires  of  Chichester  and  Lichfield  are  from 
12°  to  13°,  or  a  mean  between  the  two  propor- 
tions, and,  according  to  Ferguson,  more  pleasing 
than  either.  Although  having  more  lofty  spires, 
yet  the  English  construction  is  much  more  mas- 
sive in  appearance  than  the  Continental ;  the 
apertures  are  less  numerous,  and  the  surfaces  are 


ARCHITECTURAL  CONSTRUCTION. 


FIG.  1642.  FIG.  1640.  FIG.  1643.    FIG.  1641. 


Fio.  1645. 


Fio.  1646.        FIG.  1647. 


FIG.  1644. 


FIG.  1648. 


ARCHITECTURAL  CONSTRUCTION. 


673 


less  cut  up  and  covered  with  ornaments.     The  spires  of  Freiberg  Church,  and 
many  others  on  the  Continent,  are  open  work. 

Figs.  1640  and  1641  are  bell-cots.     Figs.  1642  to  1648  are  spires.     Fig.  1649 
is  an  apse,  or  circular  end  of  a  church,  from  German  Gothic  examples. 


FIG.  1653. 


FIG.  1654. 


Figs.  1650  and  1651  are  examples  of  spire  finials,  with  weather-cocks. 
Figs.  1652  and  1653  are  examples  of  towers  not  connected  with  church 
edifices. 

Fig.  1654  is  a  tower  of  very  recent  construction,  and  is  applied  to  the  utili- 

44 


674 


ARCHITECTURAL  CONSTRUCTION. 


tarian  purpose  of  sustaining  a  water-tank  for  the  highest  service  of  the  Croton 
in  New  York  city. 

Fig.  1655  represents  the  upper  portion  of  the  tower  of  Ivan  Veliki,  at  Mos- 
cow. The  Eussian  towers  are  generally  constructed  independent  of  their 
churches,  and  are  intended  for  the  reception  of  their  massive  bells. 

Windows. — Before  the  use  of  painted  glass,  as  very 
small  apertures  sufficed  for  the  introduction  of  the  re- 
quired quantity  of  light  into  a  church,  the  windows  of 
the  Eomanesque  churches  were  generally  small,  and  de- 
void of  tracery ;  and  as  the  Byzantine  architects,  adorn- 
ing the  walls  with  paintings,  could  not  use  stained  glass, 
they  followed  in  general  form  the  Eomanesque  window, 
apertures  with  circular  heads,  either  single  or  in  groups 
(Fig.  1656  or  Fig.  1657).  The  Norman  windows  were 
also  small,  each  consisting  of  a  single  light,  semicircular 


FIG.  1655. 


FIG.  1656. 


FIG.  1657. 


in  the  head,  and  placed  as  high  as  possible  above  the  ground ;  at  first  splayed 
on  the  inside  only,  afterward  the  windows  began  to  be  recessed  with  mould- 
ings and  jamb-shafts  in  the  angles,  as  in  Fig.  1657. 

The  Lancet,  in  general  use  in  the  early  Gothic  period,  was  of  the  simplest 
arrangement :  in  these  windows  the  glass  was  brought  within  three  or  four 
inches  of  the  outside  of  the  wall,  and  the  openings  were  widely  splayed  in  the 
interior.  The  proportions  of  these  windows  vary  considerably,  in  some  the 
height  being  but  five  times  the  width,  in  others  as  much  as  eleven;  eight  or 
nine  times  may  be  taken  as  the  average.  Lancet  windows  occur  singly  (Fig. 
1658),  or  in  groups  of  two,  three,  five,  and  seven,  rarely  of  four  and  six.  The 
triplet  (Fig.  1659)  is  the  most  beautiful  arrangement  of  lancet  windows.  It 
was  customary  to  mark  with  greater  importance  the  central  light,  by  giving  it 
additional  height,  and  in  most  cases  increased  width  also.  In  some  examples 
the  windows  of  a  lancet  triplet  are  placed  within  one  drip-stone  forming  a 
single  arch,  thus  bearing  a  strong  resemblance  to  a  single  three-light  window. 
The  first  approximation  to  tracery  appears  to  have  been  the  piercing  of  the 
space  over  a  double  lancet  window  comprised  within  a  single  drip-stone  (Fig. 
1660). 

A  traceried  window  is  a  distinctive  characteristic  of  Gothic  architecture; 
with  the  establishment  of  the  principle  of  window  tracery  the  mullions  were 
recessed  from  the  face  of  the  wall  in  which  the  window  arch  was  pierced,  and 


ARCHITECTURAL  CONSTRUCTION. 


675 


the  fine  effect  thus  produced  was  speedily  enhanced  by  the  introduction  of  dis- 
tinct orders  of  mullions,  and  by  recessing  certain  portions  of  the  tracery  from 
the  face  of  the  primary  mullions  and  their  corresponding  tracery  bars. 


FIG.  1659. 


FIG.  1658. 


FIG.  1660. 


Examples  of  window  tracery,  showing  its  constructive  centres  and  lines,  are 
given  on  pages  81  and  82,  illustrating  the  chief  varieties.  The  following  figures 
are  more  complete  in  position 
and  with  architraves,  Geomet- 


FIG.  1601. 


FIG.  1662. 


rical  and  Flowing ;  the  former  consisting  of  geometrical  figures,  as  circles, 
trefoils,  quatrefoils,  curvilinear  triangles,  lozenges,  etc. ;  while  in  flowing  tracery 
these  figures,  though  still  existing,  are  gracefully  blended  together  in  one  de- 
sign. 

Fig.  1661  represents  an  example  of  the  earlier  decorated  tracery  window- 
head,  consisting  of  two  foiled  lancets,  with  a  pointed  quatrefoil  in  the  spandrel 
between  them.  One  half  of  the  windows  in  this,  as  in  some  of  the  following 
figures,  is  drawn  in  skeleton,  to  explain  their  construction.  Fig.  1662  is  an- 
other example  of  Decorated  tracery. 

Fig.  1663  is  an  example  of  the  English  leaf  tracery;  Fig.  1664,  of  the 
.French  flamboyant.  The  difference  between  the  two  styles  is,  that  while  the 
upper  ends  of  the  English  loops  or  leaves  are  round,  or  simply  pointed,  the 
upper  ends  of  the  latter  terminate,  like  their  lower  ones,  in  angles  of  contact, 
giving  a  flamelike  form  to  the  tracery  bars  and  form  pieces. 


676 


ARCHITECTURAL  CONSTRUCTION. 


In  England  the  Perpendicular  style  succeeded  the  Decorated  ;  the  mullions, 
instead  of  diverging  in  flowing  or  curvilinear  lines,  are  carried  up  straight 
through  the  head  of  the  windows;  smaller 
mullions  spring  from  the  head  of  the  prin- 


FIG.  1663. 


FIG.  1664. 


FIG.  1665. 


cipal  lights,  and  thus  the  upper  portion  of  the  window  is  filled  with  panel-like 
compartments.  The  principal  as  well  as  the  subordinate  lights  are  foliated  in 
their  heads,  and  large  windows  are  often  divided  horizontally  by  transoms. 
The  forms  of  the  window  arches  vary  from  simple  pointed  to  the  complex 
four-centred,  more  or  less  depressed. 

Fig.  1665  ,is  an  example  of  a  Perpendicular  window. 

Fig.  1666  is  a  square-headed  window,  such  as  were  usual  in  the  clear-stories 
of  Perpendicular  architecture. 

Figs.  1667  and  1668  are  quadrants  of  circular  windows,  used  more  espe- 


FIG.  1666. 


FIG.  1667. 


FIG.  1668. 


FIG.  1669. 


cially  in  France  for  the  adornment  of  the  west 
ends  and  transepts  of  the  cathedrals. 

Besides  the  tracery  characteristic  of  Gothic 
architecture,  there  is  a  tracery  peculiar  to  the 
Saracenic  and  Moorish  style,  of  which  Fig. 
1669  may  be  taken  as  an  example — it  being  a 
window  of  one  of  the  earliest  mosques.  The 
general  form  of  the  window  and  door-heads  of 
this  style  is  that  of  the  horse-shoe,  either  cir- 
cular or  pointed. 

Doorways. — Fig.  1670  is  the  elevation  of  a 
circular-headed  doorway,  which  may  be  con- 


ARCHITECTURAL  CONSTRUCTION. 


sidered  the  type  of  many  entrances  both  in  Romanesque,  Gothic,  and  later 
styles.  It  consists  of  two  or  more  recessed  arches,  with  shafts  or  mouldings 
in  the  jambs.  In  the  earlier  styles  the 
arches  were  circular,  in  the  later  Gothic, 


FIG.  1671. 


h 


FIG.  1670. 


FIG.  1672. 


generally  pointed,  but  sometimes  circular ;  in  the  earlier,  the  angles  in  which 
the  shafts  are  placed  are  rectangular ;  in  the  latter,  the  shaft  is  often  moulded 
on  a  chamfer  plane — that  is,  a  plane  inclined  to  the  face  of  the  wall,  generally 
at  an  angle  of  45°  ;  often  the  chamfer  and  rectangular  plane  are  used  in  con- 
nection. 

Fig.  1671  is  a  simple  head  of  a  depressed  four-centred  or  Tudor-arched 
doorway,  with  a  hood  moulding. 

Fig.  1672  represents  the  incorporation  of  a  window  and  doorway.  Some- 
times the  doorway  pierces  a  buttress;  in  that  case,  the  buttress  expands  on 
either  side,  forming  a  sort  of  porch.  The  Gothic  architects  placed  doors 
where  they  were  necessary,  and  made  them  subservient  to  the  beauty  of  the 
design. 

Fig.  1673  is  an  example  of  a  gabled  doorway  with  crockets  and  finial. 

Fig.  1674  is  an  example  of  a  perpendicular  doorway,  with  a  label  or  hood 
moulding  above,  and  ornamented  spandrels. 

Fig,  1675  is  an  example  of  a  Byzantine,  and  Fig.  1676  of  a  Saracenic 
doorway. 

The  Renaissance  style  was,  originally,  but  the  revival  or  a  fair  rendering  of 
the  classical  orders  of  architecture,  with  ornaments  from  the  Byzantine  and 
Saracenic  styles. 

Garbett  divides  this  style  into  three  Italian  schools,  the  Florentine,  Vene- 
tian, and  Roman.  The,  Florentine  admits  of  little  apparent  ornament,  but 
any  degree  of  real  richness,  preserving  in  its  principal  forms  severe  contrast; 
powerful  masses  self-poised  without  corbeling,  without  arching  ;  breadth  of 


678 


ARCHITECTURAL  CONSTRUCTION. 


everything,  of  light,  of  shade,  of  ornament,  of  plain  wall ;  depth  of  recess  in 
the  openings,  of  perspective  in  the  whole  mass,  of  projection  in  the  cornice. 


FIG.  1(573. 


TIG.  1674. 


Absence  of   features  useless  to  convenience  or  stability,  admitting  of  great 
plainness,  or  of  very  florid  enrichment. 

The  aim  of  the  Venetian  school  was  splendour,  variety,  show,  and  orna- 
ment-; not  so  much  real  as  effective  ornament.     Thus,  it  rarely  contains  as 


Fio.  1675. 


icre. 


much  carving  or  minute  enrichment  as  the  Florentine  admits ;  but  it  has 
larger  ornaments,  constructed  (or  built)  ornaments,  great  features  useless 
except  for  ornament,  such  as  inaccessible  porticoes,  detached  columns,  and 
architraves  supporting  no  ceiling,  towers  built  only  for  breaking  an  outline. 

The  Roman  school  is  intermediate  in  every  respect  between  the  two  other 
schools.  It  is  better  adapted  to  churches  than  to  any  other  class  of  buildings. 
This  fitness  arises  from  the  grand,  simple,  and  unitary  effect  of  one  tall  order, 


ARCHITECTURAL  CONSTRUCTION. 


679 


generally  commencing  at  or  near  the  ground,  obliterating  the  distinction  of 
two  or  three  stories,  making  a  high  building  appear  a  single  story. 

Mouldings. — "  All  classical  and  Romanesque  architecture  is  composed  of 
bold  independent  shafts,  plain  or  fluted,  with  bold  detached  capitals  forming 
arcades  or  colonnades  where  they  are  needed,  and  of  walls  whose  apertures  are 
surrounded  by  courses  of  parallel  lines  called  mouldings,  and  have  neither 
shafts  nor  capitals.  The  shaft  system  and  moulding  system  are  entirely  sepa- 
rate ;  the  Gothic  architects  confounded  the  two  ;  they  clustered  the  shafts  till 
they  looked  like  a  group  of  mouldings,  they  shod  and  capitalled  the  mouldings 
till  they  looked  like  a  group  of  shafts."  The  mouldings  appear  in  almost  every 
conceivable  position ;  from  the  bases  of  piers  and  piers  themselves,  to  the  ribs 
of  the  fretted  vaults  which  they  sustain. 

In  the  earliest  examples  of  Norman  doorways  the  jambs  are  mostly  simply 
squared  back  from  the  walls ;  recessed  jambs  succeeded,  and  are  common  in 
both  Norman  and  Gothic  architecture  ;  and  when  thus  re- 
cessed, detached  shafts  were  placed  in  each   angle   (Fig. 
1677).     In  the  later  styles  the  shafts  were  almost  invariably 
attached  to  the  structure.      The  angles  themselves  were 
often  cut  or  chamfered  off,  and  the  mouldings  attached  to 
the   chamfer-plane.      The  arrangement  of  window  jambs, 
during  the  successive  periods,  was  in  close  accordance  with 
that  of  doorways. 

In  the  richer  examples  small   shafts  were  introduced, 
which,  rising  up  to  the  springing  of  the  window,  carried  FIG.  1677.  . 

one  or  several  of  the  arch  mouldings.     Yet  mouldings  are 
nevertheless  not  essential  accessories ;   many  windows  of  the  richest  tracery 
have  their  mullions  and  jambs  composed  of  simple  chamfers. 

Figs.  1678  to  1686  are  examples  of  arch  and  architrave  mouldings,  which, 


FIG.  1680 


FIG.  1682. 


680 


ARCHITECTURAL  CONSTRUCTION. 


FIG.  1683. 


FIG.  1684. 


FIG.  1685. 


FIG.  1686. 


even  when  not  continuous,  partook  of  the  same  general 
arrangement  as  those  in  the  jambs,  with  greater  rich- 
ness of  detail.  When  shafts  were  employed,  they  car- 
ried groups  of  mouldings  more  elaborate  than  those 
of  the  jambs,  though  still  falling  on  the  same  planes. 

Capitals  were  either  moulded  or  carved  with  foliage, 
animals,  etc.  ;  they  always  consisted  of  three  distinct 
parts  (Fig.  1687)— the  head  mould  (A),  the  bell  (B),  and  the  neck  mould  (C). 
In  Norman  examples  the  head  mould  was  almost  invariably  square;  in  the 
later  styles  it  is  circular,  or  corresponding  to  the  form  of  the 
pillar. 

Bases  consist  of  the  plinth  and  the  base  mouldings.  The 
plinth  was  square  in  the  Norman  style,  afterward  octagonal ; 
then,  assuming  the  form  of  the  base  mouldings,  it  bent  in 
and  out  with  the  outline  of  the  pier.  Base  mouldings  were 
also  extensively  used  round  the  buttresses,  towers,  and  walls 
of  churches. 

String  Courses,  of  which  Figs.  1688  to  1693  are  exam- 
ples, were  horizontal  courses  in  the  face  of  a  wall,  the  most 
usual  position  being  under  the  windows.  In  the  Norman  styles  they  were  usu- 
ally heavy  in  the  outline ;  in  the  later  styles  they  were  remarkably  light  and 
elegant ;  free  from  restraint  or  horizontality,  they  now  rose  close  under  the  sill 


FIG.  1691. 


FIG.  1692. 


FIG.  1693. 


ARCHITECTURAL  CONSTRUCTION. 


681 


of  the  window,  and  then  suddenly  dropping  to  accommodate  themselves  to  the 
arch  of  a  low  doorway,  and  again  .rising  to  run  immediately  under  the  adjoin- 
ing window.  In  this  way  the  string  courses  frequently  served  the  purpose  of  a 
drip-stone  or  hood  moulding  over  doors ;  occasionally  the  hood  mould  was  con- 
tinued from  one  window  to  the  other. 

Cornices  are  not  an  essential  feature  in  Gothic  architecture.     In  the  Nor- 
man and  early  English  styles  the  cornice  was  a  sort  of  enlarged, 
projecting  string  course,  forming  a  drip-stone  beneath  the  roof, 
which,  if  supported  on  brackets  or  corbels,  was  termed  the  corbel 
table. 

The  earliest  moulding  in  Norman  work  is  a  circular  bead 
strip,  worked  out  of  the  edges  of  a  recessed  arch,  called  a  circu- 
lar boiotel  (Fig.  1694).     From  a  circular  form  the  bowtel  soon  be- 
came pointed,  and,  by  an  easy  transition,  into  the  bowtel  of  one,  two,  or  three 
fillets. 

Figs.  1695  to  1700  are  sections  of  Komanesque  drip-  or  cap-stones,  adapted 
to  different  pitches  of  roof. 

Fig.  1701  is  the  scroll  moulding ;  a  simple  filleted  bowtel,  with  the  fillet 


FIG.  1694. 


FIG.  1C99. 


FIG.  1700. 


682 


ARCHITECTURAL  CONSTRUCTION. 


undeveloped  on  one  side,  as  shown  by  the  dotted  lines.  If  this  moulding  be 
cut  in  half,  through  the  centre  of  the  fillet,  we  have  on  the  developed  side  the 
moulding  now  termed  by  carpenters  the 
rule  joint,  which,  by  rounding  off  the 
corners  by  reverse  curves,  becomes  the 
wave  moulding. 


FIG.  1702. 


FIG.  1703. 


FIG.  1701. 

Fig.  1702  is  a  Gothic  example  of  the 
filleted  bowtel  with  prominent  alternate 
hollows. 

Fig.  1703  is  an  example  of  the  perpendicular  style,  an  insignificant  hollow 
separating  groups  of  mouldings. 

Figs.  1704  to  1709  are  examples  of  moulded  timbers,  used  largely  in  open- 
timbered  roofs  and  for  exposed  beams.  It  is  still  the  custom,  when  the  fram- 
ing is  not  covered  in  with  plastering  or  ceiling,  to  corner  the  edges  of  the  joists 
and  beams,  at  an  angle  of  45°,  for  about  1*  on  each  face,  but  not  extending 
close  to  the  joint  or  wall ;  this  is  called  stop-chamfering. 


FIG.  1704. 


FIG.  1705. 


FIG.  1706. 


FIG.  1707. 


FIG.  1708. 


FIG.  1709. 


Ornament. — Architectural  ornament  is  of  two  kinds,  constructive  and  deco- 
rative. By  the  former  is  meant  all  those  contrivances,  such  as  capitals,  brack- 
ets, vaulting-shafts,  and  the  like,  which  serve  to  explain  or  give  expression  to 
the  construction ;  by  the  latter,  such  as  mouldings,  frets,  foliage,  etc.,  which 
give  grace  and  life,  either  to  the  actual  constructive  form,  or  to  the  construe- 


ARCHITECTURAL   CONSTRUCTION. 


683 


tive  decoration.    Mouldings  of  the  different  styles  have  been  already  treated  of ; 
it  is  proposed  to  give  now  what  are  even  more  purely  decorations  of  a  style. 

In  the  Grecian  orders  the  Doric  (Fig.  1590)  has  the  triglyph  mutules  and 
guttae;  the  Ionic  (Fig.  1596)  has  various  mouldings  of  the  cornice,  frieze, 
abacus,  and  neck  of  the  column  enriched.  The  principal  ornament  of  the 
neck  of  the  column  is  the  anthemion,  commonly  known,  in  its  most  simple 
form,  as  the  honeysuckle  or  palmetto ;  in  the  anthemion,  as  represented  in  the 
figure,  the  palmetto  alternates  with  the  lily  or  some  analogous  form.  The 
ornament  of  the  abacus  is  the  egg  and  dart  (Fig.  1710)  ;  the  ornament  of  the 


FIG.  1710. 


FIG.  1711. 


frieze  and  cornice  (Fig.  1711).  The  fret  (Fig.  1712)  and  the  guilloche  (Fig. 
1713)  are  also  common  Greek  ornaments,  used  to  adorn  the  soffits  of  beams 
and  ceilings.  The  acanthus  is  the  distinctive  ornament  of  the  Corinthian,  of 
which  a  leaf  is  represented  in  front  and  side  view  (Figs.  1714  and  1715). 


Fio.  1712. 


FIG.  1713. 


FIG.  1714. 


FIG.  1715. 


Figs.  1716,  1717,  and  1718  are  the  side  elevation,  front  elevation,  and  sec- 
tion of  a  Greek  bracket,  the  principal  ornaments  of  which  are  taken  from  the 
anthemion  and  acanthus. 

Fig.  1719  is  an  elevation  of  a  portion  of  an  enriched  cornice  from  the 
temple  of  Jupiter  Stator,  at  Rome,  of  the  Corinthian  order  of  architecture. 
Fig.  1720  is  the  under  side  of  the  modillion,  on  a  larger  scale. 

The  chief  characteristic  of  Roman  ornament  is  its  uniform  magnificence,  an 
enrichment  of  the  Greek.  The  most  used  elements  of  the  Roman  decorations 
are  the  scroll  and  the  acanthus.  The  acanthus  of  the  Greeks  is  the  narrow 
prickly  acanthus ;  that  of  the  Roman,  the  soft  acanthus.  For  capitals  the 
Roman  acanthus  is  commonly  composed  of  conventional  clusters  of  olive-leaves. 
Fig.  1721  represents  a  Roman  acanthus  scroll. 


ARCHITECTURAL  CONSTRUCTION. 


The  free  introduction  of  monsters  and  animals  is  likewise  a  characteristic 
of  Greek  and  Roman  ornament,  as  the  sphinx,  the  triton,  the  griffin,  and 
others ;  they  occur,  however,  more  abundantly  in  the  Roman. 


FIG.  17 


FIG.  1717. 

Symbols  are  the  foundation  of  decorations  in  the  Byzantine  and  Romanesque. 
The  early  symbols  were  the  monogram  of  Christ,  the  lily,  the  cross,  the  ser- 
pent, the  fish,  the  aureole,  or  vesica  piscis,  and  the  circle  or  nimbus,  the  trefoil 
and  quatrefoil,  the  first  having  reference  to  the  Trinity,  the  second  to  the 

four  Evangelists.  Occasionally  the 
symbolic  images  of  the  Evangelists,  the 
angel,  the  lion,  the  ox,  and  the  eagle, 


FIG.  1719. 


ARCHITECTURAL  CONSTRUCTION. 


685 


are  represented  within  these  circles.     The  hand  in  the  attitude  of  benediction, 
and  the  lily  (the  fleur-de-lis),  the  emblem  of  the  virgin  and  purity,  are  com- 


FIG.  1721. 


mon ;  also  a  peculiarly  formed  leaf,  somewhat  resembling  the  leaf  of  the  ordi- 
nary thistle.  The  serpent  figures  largely  in  Byzantine  art  as  the  instrument  of 
the  fall,  and  one  type  of  the  redemption. 


FIG.  1722. 


Pagan  ornaments,  under  certain  symbolic  modifications,  were  admitted  into 
Christian  decorations.  Thus  the  foliations  of  the  scroll  were  terminated  by 
lilies,  or  by  leaves  of  three,  four,  and  five  blades,  the  number  of  blades  being 
significant;  and  in  a  similar  way  the  anthemion  and  every  other  ancient  orna- 
ment. In  the  Byzantine,  all  their  imitations  of  natural  forms  were  invariably 
conventional ;  it  is  the  same  even  with  animals  and  the  human  figure ;  every 
saint  had  his  prescribed  colours,  proportions,  and  symbols. 

The  Saracenic  was  the  period  of  gorgeous  diapers  (Figs.  1722  and  1723),  for 
their  habit  of  decorating  the  entire  surfaces  of  their  apartments  was  highly 
favourable  to  the  development  of  this  class  of  design.  The  Alhambra  displays 
almost  endless  specimens,  and  all  are  in  relief  and  enriched  with  gold  and  colour, 
chiefly  blue  and  red.  The  religious  cycles  and  symbolic  figures  of  the  By- 
zantine are  excluded.  Mere  curves  and  angles  or  interlacings  were  now  to  bear 
the  chief  burden  of  a  design,  but  distinguished  by  a  variety  of  colour.  The 
curves,  however,  very  naturally  fell  into  standard  forms  and  floral  shapes,  and 


686 


ARCHITECTURAL   CONSTRUCTION. 


the  lines  and  angles  were  soon  developed  into  a  very  characteristic  species  of 
tracery,  or  interlaid  strap- work,  very  agreeably  diversified  by  the  ornamental 


FIG.  1733. 


introduction  of  the  inscriptions,  which  last  custom  of  elaborating  inscriptions 
with  their  designs  was  peculiarly  Saracenic.  Although  flowers  were  not  palpa- 
bly admitted,  yet  the  great  mass  of  the  minor  details  of  Saracenic  designs  are 
composed  of  flower  forms  disguised — the  very  inscriptions  are  sometimes  thus 
grouped  as  flowers ;  still,  no  actual  flower  ever  occurs,  as  the  exclusion  of  all 
natural  images  is  fundamental  to  the  style  in  its  purity. 

All  the  symbolic  elements  of  the  Byzantine  are  continued  in  the  Gothic. 
Ornamentally,  the  Gothic  is  the  geometrical  and  pointed  element  elaborated  to 
the  utmost ;  its  only  peculiarities  are  its  combinations  of  details ;  at  first  the 
conventional  and  geometrical  prevailing,  and  afterward  these  combined  with 
the  elaboration  of  natural  objects  in  its  decoration.  The  most  striking  feature 
of  all  Gothic  work  is  the  wonderful  elaboration  of  its  geometric  tracery ;  vesi- 
cas,  trefoils,  quatrefoils,  cinquefoils,  and  an  infinity  of  geometric  varieties  be- 
sides. The  tracery  is  so  paramount  a  characteristic  that  the  three  English 
varieties,  the  early  English,  the  decorated,  and  the  perpendicular,  and  the 
French  flamboyant,  are  distinguished  almost  exclusively  by  this  feature.  (See 
Figs.  1661  to  1665.) 

The  ornamental  mouldings  used  in  the  decorative  details  are  numerous, 
among  which  the  more  common  is  the  chevron  or  zigzag  (Fig.  1724),  simple 
as  the  indented,  or  duplicated,  triplicated,  or  quadrupled  ;  the  billet,  the  pris- 
matic billet,  the  square  billet,  and  the  alternate  billet  (Fig.  1725) ;  the  star 
(Fig.  1726),  the  fir-cone;  the  cable  (Fig.  1727);  the  embattled  (Fig.  1728); 
the  nail-head  (Fig.  1729) ;  the  dog-tooth  (Fig.  1730) ;  the  ball-flower  (Fig. 
1731) ;  and  the  serpentine  vine-scroll. 


Fio.  1724. 


FIG.  1725. 


FIG.  17^6. 


The  crocket,  in  its  earliest  form,  was  the  simple  arrow-head  of  the  episco- 
pal pastoral  staff ;  subsequently  finished  with  a  trefoil,  and  afterward  still  fur- 
ther enriched.  Figs.  1732  and  1733  are  early  English  crockets;  Fig.  1734  a 
decorated  one.  Fig.  1735  is  a  finial  of  the  same  style.  Both  finials  and  crock- 
ets in  detail  display  a  variety  of  forms. 


ARCHITECTURAL  CONSTRUCTION. 


687 


The  parapets  of  the  early  English  style  are  often  a  simple  horizontal  course, 
supported  by  a  corbel  table,  sometimes  relieved  by  a  series  of  sunk  blank  trefoil- 


FIG.  1728. 


FIG.  1727. 


FIG.  1729. 

headed  panels ;  sometimes 
a  low  embattled  parapet 
crowns  the  wall.  In  the 
decorated  style  the  hori- 
zontal parapet  is  some- 
times pierced  with  trefoils,  sometimes  with  wavy,  flowing  tracery  (Fig.  1736). 
Grotesque  spouts  or  gargoyles  discharge  the  water  from  the  gutters.  The  para- 


FIG.  1730. 


FIG.  1731. 


FIG.  1732. 


FIG.  1734. 


FIG.  1733. 


FIG.  1735. 


pets  of  the  perpendicular  style  are  frequently  embattled  (Fig.  1737),  covered 
with  sunk  or  pierced  panelling,  and  ornamented  with  quatrefoil,  or  small  tre- 


FIG.  1737. 


FIG.  1736. 


foil-headed  arches  ;  sometimes  not  em- 
battled but  covered  with  sunk  or 
pierced  quatrefoils  in  circles,  or  with 
trefoils  in  triangular  spaces,  as  in  Fig. 


m 


FlG-  ir38> 


Among  the  varieties  of  ornamental 
work,  the  mode  of  covering  small  plain  surfaces  with  diapering  (Fig.  1739) 
was  sometimes  used,  the  design  being  in  exact  accordance  with  the  architec- 


688 


ARCHITECTURAL  CONSTRUCTION. 


tural  features  and  details  of  the  style.     The  rose  (Fig.  1740),  the  badge  of  the 
houses  of  York  and  Lancaster,  is  often  met  with  in  the  perpendicular  style ; 


FIG.  1740. 


FIG.  1739. 

and  tendrils,  leaves,  and  fruit  of  the  vine  are  carved  in  great  profusion  in  the 
hollows  of  rich  cornice  mouldings,  especially  on  screen-work  in  the  interior  of 
a  church.  Fig.  1741,  in  its  original  type  a  Byzantine  ornament,  an  alternate 
lily  and  cross,  is  a  common  finish  to  the  cornice  of  rich  screen-work  in  the  lat- 
est Gothic,  and  is  known  under  the  name  of  the  Tudor  flower. 

Sculptured  foliage  (Figs.  1742  to  1747) 
is  much  used  in  capitals,  brackets,  corbels, 
bosses,  and  crockets.  Among  the  forms  of 
foliage  the  trefoil  is  most  predominant. 

The  Ornaments  of  the  Renaissance. — The 
term  Eeuaissance  is  used  in  a  double  sense; 
Flo  1741  in  a  general  sense   implying  the  revival  of 

art,  and  specially  signifying  a  peculiar  style 

of  ornament.  It  is  also  sometimes,  in  a  very  confined  sense,  applied  in  refer- 
ence to  ornament  of  the  style  of  Benvenuto  Cellini ;  or,  as  it  is  sometimes  des- 
ignated, the  Henry  II  (of  France)  style. 

The  mixture  of  various  elements  is  one  of  the  essentials  of  this  style.    These 


Fio.  1742. 


FIG.  1743. 


FIG.  1744. 


FIG.  1745. 


FIG.  1? 


FIG.  1747. 


ARCHITECTURAL  CONSTRUCTION. 


689 


elements  are  the  classical  ornaments ;  unnatural  and  natural  flowers  and  foil- 
asre;  men  and  animals,  natural  and  grotesque;    cartouches,  or  pierced  and 

shields,   in    great    promi- 


scrolled 

nence  ;   tracery    independent, 


and 


developed  from  the  scrolls  of  the 
cartouches ,  and  jewel  forms  (Figs. 
1748  and  1749). 

The  Elizabethan  is  a  partial 
elaboration  of  the  same  style;  the 
present  Elizabethan  exhibits  a  very 
striking  preponderance  of  strap  and 
shield  work  ;  but  the  earlier  is 
much  nearer  allied  to  the  Continen- 
tal styles  of  the  time,  classical  orna- 
ments but  rude  in  detail,  occasional 
scroll  and  arabesque  work,  and  strap- 
work,  holding  a  much  more  promi- 
nent place  than  the  pierced  or 
scrolled  shields.  Fig.  1750  is  an  ex- 
ample of  the  style  from  the  old 
guard  chamber,  Westminster. 

Of  the   earliest  and   transition 

styles  of  Renaissance  ornament  are  the  Tricento  and  the  Quatrecento.  The 
great  features  of  the  first  are  its  intricate  tracery  and  delicate  scroll-work  of 
conventional  foliage,  the  style  being  but  a  slight  remove  from  the  Byzantine 
and  Saracenic ;  of  the  second,  elaborate  natural  imitations  of  fruit,  flowers, 
birds,  or  animals  (Fig.  1751),  all  disposed  simply  with  a  view  to  the  ornamen- 
tal ;  also  occasional  cartouches,  or  scrolled  shield-work. 


FIG.  1743. 


FIG.  1749. 

The  Renaissance  is  something  more  approximative  to  a  combination  of  pre- 
vious styles  than  a  revival  of  any  in  particular,  developed  solely  on  aesthetic 
principles,  from  a  love  of  the  forms  and  harmonies  themselves,  as  varieties  of 
effect  and  arrangements  of  beauty,  not  because  they  had  any  particular  signi- 
fication, or  from  any  superstitious  attachment  to  them  as  heirlooms. 

Fig.  1752  is  an  example  of  ornament  in  the  Cinquecento  style.  The  ara- 
besque scroll-work  is  the  most  prominent  feature  of  the  Cinquecento,  and  with 
this  in  its  elements,  it  combines  every  other  feature  of  classical  art,  with  the 
unlimited  choice  of  natural  and  conventional  imitations  from  the  entire  animal 
45 


690 


ARCHITECTURAL  CONSTRUCTION. 


and  vegetable  kingdom,  both  arbitrarily  disposed  and  combined.  Absolute 
works  of  art,  such  as  vases  and  implements,  and  instruments  of  all  kinds,  are 
prominent  elements  of 
the  Cinquecento  ara- 
besque, but  cartouches 
and  strap-work  wholly 


FIG.  1750. 


FIQ.  1751. 


FIG.  1752. 


disappear  from  the  best  examples.     Another  chief  feature  of  the  Cinquecento 
is  the  admirable  play  of  colour  in  its  arabesques  and  scrolls ;  and  it  is  worthy 

of  note  that  the  three  secondary  colours — 
orange,  green,  and  purple — perform  the  chief 
parts  in  all  the  coloured  decorations. 

Fig.  1753  is  an  example  of  the  Louis 
Quatorze  style  of  ornament.  The  great  medi- 
um of  this  style  was  gilt  stucco-work,  and 
this  absence  of  colour  seems  to  have  led  to  its 
most  striking  characteristic,  infinite  play  of 
light,  of  shade  ;  colour,  or  mere  beauty  of  form 
in  detail,  having  no  part  in  it  whatever.  Flat 
surfaces  are  not  admitted ;  all  are  concave  or 
convex  :  this  constant  varying  of  the  surface 
gives  every  point  of  view  its  high  lights  and 
brilliant  contrasts. 

The  Louis  Quinze  style  differs  from  that 
of   Louis   Quatorze   chiefly  in  its  absence  of 
symmetry  ;  in  many  of  its  examples  it  is  an 
almost  random   dispersion  of  the  scroll  and 
shell,  mixed  only  with  that  peculiar  crimping  of  shell-work,  the  coquillage. 


FIG.  1753. 


ARCHITECTURAL  CONSTRUCTION.  691 

The  ornaments  of  which  we  have  thus  given  examples  are,  in  general, 
applied  to  interior  decorations,  to  friezes,  pilasters,  panels,  architraves,  the 
faces  and  soffits  of  arches,  ceilings,  etc.,  to  furniture,  and  to  art-manufactures 
in  general.  For  exteriors  these  ornaments  are  sparingly  applied  ;  shield  and 
scroll-work,  of  the  later  Elizabethan  or  Eenaissance  style,  is  sometimes  used, 
but  very  seldom  tracery. 

Principles  of  Design. — Professedly  treating  of  architecture  only  in  its  most 
mechanical  phase  of  drawing,  the  history  of  it  as  an  art,  and  the  distinctions 
of  styles,  have  been  but  briefly  treated.  To  one  anxious  to  acquire  knowledge 
in  this  department  we  refer,  as  the  very  best  compendium  within  our  knowl- 
edge, to  Ferguson's  "  Hand-Book  of  Architecture."  The  study  of  this  work 
will  give  direction  to  a  person's  observation,  but,  without  referring  to  actual 
examples,  mere  reading  will  be  of  little  use.  Drawings  give  general  ideas  of 
the  character  of  buildings,  but  no  idea  of  size  or  of  the  surroundings  of  a 
building.  Many  a  weak  design,  especially  in  cast-iron  buildings,  acquires  a 
sort  of  strength  by  the  number  of  its  repetitions,  giving  an  idea  of  extent ;  and 
many  a  beautiful  design  on  paper  has  failed  in  its  execution,  being  dwarfed  by 
its  surroundings.  With  regard  to  the  style  of  a  building,  there  are  none  of  the 
ancient  styles  in  their  purity  adapted  to  present  requirements ;  our  churches 
and  theatres  are  more  for  the  gratification  of  the  ear  than  the  eye,  and  the 
comforts  of  our  domestic  architecture,  and  the  requirements  of  our  stores  and 
warehouses,  are  almost  the  growth  of  the  present  century.  For  a  design,  look 
first  to  the  requirements  of  the  structure,  the  purposes  to  which  it  is  to  be 
applied  ;  sketch  the  plan  first,  arrange  the  divisions  of  rooms,  the  openings  for 
doors  and  windows,  construct  the  sections,  and  then  the  elevations,  first  in 
plain  outline  ;  modify  each  by  the  exigencies  of  construction. 

"  Construction,  including  in  the  term  the  disposition  of  a  building  in  ref- 
erence to  its  uses,  is  by  some  supposed  to  be  the  common  part  of  the  art  of 
architecture,  but  it  is  really  the  bone,  muscle,  and  nerve  of  architecture,  and 
the  arts  of  construction  are  those  to  which  the  true  architect  will  look,  rather 
than  to  rules  and  examples,  for  the  means  of  producing  two  at  least  of  the 
three  essential  conditions  of  building  well,  commodity,  firmness,  and  delight, 
which  conditions  have  been  aptly  said  to  be  the  end  of  architecture  as  of  all 
creative  arts. 

"  The  two  great  principles  of  the  art  are :  First,  that  there  should  be  no 
features  about  a  building  which  are  not  necessary  for  convenience,  construc- 
tion, or  propriety ;  second,  that  all  ornament  should  consist  of  enrichment  of 
the  essential  construction  of  the  building. 

"  The  neglect  of  these  two  rules  is  the  cause  of  all  the  bad  architecture  of 
the  present  time.  Architectural  features  are  continually  tacked  on  buildings 
with  which  they  have  no  connection,  merely  for  the  sake  of  what  is  termed 
effect,  and  ornaments  are  continually  constructed  instead  of  forming  the  deco- 
ration of  construction  to  which  in  good  taste  they  should  always  be  subservient. 
The  taste  of  the  artist  ought  to  be  held  merely  ancillary  to  truthful  disposition 
•  for  structure  and  service.  The  soundest  construction  is  the  most  apt  in  the 
production,  or  the  reproduction,  it  may  be,  of  real  art.  The  Eddystone  Light- 
house is  well  adapted  to  its  uses ;  it  is  commodious,  firm  and  stable  almost  to  a 
miracle,  and  its  form  is  as  beautiful  in  outline  to  the  delight  of  the  eye  as  it  is 


(592  ARCHITECTURAL  CONSTRUCTION. 

well  adapted  to  break  and  mitigate  the  force  of  the  sea  in  defence  of  its  own 
structure.  The  English  Exhibition  Building  of  1851  was  most  commodious  for 
the  purposes  of  an  exhibition,  firm  enough  for  the  temporary  purpose  required 
of  it,  and  there  was  delight  in  the  simplicity  and  truth  of  its  combinations ;  and 
all  this  may  be  said  to  have  grown  out  of  propriety  of  construction,  as  applied 
to  the  material,  cast-iron.  The  use  of  unfitting  material,  or  fitting  material 
inappropriately,  leads  almost  entirely  to  incommodiousness,  infirmity,  and 
offence,  or  some  of  them. 

"  Out  of  truth  in  structure,  and  that  structure  of  a  very  inartificial  sort, 
grow  the  beautiful  forms  of  the  admirable  proportions  found  in  the  works  of 
the  Greeks ;  and  out  of  truth  in  structure,  with  the  strictest  regard  to  the  ne- 
cessities of  the  composition  and  of  the  material  employed,  and  that  structure 
as  full  of  artifice  as  the  artifice  employed  is  of  truth  and  simplicity,  grew  the 
classical  works  vulgarly  called  Gothic,  but  now  characteristically  designated  as 
Pointed,  from  the  arch  which  is  the  basis  of  the  style.  Structural  untruth  is 
not  to  be  justified  by  authority ;  neither  Sir  Christopher  Wren,  nor  the  Athe- 
nian exemplars  of  Doric  or  Ionic  in  the  Propylaeum  and  in  the  Minerva  Polias, 
with  their  irregular  and  inordinately  wide  intercolumniation,  can  persuade 
even  the  untutored  eye  to  accept  weakness  for  strength, -or  what  is  false  for 
truth. 

"  The  Greek  examples  offer  the  most  beautiful  forms  for  mouldings,  and 
the  Grecian  mode  of  enriching  them  is  unsurpassed.  It  should  be  borne  in 
mind  that  the  object  in  architectural  enrichment  is  not  to  show  ornament,  but 
to  enrich  the  surface  by  producing  an  effective  and  pleasing  variety  of  light  and 
shade;  but  still,  although  ornament  should  be  a  secondary  consideration,  it 
will  develop  itself,  and  therefore  should  be  of  elegant  form  and  composition." 

We  have  quoted  thus  at  some  length  from  the  article  "Architecture," 
"  Encyclopaedia  Britanuica,"  because  with  many  authority  is  necessary,  and 
they  distrust  their  own  powers  of  observation  and  analysis ;  all  must  feel  the 
truth  of  the  above,  but  in  practice  it  is  very  little  appreciated  or  carried  out. 
The  present  taste  in  architecture,  as  in  the  theatre,  is  for  the  spectacular; 
breadth  or  dignity  of  effect  is  not  popular ;  edifices  are  not  only  covered  with, 
but  built  up  in  ornament ;  and  construction  is  but  secondary.  The  French, 
having  a  building-stone  that  is  very  easily  worked,  cut  merely  the  joints,  leav- 
ing the  rough  outer  surface  to  be  worked  after  it  is  laid ;  chopping  out  mould- 
ings and  ornaments  almost  as  readily  as  though  it  were  in  plaster,  and  the  sur- 
face when  finished  is  covered  with  enrichments  in  low  relief.  The  fashion  thus 
set  is  imitated  in  this  country  at  immense  cost,  in  the  most  unfitting  materials, 
marble  and  granite.  Our  architectural  buildings  express  fitly  our  condition — 
a  rich  country,  recent  and  easily  acquired  wealth,  and  a  desire  and  rivalry  to 
exhibit  it,  or  a  display  as  a  means  of  advertising,  and  in  this  truth  of  expression 
will  have  an  archaeological  interest;  although  it  does  not  contribute  much  to 
present  excellence  in  construction,  it  still  has  this  value :  that  the  architect  or 
constructor  need  be  governed  by  no  rules  or  principles — he  can  make  experi- 
ments on  a  pretty  extensive  scale,  and  out  of  much  bad  construction  even  forms 
and  ornament  may  spring  up  which  will  stand  the  test  of  time,  and  form  a 
nucleus  of  a  new  style  adapted  to  the  present  wants. 

Cast-iron  as  a  building  material,  with  the  exception  of  exhibition  buildings, 


ARCHITECTURAL  CONSTRUCTION.  (593 

has  seldom  been  treated  distinctively ;  buildings  erected  with  it  have  been 
copies  of  those  in  stone,  and  have  been  even  imitated  in  colour.  For  the  first 
story  of  stores,  where  space  is  necessary  for  light  and  the  exhibition  of  wares, 
cast-iron  columns  are  almost  invariably  used,  but  are  objected  to  architecturally, 
that  they  look  too  weak  for  the  support  of  the  piles  of  brick  and  stone  above 
them.  The  objection  should  not  be  to  the  use,  but  that  the  truth  of  the  ade- 
quate strength  of  the  cast-iron  is  not  conveyed  by  the  form  or  col^-1  • 
one  objects  that  the  ankles  of  Atlas  look  too  light  to  support  the  massive  ngure 
and  globe,  or  wishes  him  seated  to  give  the  idea  of  stability ;  so  if  the  columns 
and  lintels  were  some  other  form  than  Greek  or  Roman  with  immense  inter- 
columniations,  and  coloured  fitly,  the  appearance  of  weakness  would  be  entirely 
lost  sight  of. 

Improvements  in  the  manufacture  of  iron  and  steel  have  led  up  to  the 
skeleton  construction  (page  565) — frames  of  cast  or  rolled  iron  and  steel  framed 
and  set  before  any  of  the  nr  onry  except  that  of  the  foundations  is  laid.  All 
the  columns,  girders,  and  Learns  are  bolted  together,  built  into,  and  covered 
with  masonry  to  add  to  the  rigidity  of  the  structure  and  for  protection  against 
fire.  The  framing  is  square,  but,  for  variety  and  design,  arches,  soffits,  and  orna- 
mental clothing  is  made  in  masonry.  Little  in  exterior  form  can  be  considered 
a  necessity  of  construction,  and  there  is  as  yet  no  standard  of  finish.  The 
function  of  the  metal,  like  the  bone  in  the  animal  structure,  is  to  give  strength 
to  sustain  it ;  the  masonry  is  the  muscle  to  stiffen,  protect,  and  ornament  it. 
Constructive  expedients,  like  roofs,  reduce  the  appearance  of  height,  and  are 
objectionable  from  the  necessity  of  gutters  and  leaders. 

In  conclusion,  the  draughtsman  should  be  conversant  with  classic  and  later 
styles ;  still,  as  he  must  design  to  suit  the  necessities  of  the  times,  and  the 
requirements  of  present  tastes  and  fashions  of  buildings,  he  should  keep  him- 
self posted  on  what  is  being  done,  and  he  will  find  it  very  convenient  to  have  a 
scrap-book  of  cuts  from  which  to  draw  parts  of  a  design,  and  afford  him  ready 
means  of  combinations.  He  will  find  much  in  illustrated  magazines  and  news- 
papers, many  cuts  unpromising  as  a  whole,  yet  fruitful  in  suggestions  of  parts ; 
many  an  agreeable  outline  unsatisfactorily  filled  up  ;  many  that  are  only  valuable 
as  showing  dimensions  requisite  for  certain  uses.  But  the  larger  the  collection 
the  better  for  the  draughtsman ;  it  will  save  time  to  know,  as  far  as  possible, 
what  has  been  done,  that  he  may  judge  what  forms  and  proportions  it  will  be 
best  for  him  to  use,  and  what  to  avoid. 

It  has  been  our  practice  to  select,  from  papers  and  magazines,  cuts  which 
we  considered  of  value,  and  arrange  them  in  scrap-books  with  appropriate 
headings.  In  the  Appendix  a  few  pages  of  "  scraps  "  are  given  as  illustrations. 


ISOMETRICAL   DRAWING. 


PROFESSOR  FARISH,  of  Cambridge,  has  given  the  term  Isometrical  Per- 
spective to  a  particular  projection  which  represents  a  cube,  as  in  Fig.  1754. 
The  words  imply  that  the  measure  of  the  representations  of  the  lines  forming 
the  sides  of  each  face  are  equal. 

The  principle  of  isometric  representation  consists  in  selecting,  for  the  plane 
of  the  projection,  one  equally  inclined  to  three  principal  axes,  at  right  angles 
to  each  other,  so  that  all  straight  lines 
coincident  with  or  parallel  to  these 
axes  are  drawn  in  projection  to  the 


FIG.  1754. 


same  scale.  The  axes  are  called  iso- 
metric axes,  and  all  lines  parallel  to 
them  are  called  isometric  lines.  The 

planes  containing  the  isometric  axes  are  isometric  planes ;  the  point  in  the 
object  projected,  assumed  as  the  origin  of  the  axes,  is  called  the  regulating- 
point. 

To  draw  the  isometrical  projection  of  a  cube  (Fig.  1755),  draw  the  horizontal 
line  A  B  indefinitely ;  at  the  point  D  erect  the  perpendicular  D  F,  equal  to  one 
side  of  the  cube  required;  through  D  draw  the  lines  D  b  and  D/to  the  right 
and  left,  making/D  B  and  b  D  A  each  equal  an  angle  of  30°.  Consequently, 
the  angles  F  D/  and  FD  b  are  each  equal  to  60°.  Make  D  I  and  D/each 
equal  to  the  side  of  the  cube,  and  at  b  and /erect  perpendiculars,  making  ba 
and/e  each  equal  to  the  side  of  the  cube  ;  connect  F  a  and  F  e,  and  draw  eg 
parallel  to  a  F,  and  a  g  parallel  to  F  e,  and  we  obtain  the  projection  of  the 
cube. 

If  from  the  point  F,  with  a  radius  F  D,  a  circle  be  described,  and  com- 
mencing at  the  point  D,  radii  be  laid  off  around  the  circumference,  forming  a 

694 


ISOMETRICAL  DRAWING. 


695 


regular  inscribed  hexagon,  and  the  points  D  a  e  be  connected  with  the  centre 
of  the  circle  F,  we  have  an  isometrical  representation  of  a  cube.  The  point  D 
is  called  the  regulating -point. 

On  page  123,  Fig.  255,  is  shown  the 
orthographic  projection  of  a  parallelo- 
pipedon  on  the  several  planes,  and  Fig. 
254  the  revolution  of  these  planes  and 
their  cubical  representation.  Fig.  1756  is 
the  representation  of  the  same  solid  in  iso- 
metric perspective,  producing  nearly  the 
same  effect.  Measures  are  transferred  di- 
rectly from  plans  and  elevations  in  or- 
thographic projections  to  those  in  isom- 
etry.  The  isometric  scale  adopted  ap- 
plies only  to  isometric  lines,  as  F  D,  F  a, 
and  F  e  (Fig.  1755),  or  lines  parallel 
thereto ;  the  diagonals  which  are  equal  to 
each  other,  and  longer  than  the  sides  of 
the  cube,  are  the  one  less,  the  other  greater. 

Understanding  the  isometrical  projec- 
tion of  a  cube,  any  surface  or  solid  may  be 
similarly  constructed,  since  it  is  easy  to 
suppose  a  cube  sufficiently  large  to  con- 
tain within  it  the  whole  of  the  model  in- 
tended to  be  represented,  and,  as  hereafter 
will  be  further  illustrated,  the  position  of 

any  point  on  or  within  the  cube,  the  direction  of  any  line,  or  the  inclination  of 
any  plane  to  which  it  may  be  cut,  can  be  easily  ascertained  and  represented. 

In  Figs.  1754  and  1755  one  face  of  the  cube  appears  horizontal,  and  the 
other  two  faces  appear  vertical.     If  now  the  figures  be  inverted,  that  which 


Fio.  1756. 


FIG.  1757. 


Fio.  1759. 


696 


ISOMETRICAL  DRAWING. 


before  appeared  to  be  the  top  of  the  object  will  now  appear  to  be  its  under 
side. 

The  angle  of  the  cube  formed  by  the  three  radii  meeting  in  the  centre  of 
the  hexagon  may  be  made  to  appear  either  an  internal  or  external  angle,  in 
the  one  case  the  faces  representing  the  interior,  and  in  the  other  the  exterior  of 
a  cube. 

Figs.  1757,  1758,  and  1759  illustrate  the  application  of  isometrical  drawing 
to  simple  combinations  of  the  cube  and  parallelopipedon.  The  mode  of  con- 
struction of  these  figures  will  be  easily  understood  by  inspection,  as  they  con- 
tain no  lines  except  isometrical  ones. 

To  draw  Angles  to  the  Boundary  Lines  of  an  Isometrical  Cube. — Draw  a 
square  (Fig.  1760)  whose  sides  are  equal  to  those  of  the  isometrical  cube  A 


(Fig.  1761),  and  from  any  of  its  angles  describe  a  quadrant,  which  divide 
into  90°,  and  draw  radii  through  the  divisions  meeting  the  sides  of  the  square. 
These  will  then  form  a  scale  to  be  applied  to  the  faces  of  the  cube ;  thus,  on 
D  E,  or  any  other,  by  making  the  same  divisions  along  their  respective  edges. 

As  the  figure  is  bounded  by  twelve  isometrical  lines,  and  the  scale  of  tan- 
gents may  be  applied  two  ways  to  each,  it  can  be  applied  therefore  twenty-four 
ways  in  all,  affording  a  simple  means  of  drawing,  on  the  isometrical  faces  of 
the  cube,  lines  at  any  angles  with  their  boundaries. 

Figs.  1762  to  1767  show  the  section  of  the  cube  by  single  planes,  at  various 
inclinations  to  the  faces  of  the  cubes.  Figs.  1768  and  1769  are  the  same  cube, 
but  turned  round,  with  pieces  cut  out  of  it.  Fig.  1770  is  a  cube  cut  by  two 
planes  forming  the  projection  of  a  roof.  Fig.  1771  is  a  cube  with  all  of  the 
angles  cut  off  by  planes,  so  as  to  leave  each  face  an  octagon.  Fig.  1772  repre- 
sents the  angles  cut  off  by  planes  perpendicular  to  the  base  of  the  cube,  form- 
ing thereby  a  regular  octagonal  prism.  By  drawing  lines  from  each  of  the 
angles  of  an  octagonal  base  to  the  centre  point  of  the  upper  face  of  the  cube, 
we  have  the  isometrical  representation  of  an  octagonal  pyramid. 

As  the  lines  of  construction  have  all  been  retained  in  these  figures,  they  will 
be  easily  understood  and  copied,  and  are  sufficient  illustrations  of  the  method 
of  representing  any  solid  by  inclosing  it  in  a  cube. 


ISOMETRICAL  DRAWING. 


697 


FIG.  1763. 


FIG.  1763. 


FIG.  1761. 


FIG.  1765. 


FIG.  17C6. 


FIG.  1767. 


FIG.  1768. 


FIG.  1769. 


FIH.  1770. 


FIG.  1772. 


698 


ISOMETRICAL   DRAWING. 


In  the  application  of  this  species  of  projection  to  curved  lines,  let  A  B 
(Fig.  1773)  be  the  side  of  a  cube  with  a  circle  inscribed ;  and  all  the  faces  of  a 
cube  are  to  have  similarly  inscribed  circles.  Draw  the  diagonals  A  B,  0  D,  and 
at  their  intersection  with  the  circumference,  lines  parallel  to  A  C,  B  D.  Now 


FIG.  1773. 


FIG.  1774. 

draw  the  isometrical  projection  of  the  cube  (Fig.  1774),  and  lay  out  on  the 
several  faces  the  diagonals  and  the  parallels ;  the  projection  of  the  circle  will 
be  an  ellipse,  of  which  the  diagonals  being  the  axes,  their  extremities  are  de- 
fined by  their  intersections  /6,  e  5,  a  2,  b  1,  d  3,  c  4,  with  the  parallels  ;  having 
thus  the  major  and  minor  axes,  construct  the  ellipse  by  the  trammel,  or,  since 
the  curve  is  tangent  at  the  centre  of  the  sides,  we  have  eight  points  in  the 
curve ;  it  may  be  put  in  by  curves  or  by  the  hand. 

To  divide  the  Circumference  of  a  Circle. — First  method:  On  the  centre  of 
the  line  A  B  (Fig.  1775)  erect  a  perpendicular,  C  D,  making  it  equal  to  C  A  or 
C  B ;  then  from  D,  with  any  radius,  describe  an  arc  and  divide  it  in  the  ratio 


FIG.  1775. 


ISOMETRICAL   DRAWING. 


699 


required,  and  draw  through  the  divisions  radii  from  D  meeting  A  B  ;  then 
from  the  isometric  centre  of  the~  circle  draw  radii  from  the  divisions  on  A  B, 
cutting  the  circumference  in  the  points  required. 

Second  method :  On  the  major  axis  of  the  ellipse  describe  a  semicircle,  and 
divide  it  in  the  manner  required.     Through  the  points  of  division  draw  lines 


FIG.  1777. 

perpendicular  to  A  E,  which  will  divide  the  circumference  of  the  ellipse  in  the 
same  ratio.  On  the  right  hand  of  the  figure  both  methods  are  shown  in  com- 
bination, and  the  intersections  of  the  lines  give  the  points  in  the  ellipse. 

Fig.  1776  is  an  isometrical  projection  of  a  bevel-wheel,  with  a  half-plan 
(Fig.  1777)  beneath,  and  projected  lines  explanatory  of  the  method  to  be 
adopted  in  drawing  the  teeth,  and  of  which  only  half  are  shown  as  cut.  It 
will  be  seen,  by  reference  to  the  second  method  given  above  for  the  division  of 
the  circumference  of  a  circle,  that  the  semicircle  is  described  directly  on  the 
major  axis  of  the  ellipse.  In  practice  it  will  be  found  more  convenient,  when 
a  full  drawing  is  to  be  made,  to  draw  the  semicircle  on  a  line  parallel  to  the 
major  axis,  and  entirely  without  the  lines  of  the  main  drawing ;  and  also,  as  in 
the  example  of  the  bevel-gear,  complete  on  the  semicircle,  or  half-plan,  the 
drawings  of  all  lines,  the  intersections  of  which  with  circles  it  will  be  necessary 
to  project  on  the  isometrical  drawing. 

Fig.  1778  is  an  isometrical  projection  of  a  complete  pillow-block,  with  its 
hold-down  bolts.  By  reference  to  Fig.  700  and  Figs.  563  and  564,  it  will  be 


700 


ISOMETRIC  A  L  DRAWING. 


FIG.  1778. 


seen  how  graphically  these  forms  of  gearing  are  given  by  isometry.     Fig.  1779 
is  an  isometrical  projection  of  a  water-closet  cistern  with  a  standard  waste. 


FIG.  1 


ISOMETRICAL  DRAWING. 


701 


702 


ISOMETRICAL   DRAWING. 


Fig.  1780  is  an  isometrical  projection  of  a  culvert,  such  as  were  built  be- 
neath the  Croton  Aqueduct. 

Fig.  1016  is  an  isometrical  view  of  the  overflow  and  outlet  of  the  Victoria 
and  Eegent  Street  sewers  in  the  Thames  embankment. 

Fig.  1781  is  an  isometrical  elevation  of  the  roof-truss  (Fig.  1151). 

Figs.  1782  and  1783  are  the  elevation  and  section  in  isometry  of  the  district 
school-house  given  in  Figs.  1495  and  1496.  To  bring  the  drawing  within  the 
limits  of  the  page,  the  scale  has  been  necessarily  reduced,  but  it  is  given  in 
the  figure  as  it  should  always  be,  either  drawn  or  written,  on  all  drawings 
to  a  scale,  not  intended  for  mere  pictures  or  illustrations.  The  section  is 
drawn  at  the  height  of  8  feet  above  the  base  course,  and  higher  than  is  usual 
in  such  sections,  but  it  was  necessary  on  account  of  the  extra  height  of  the 
window-sill  above  the  floor,  desirable  in  all  school-rooms.  Fig.  1783  is  more 


FIG.  1781. 

graphic  than  the  plan  (Fig.  1496),  especially  when  more  detail  is  to  be  shown, 
but  there  is  nothing  in  the  present  drawing  that  can  not  be  nearly  as  well 
shown  by  the  plan ;  and  to  a  mechanic,  for  the  purposes  of  construction,  the 
plan  is  the  simpler. 

By  comparing  the  elevation  (Fig.  1782)  with  the  perspective  (Fig.  1799), 
the  former  appears  distorted  and  out  of  drawing,  but  it  is  much  more  readily 


ISOMETRICAL  DRAWING. 


703 


FIG.  1783. 


704 


ISOMETRICAL  DRAWING. 


drawn,  and  has  this  great  convenience,  that  it  is  drawn  to  and  can  be  measured 
by  a  scale  on  the  isometric  lines. 

Fig.  1784  is  the  isometrical  projection,  of  the  wave-line  principle,  of  ship 


\\\\\\\\\\ 
\\\\\\\\X\ 


FIG.  1784. 


construction,  from   Russell's  "Naval  Architecture" — as  explained  and  illus- 
trated on  pages  545,  546,  and  54.7. 


ISOMETRICAL   DRAWING. 


705 


PERSPECTIVE   DRAWING. 


THE  science  of  Perspective  is  the  representation  by  geometrical  rules,  upon 
a  plane  surface,  of  objects  as  they  appear  to  the  eye,  from  any  point  of  view. 

All  the  points  of  the  surface  of  a  body  are  visible  by  means  of  luminous 
rays  proceeding  from  these  points  to  the  eye.  Thus,  let  the  line  A  B  .(Fig. 
1785)  be  placed  before  the  eye,  C,  the  lines  drawn  from  the  different  points  1, 
2,  3,  4,  etc.,  represent  the  visual  rays  emanating  from  each  of  these  points.  If 
in  the  place  of  a  line  a  surface  is  substituted,  the  result  will  be  a  pyramid  of 
rays. 

The  greatest  angle  under  which  one  or  more  objects  can  be  distinctly  seen 
is  one  of  90°.  If  between  the  object  and  the  eye  there  be  interposed  a  trans- 
parent plane,  the  intersections  of  this  plane  with  the  visual  rays  are  termed 

perspectives  of  the  points  from  which  the 
rays  emanate.  In  the  operations  of  projec- 
tion, several  important  planes  are  employed 
in  perspective,  as : 

1.  The  horizontal  plane  A  B  (Fig.  1786), 
on  which  the  spectator  and  the  object  viewed 
are  supposed  to  stand,  for  convenience  sup- 
posed perfectly  level,  is  termed  the  ground 
plane. 

2.  The  plane  G  N,  which  has  been  con- 
sidered as  a  transparent  plane  placed  in  front 
of  the  spectator,  on  which  the  objects  are 

delineated,  is  called  the  plane  of  perspective  or  the  plane  of  the  picture.  The 
intersection  G  L  of  the  first  and  second  planes  is  called  the  line  of  projection, 
the  ground,  or  base  line  of  the  picture. 

3.  The  plane  E  F  passing  horizontally  through  the  eye  of  the  spectator,  and 
cutting  the  plane  of  the  picture  at  right  angles,  is  called  the  horizontal  plane, 
and  its  intersection  at  D  D  with  the  plane  of  the  picture  is  called  the  horizon 
line,  the  horizon  of  the  picture,  or  simply  the  horizon. 

706 


FlO.  1785. 


PERSPECTIVE   DRAWING. 


707 


4.  The  plane  S  T  passing  vertically  through  the  eye  of  the  spectator,  and 
cutting  each  of  the  other  planes  at  a  right  angle,  is  called  the  central  plane. 

Point  of  view,  or  point  of  sight,  is  the  point  where  the  eye  is  supposed  to 
be  placed  to  view  the  object,  as  at  C,  and  is  the  vertex  of  the  optical  pyramid. 
Its  projection  on  the  ground  plane  at  S  is  termed  the  station  point. 


FIG.  1786. 

The  projection  of  any  point  on  the  ground  plane  is  called  the  seat  of  that 
point. 

Centre  of  view,  or  centre  of  picture  (commonly,  though  erroneously,  called 
the  point  of  sight),  is  the  point  V  where  the  central  vertical  line  intersects  the 
horizon  line ;  a  line  drawn  from  this  point  to  the  eye  would  be  in  every  way 
perpendicular  to  the  plane  of  the  picture. 

Points  of  distance  are  points  on  the  horizon  as  remote  from  the  centre  of 
view  as  the  eye. 

Vanishing  points  are  points  in  a  picture  to  which  the  perspective  of  all 
lines  converge  that  in  the  original  object  are  parallel  to  each  other. 

The  vanishing  point  of  any  line  or  system  of  parallel  lines  is  found  by  pass- 
ing a  line  through  the  point  of  sight  parallel  to  the  given  line,  or  system  of 
lines.  Its  intersection  with  the  plane  of  the  picture  will  be  the  vanishing 
point  desired.  Therefore  the  vanishing  points  of  all  horizontal  lines  lie  on  the 
horizon,  and  the  vanishing  points  of  horizontal  lines  making  an  angle  of  45° 
with  the  ground  line  are  at  the  points  of  distance. 

Parallel  Perspective. — An  object  is  said  to  be  seen  in  parallel  perspective 
when  one  of  its  sides  is  parallel  to  the  plane  of  the  picture. 

Angular  Perspective. — An  object  is  said  to  be  seen  in  angular  perspective 
when  none  of  its  sides  are  parallel  to  the  picture. 

The  vanishing  points  of  all  lines  parallel  to  the  plane  of  perspective  are  at 
infinity,  or,  in  other  words,  such  lines  have  no  vanishing  points. 

The  perspectives  of  lines  parallel  to  the  perspective  plane  are  parallel  to 
their  projections  on  that  plane. 

The  process  of  finding  the  perspective  of  lines,  plane  figures,  and  solids 
consists  merely  in  finding  the  perspectives  of  established  points  and  connecting 
them. 

To  find  the  Perspective  of  Two  Squares  in  the  Ground  Plane  whose  Sides 


708 


PERSPECTIVE   DRAWING, 


are  Parallel  and  Perpendicular  to  the  Perspective  Plane  (Fig.  1787). — Let  G  L 
be  the  ground  line,  a  b  d  c  and  e  f  h  g  the  horizontal  projections  of  the  two 
squares;  S'  is  the  horizontal,  and  S  the  vertical  projection  of  the  point  of 
sight ;  a  b  in  the  ground  line  is  the  vertical  projection  of  the  two  squares. 


FIG.  1787. 


FIG.  1788. 


Draw  a  S  and  b  S ;  these  will  be  the  indefinite  perspectives  of  the  sides  of 
the  squares  perpendicular  to  the  perspective  plane.  Draw  h  S' ;  where  this 
line  intersects  the  ground  line,  project  it  vertically  to  h^  on  b  S,  which  is  the 
perspective  of  h ;  the  line  g  h,  being  parallel  to  the  perspective  plane,  is  parallel 
to  the  ground  line,  and  is  shown  at  gl  hv  In  the  same  way  e^  /i  and  cv  dl  are 
found.  The  perspectives  of  the  diagonals  are  the  lines  connecting  the  corners. 

The  line  a  b  is  in  the  perspective  plane,  and  is  its  own  perspective.  All 
lines  or  plane  figures  lying  in  the  perspective  plane  appear  in  perspective  in 
their  true  form  and  size. 

To  find  the  Perspectives  of  Two  Cubes  whose  Sides  are  Parallel  and  Perpen- 
dicular to  the  Perspective  Plane  (Fig.  1788). — a  b  c  d  is  the  vertical,  and  a'  b' 
o'  ri  and/'  e'  h'  g'  the  horizontal,  projections  of  the  cubes.  Draw  a  S,  b  S,  c  S, 
and  d  S.  These  will  be  the  indefinite  perspectives  of  the  edges  of  the  cubes 
perpendicular  to  the  perspective  plane.  Draw  S'  g' ;  where  this  strikes  the 
ground  line,  project  to  rt  and  gl  on  S  a  and  S  d,  which  will  be  the  perspectives 
of  the  two  corners  horizontally  projected  at  g'  and  vertically  projected  at  a  and 
d;  g-i  h^  drawn  parallel  to  the  ground  line  and  limited  by  S  c  and  S  a,  is  the 
perspective  of  g'  h'.  In  a  similar  manner  the  perspectives  of  all  other  points 
and  edges  are  found. 

From  the  drawing  of  a  square  in  parallel  perspective,  we  deduce  rules  for 
the  construction  of  a  scale  in  perspective.  Let  D  G  L  D  (Fig.  1789)  be  the 


PERSPECTIVE  DRAWING. 


709 


plane  of  the  picture.     From  S'~lay  off  the  distance  o  S'  equal  to  some  unit  of 
measure,  as  may  be  most  convenient ;  from  o  draw  the  diagonal  to  D  the  point 


FIG.  1789. 


of  distance ;  now  draw  1  1'  parallel  to  the  ground  line  G  L,  again  draw  from  1' 
the  diagonal  1'  D,  and  lay  off  the  parallel  2  2',  proceed  in  the  same  way  with 
the  diagonal  2'  D  and  the  parallel  3  3',  and  extend  the  construction  as  far  as 
may  be  necessary.  It  is  evident  o  S'  1  1',  1'  1  2  2',  2'  2  3  3'  are  the  perspective 
projections  of  equal  squares,  and  therefore  o  S',  1  1',  2  2'  3  3',  etc.,  and  S'  1, 
1  2,  2  3,  etc.,  are  equal  to  each  other,  and  that  if  o  S'  is  set  off  to  represent  any 
unit  of  measure,  as  one  foot,  one  yard,  or  ten  feet,  etc.,  each  of  these  lines 
represents  the  same  distance,  the  one  being  measured  parallel  to  the  base  line, 
the  others  perpendicular  to  it.  In  making  a  perspective  drawing  a  scale  thus 
placed  will  be  found  convenient ;  which  in  the  centre  of  the  picture  might 
interfere  with  the  construction  lines  of  the  object  to  be  put  in  perspective,  is 
better  transferred  to  the  side  of  the  picture  a  G  o,  the  diagonals  to  be  laid  off 
to  a  point  to  the  right  of  D  equal  to  the  point  of  distance. 

The  scales  thus  projected  are  for  lines  in  the  base  or  ground  plane ;  for  lines 
perpendicular  to  this  plane  the  following  construction  is  to  be  adopted  :  Upon 
any  point  of  the  base  line  removed  from  S',  as  a,  for  instance,  erect  a  perpen- 
dicular, a  d ;  on  this  line,  lay  off  as  many  of  the  units  o  S'  as  may  be  necessary ; 
in  this  example  three  have  been  laid  off,  that  is,  a  d  =  3  o  S'.  From  a  and  d 
draw  lines  to  the  centre  of  view,  and  extend  the  parallels  1  1',  2  2',  33';  at  the 
intersection  of  these  lines  with  a  V  erect  perpendiculars.  The  portions  com- 
prehended between  the  lines  a  V  and  d  V  will  be  the  perspective  representa- 
tions of  the  line  a  d,  in  planes  at  distances  of  1,  2,  3,  o  S'  from  the  base  line, 
and  as  #,  c,  d  are  laid  off  at  intervals  equal  to  o  S',  by  drawing  the  lines  c  V 
and  b"V  nine  equal  squares  are  constructed,  of  which  the  sides  correspond  to 
the  unit  of  measure  o  S'. 

To  find  the  Scale  for  the  Perspective  of  any  Line  Oblique  to  the  Perspective 
Plane  (Fig.  1790). — Let  A  B  be  the  perspective  of  any  line  oblique  to  the 
perspective  plane  and  V  its  vanishing  point ;  through  the  extremity  A  draw  any 
line  A  7 ;  divide  it  into  as  many  parts  as  is  desired  to  divide  the  perspective 
line  A  B,  here  seven.  Draw  7  B.  Connect  the  remaining  points  6,  5,  4,  etc., 
withV ;  where  these  lines  intersect  the  line  7  B  they  are  projected  on  A  B,  par- 
allel to  A  7.  The  divisions  A  6",  6*  5",  etc.,  are  the  perspectives  of  the  seven 


T10 


PERSPECTIVE   DRAWING. 


equal  divisions  of  A  B.     If  the  line  A  B  is  fourteen  feet  long,  the  divisions 
A  6",  6"  5",  5"  4*  are  each  equal  to  two  feet. 

To  find  the  Perspective  of  a  Hexagonal  Prism  with  a  Pyramidal  Top  (Fig. 

1791). — The  perspective  plane 
in  the  original  position  is  a  pro- 
file plane;  abfie  is  the  verti- 
cal and  c'  b'  c0'  d0'  e'  d'  the  hori- 
zontal projection  of  the  figure. 
M  N  is  the  profile  perspective 
plane  in  which  the  edge  of  the 
prism  e  i  lies.  S  is  the  vertical 
and  S'  the  horizontal  projection 
of  the  point  of  sight.  Draw  rays 
.  of  light  at  S  a  and  S'  a',  S  c, 
S'  c',  S  d,  S'  d\  et*  These  rays 
pierce  the  profile  perspective  plane  at  points  at  GI  d^  etc. 

All  the  points  in  sight  being  thus  fixed,  the  profile  perspective  plane  is  then 
transferred  to  the  position  M!  Nt  and  revolved  about  its  vertical  trace  into  the 
plane  of  the  paper.  Thus,  the  point  projected  at  a"  and  a',  the  perspective  of  the 
point  originally  projected  at  a  and  a'  is  transferred  to  a'"  and  revolved  to  a",  which 


FIG.  1790. 


Fio.  1791. 


is  its  final  position.  All  other  points  are  treated  in  the  same  way.  The  edge  e  i 
lying  in  the  perspective  plane  is  the  same  length  in  perspective  as  in  projection. 

The  transposition  of  the  profile  plane  from  M  N  to  Mt  N,  is  only  necessary 
to  avoid  complicating  the  perspective  with  the  projections. 

Method  of  Perpendiculars  and  Diagonals,  to  find  the  Perspective  of  a  Pave- 
ment in  Parallel  Perspective  (Fig.  1792). — a  b  d  c  is  the  pavement,  the  square 
blocks  running  diagonally  across  it. 


PERSPECTIVE  DRAWING. 


m 


The  projection  of  the  pavement  being  revolved  so  as  to  appear  below  the 
ground  line,  diagonals  drawn  through  points  of  it  to  the  right  will  vanish  in 
the  point  of  distance  to  the  left  and  vice  versa. 


FIG.  1792. 


FIG.  1793. 


The  sides  of  the  pavement,  being  perpendicular  to  the  perspective  plane,  are 
their  own  perpendiculars.  Thus  S  a  and  S  b  are  their  perspectives.  The  lines  of 
division  of  the  blocks,  being  at  45°,  are  their  own  diagonals  and  vanish  atD  and  D,. 

To  find  the  Perspective  of  a  Cube  in  Parallel  Perspective  (Fig.  1793),  a  b  d  c 
is  the  horizontal  projection  of  the  cube.  The  face  a  bf  e  being  in  the  plane 
of  perspective,  appears  in  full  size.  From  the  point  c  the  diagonal  c  x  disap- 
pears at  D,,  and  the  perpendicular  at  S.  Their  intersection  cz  is  the  perspective 
of  the  lower  corner ;  dz  is  found  in  the  same  way ;  c  and  d  are  found  by  pro- 
jecting up  vertically  from  c2  and  d2  and  intersecting  S  e  and  S  /,  or  they  could 
be  found  by  constructing  diagonals  in  the  plane  Y  Y  of  the  top. 

To  find  the  Perspective  of  the  Frustrum  of  a  Right  Square  Pyramid  by  Per- 


712 


PERSPECTIVE   DRAWING. 


pendiculars  and  Diagonals  (Fig.  1794). — a  b  c  d  is  the  horizontal  projection  of 
the  base  and  efg  h  of  the  top  of  the  pyramid.  The  point  of  sight  is  projected 
at  S'  and  S  ;  D  and  Dj  are  the  points  of  distance. 

The  perspective  of  each  point  is  found  by  drawing  its  perpendicular  and 
diagonal  and  fixing  the  intersection  of  their  perspectives.  The  perpendiculars 
and  diagonals  must  lie  in  their  proper  plane.  Thus  those  at  the  top  of  the 
pyramid  must  be  projected  up  to  the  plane  s  t. 

To  find  the  Perspective  of  a  Horizontal  Circle  (Fig.  1795). — To  find  the  per- 
spective of  any  curve  it  is  merely  necessary  to  find  the  perspectives  of  enough 


Fro.  1795.  Fm.  1796. 

points  on  it  to  enable  the  perspective  curve  to  be  traced  through  them  \agec 
is  the  horizontal  circle.  Take  any  number  of  equidistant  points  on  it,  as  a  b  c, 
etc.  Their  perspectives  are  found  by  the  usual  method  of  perpendiculars  and 
diagonals  at  a^  b^  cl5  etc.  The  curve  traced  through  these  perspective  points  is 
the  perspective  of  the  circle.  This  curve  is  an  ellipse. 

To  find  the  Perspective  of  a  Circle  in  a  Profile  Plane  (Fig.  1796). — a1  h'  is  the 
horizontal  and  e  d  the  vertical  projection  of  the  circle.  As  before,  a  number  of 
points  are  taken  on  the  circle,  the  location  of  these  points  on  the  horizontal 
and  vertical  projections  of  the  circumference  are  found  by  revolving  the  cir- 
cle about  its  horizontal  diameter  parallel  to  the  horizontal  plane  of  projection. 
The  vertical  distance  of  all  points  on  the  circumference  from  the  diameter  a'  hr 
are  thus  ascertained  and  set  off  on  the  vertical  projection  of  the  circle. 

M  M,  N  N,  0  0,  P  P,  and  Q  Q  are  the  vertical  traces  of  the  horizontal 
planes  in  which  the  points  taken  lie.  Perpendiculars  and  diagonals  drawn 
from  these  points  and  carried  up  to  get  the  points  in  the  correct  planes  give 
0i  c\  0*1  </n  etc.,  as  the  perspective  of  the  circle. 

The  projection  of  the  circle  is  only  necessary  to  give  the  height  above  the 
ground  line  of  the  planes  M  M,  N  N,  etc.,  in  which  lie  the  points  taken  on  the 


PERSPECTIVE   DRAWING. 


713 


circle.     Had  the  circle  been  in  any  vertical  plane  other  than  a  profile  plane,  the 
mode  of  proceeding  would  have  been  the  same. 

To  find  the  Perspective  of  a  Cylinder  whose  Axis  is  Horizontal  and  at  an 
Angle  of  45°  'with  the  Perspective  Plane  (Fig.  1797). — a  ejfis  the  horizontal 


FlG.  1797. 


FIG.  1798. 


projection  of  the  cylinder.  The  base/y  is  revolved  parallel  to  the  horizontal 
plane  and  shown  at  s  f  h"  j  and  equidistant  points  taken  on  it.  Set  off  above 
the  ground  line  the  heights  s  t,s  h,s  u,  and  s  h'  and  draw  horizontal  lines 
through  them.  These  lines  will  be  traces  on  the  perspective  plane  of  horizontal 
planes  passing  through  the  assumed  points  and  corresponding  points  on  the  other 
base.  Then  finding  the  perspectives  of  diagonal  and  perpendicular  lines  passing 
through  these  points,  the  perspectives  of  corresponding  points  on  the  bases 
through  which  the  perspective  curves  can  be  drawn. 

To  find  the  Perspective  of  an  Octagonal  Prism  with  its  Axis  Horizontal  and 
making  an  Angle  of  45°  with  the  Perspective  Plane  (Fig.  1798). — a  d  h  e  is  the 
horizontal  projection  of  the  prism.  M  M,  N  N,  and  0  0  are  the  traces  on  the 
perspective  plane  of  the  horizontal  planes  containing  the  edges  of  the  prism. 
The  perspectives  of  the  points  abed,  etc.,  from  the  perspectives  of  the  edges 
vanishing  at  D,  and  of  the  perpendiculars  vanishing  at  S.  The  intersections 
of  these  perspectives  give  the  points  desired. 

To  draw  the  Elevation  of  a  Building  in  Angular  Perspective  (Fig.  1799).— 
The  plan  of  the  two  sides  which  are  to  appear  in  perspective  are  drawn,  all 
openings,  projections,  and  roof  plan  being  indicated.  This  plan,  c,  a,  #,  is 
placed  at  the  top  and  about  the  centre  of  the  drawing  board  in  any  desired 
position  ;  a  line  P  P',  known  as  the  picture  plane  or  plane  of  measures,  is  drawn 
of  indefinite  length.  For  convenience  in  measuring  heights  it  is  usual,  though 
not  necessary,  to  draw  P  P'  through  the  point  a  of  the  building. 


PERSPECTIVE   DRAWING. 

The  station  point  S  is  selected,  largely  a  matter  of  judgment,  and  lines 
drawn  through  S  parallel  to  the  sides  of  the  building  and  intersecting  the  pic- 
ture plane  at  P  P' ;  from  P  and  P'  perpendiculars  are  dropped  of  indefinite 
length  ;  the  ground  line  G  L,  parallel  to  P  P',  is  drawn  at  any  convenient  place, 
and  the  horizon  drawn  parallel  and  about  six  feet  above,  and  intersecting  the 
perpendiculars  at  V  V,  the  vanishing  points,  all  lines  parallel  to  a  c  vanishing 
at  V  and  those  parallel  to  a  b  at  V  ;  lines  are  drawn  from  all  points  in  the 
plan  which  are  to  appear  in  the  perspective  to  S  intersecting  P  P'  and  then 
transferred  by  vertical  lines  to  the  portion  of  the  paper  reserved  for  the  per- 
spective drawing  ;  the  horizontal  measures  are  thus  obtained.  For  the  vertical 
ones  the  sides  of  the  plan  a  c  and  a  I  are  extended  till  they  cut  P  P' ;  at  d  and  e 
perpendiculars  are  dropped  from  these  points  which  are  lines  of  heights.  Ele- 
vations drawn  to  the  same  scales  as  the  plan  are  placed  to  the  right  and  left 
of  space  reserved  for  the  perspective  on  G-  L  ;  heights  are  transferred  from  the 
elevation  on  the  left  to  line  of  heights  e  e'  and  vanish  at  V,  heights  on  the 
right  to  d  d'  and  vanish  at  V.  The  remaining  lines  and  filling  in  of  details 
will  be  understood  from  the  drawing. 

Fig.  1800,  the  building  sketched  on  page  592,  is  shown  in  angular  perspec- 
tive. The  general  construction  will  be  understood  from  the  description  of  Fig. 
1799,  the  same  letters  being  used  to  describe  similar  lines.  Additional  lines  of 
measures  must  be  taken  where  there  are  recesses,  projections,  chimneys,  etc.,  to 
locate.  Thus,  take  the  chimney/;  the  line  of  heights  for  this  is  obtained  by 
continuing  the  line  of  chimney  till  it  intersects  P  P'  at  /',  a  perpendicular  is 
dropped  from  this  point,  and  the  height  transferred  to  this  line  from  the  eleva- 
tion ;  a  vanishing  point  drawn  from  this  intersection  to  V  intersects  the  hori- 
zontal limits  of  the  chimney  and  gives  the  height ;  the  bay  window  similarly. 

At  page  906  is  a  general  diagram  showing  the  principal  constructive  lines 
necessary  in  rendering  a  building  in  perspective. 

Fig.  1800  A  illustrates  a  method  whereby  the  orthographic  plan  is  dispensed 
with  and  a  perspective  plan  substituted,  from  which  the  vertical  lines  and  hori- 
zontal measures  may  be  taken  directly. 

The  horizon,  vanishing  points,  and  point  of  sight  are  determined  as  in  the 
previous  examples.  Describe  arcs  from  the  vanishing  points  through  the  point 
of  sight.  The  intersection  of  these  arcs  with  the  horizon  are  the  points  of  dis- 
tance. A  line  of  measures  is  taken  parallel  to  and  at  any  convenient  distance 
above  or  below  the  horizon,  and  a  point,  indicating  the  corner  of  the  building, 
located  where  desired  on  it ;  to  the  right  and  left  of  this  point  the  horizontal 
measures  of  the  two  sides  of  the  building  are  laid  off  to  scale ;  from  the  corner 
of  the  building  to  each  vanishing  point  lines  are  drawn  representing  the  sides 
of  the  plan.  The  extreme  limits  of  the  building  laid  off  on  the  line  of  meas^ 
ures  vanish  at  the  points  of  distance ;  that  to  the  left  of  the  corner  to  the  point 
of  distance  to  the  right,  and  vice  versa.  Where  these  lines  intersect  the  sides 
of  the  building  are  the  limits  of  the  perspective  plan.  These  lines  may  then  be 
transferred  by  perpendiculars  to  the  perspective  elevation. 

The  perspective  plan  described  above  is  shown  on  a  larger  scale  in  Fig. 
1800  B,  the  dimensions  of  the  doors  and  windows  of  the  plan  being  laid  off  on 
the  line  of  measures  and  carried  to  their  respective  points  of  distance  as  de^ 
scribed  in  obtaining  the  perspective  limits  of  the  building. 


PERSPECTIVE   DRAWING. 


715 


I   '         H 


E 
E 


T16 


PERSPECTIVE  DRAWING. 


To  draw  in  Parallel  Perspective  the  Interior  of  a  Room,     (Fig.  1801). — Let  a 
b  c  d  be  the  plan  of  the  room.    A  line  P  P',  known  as  the  picture  plane  of  meas- 

*  1  1  * 


'-i                                         "^ 

$                                          « 
^                                         j- 

:$                                                                $;          ffor/zon 

1 

«5 

1 

i^^X--^                                               ^ 

^  i 

's**       i 

-""   "^^   ^    ' 

\                        ^     ^  ^            ""*  —                                                                                               ^ 

^''         --L 

\                                      --^               \ 

/        / 

^**                     •**"                        [^ 

/         ; 

\          NV-     ^""^     ~~^~-V        ^" 

^-""        ^-'  i 

xX        / 

*                                ^^           \^~~~^^^"'* 

V                         ^                1 

/         / 

\                                 ^^^~^f^^    """*" 

•^  '"'         1 

/        / 

S?SK^           / 

/           / 

\                                                 ^-^         v^x^          ^ 

^^XN                       1 

/          / 

\                                         ^^"       line   \of^^>^^ 

'ensures    NI            y 

/       / 

\                                                   X                     \ 

/         / 

\                                         x               \ 

/      / 

/ 

K  / 


int  of  S iff/it 


FIG.  1800.— A. 


FIG.  1800.— B. 

ures,  is  drawn  far  enough  forward  to  include  all  that  is  desired  to  be  shown  in 
perspective  and  usually  parallel  to  the  rear  of  the  room.  S  is  taken  outside  the 
room  and  as  far  away  from  the  plan  as  the  size  of  the  board  will  admit  of.  In 
this  example  S  has  been  taken  to  the  right  of  the  centre  of  the  room ;  if  taken 
in  the  centre,  the  perspective  would  be  symmetrical.  The  points  a  and  d  of  the 
plan  subtend  the  greatest  angle,  which  should  never  be  over  60°.  The  same 
may  be  said  of  the  vertical  angle,  a  greater  angle  causing  distortion.  Dotted 
lines  show  rays  from  various  points  intersecting  P  P'  and  establishing  the  posi- 
tion of  the  vertical  lines.  The  ground  line  G  L  is  drawn  parallel  to  P  P',  and 
the  horizon  drawn  at  a  suitable  elevation.  A  perpendicular  erected  at  S  and 
intersecting  the  horizon  at  V  gives  the  vanishing  point  for  all  lines  parallel  to 
a  b  and  d  c.  Vertical  heights  are  laid  off  on  either  a  a'  or  d  dr,  and  transferred 
to  their  proper  position  in  the  perspective. 

To  draw  an  Arched  Bridge  in  Angular  Perspective. — Let  A  and  B  (Fig. 
1802)  be  the  plans  of  the  piers  ;  on  the  line  a  p,  one  of  the  sides  of  the  bridge, 
lay  down  the  curve  of  the  arch  as  it  would  appear  in  elevation,  in  this  example 
an  ellipse.  Divide  the  width  of  the  arch  as  at  b  c  d  e  f  g  h,  carry  up  lines  per- 
pendicular to  b  h  until  they  intersect  the  curve  of  the  arch,  and  through  these 
points  draw  lines  parallel  to  b  h  as  k  I  and  m ;  let  o  r  be  the  height  of  the  para- 


PERSPECTIVE  DRAWING. 


717 


718 


PERSPECTIVE   DRAWING. 


pet  of  the  bridge  above  the  spring  of  the  arch.     Through  the  station  point 
draw  lines  parallel  to  the  side  a  h  and  end  a  a  of  the  bridge,  till  they  intersect 


FIG.  1801. 


the  assumed  base  line  M  M  ;  project  these  intersections  to  the  horizon  line  of 
the  picture  for  the  vanishing  points  D,  D'  of  perspective  lines  parallel  to  a  h 
and  a  $.  Let  fall  a  perpendicular  from  a  to  a',  and  on  this  perpendicular  set 
off  from  a'  the  heights  s  &,  s  I,  s  m,  and  s  r ;  from  a'  and  r'  draw  lines  to  D  and 
D',  and  from  the  points  m',  l\  Tc1  to  D'.  Draw  rays  from  the  points  a  b  c  d  efg 
h  to  the  station  point  S,  and  project  their  intersection  with  the  base  lines  to  the 
perspective  line  a'  D'  as  in  previous  examples  ;  the  intersection  of  the  lines  Tc' 
D',  /'  D',  m'  D'  by  the  perpendiculars  thus  projected  will  establish  the  points 


PERSPECTIVE  DRAWING. 


719 


of  the  curve  of  the  arch  on  the  side  nearest  the  spectator.  To  determine  the 
position  of  the  opposite  side  of  the  arch,  from  a",  the  perspective  of  the  corner 
of  the  pier  a"  draw  a"  D',  and  from  h'  draw  lines  to  D ;  the  line  /*'  p'  will  be 


FIG.  1802. 


the  perspective  width  of  the  pier ;  draw  k'  D ;  and  from  &",  k"  D' ;  from  g" 
the  intersection  of  the  curve  of  the  arch  by  the  perpendicular  to  g1,  draw  g*  D, 
the  intersection  with  k"  D'  will  be  one  point  in  the  curve  of  the  arch  on  the 
opposite  side  of  the  bridge  ;  in  the  same  way,  from  any  point  in  the  nearer 
arc  draw  lines  to  D,  and  the  intersection  with  lines  in  the  same  planes  on  the 
opposite  side  of  the  bridge  will  furnish  points  for  the  further  arch  ;  all  below 
the  first  only  will  be  visible  to  the  spectator. 

To  draw  in  Perspective  a  Flight  of  Stairs  (Fig.  1803). — Lay  off  the  base 
line,  horizon,  centre  of  view,  and  point  of  distance  of  the  picture  ;  construct 
the  solid  a  b  c  d,  efg  h,  containing  the  stairs,  and  in  the  required  position  in 
the  plane  of  the  picture  ;  divide  the  rise  a  c  into  equal  parts  according  to  the 
number  of  stairs,  nine,  for  instance ;  divide  perspectively  the  line  a  b  into  one 
less  (eight)  number  of  parts  ;  at  the  points  of  division  of  this  latter  erect  per- 
pendiculars, and  through  the  former  draw  lines  to  the  centre  of  view  ;  one  will 
form  the  rise  and  the  other  the  tread  of  the  steps.  From  the  top  of  the  first 
step  to  the  top  of  the  upper  continue  a  line  a  d,  till  it  meets  the  perpendicular 
S'  V  prolonged  in  v ;  this  line  will  be  the  inclination  or  pitch  of  the  stairs  ;  if 
through  the  top  of  the  step  at  the  other  extremity  a  similar  line  be  drawn,  it 


720 


PERSPECTIVE   DRAWING. 


will  meet  the  central  perpendicular  at  the  same  point  #,  and  will  define  the 
length  of  the  lines  of  nosing  of  the  steps,  and  the  other  lines  may  be  completed. 


D 


-tfr 


0 


FIG.  180S. 

As  the  pitch  lines  of  both  sides  of  the  stairs  meet  the  central  vertical  in  the 
same  point,  in  like  manner  v  will  be  the  vanishing  point  of  all  lines  having  a 
similar  inclination  to  the  plane  of  the  picture.  The  projection  of  the  other 
flight  of  stairs  will  be  easily  understood  from  the  lines  of  construction  perpen- 
dicular to  the  base  line  or  parallel  thereto,  lying  in  planes. 

To  find  the  Reflection  of  Objects  in  the  Water. — Let  B  (Fig.  1804)  be  a  cube 
suspended  above  the  water ;  find  the  reflection  of  the  point  a  by  letting  fall 
a  perpendicular  from  it,  and  setting  off  the  distance  a'  w  below  the  plane  of 
the  water  equal  to  the  line  a  w  above  this  line ;  the  line  w  f  will  also  be  equal 


D 


Fid.  1804. 


PERSPECTIVE   DRAWING.  721 

to  the  line  w /;  find  in  the  same  way  the  points  V  and  e',  through  these  points 
construct  perspectively  a  cube  in  this  lower  plane,  for  the  reflection  of  the  cube 
above. 

To  find  the  reflection  of  the  square  pillar  D  removed  from  the  shore  :  sup- 
pose the  plane  of, the  water  extended  beneath  the  pillar,  and  proceed  as  in  the 
previous  example. 

The  lines  of  an  object  which  meet  in  the  centre  of  view  V,  in  the  original, 
have  their  corresponding  reflected  lines  converging  to  the  same  point.  If  the 
originals  converge  to  the  points  of  distance,  the  reflected  ones  will  do  the  same. 
To  find  the  reflection  of  any  inclined  line,  find  the  reflection  of  the  rectangle 
of  which  it  is  the  diagonal,  if  the  plane  of  the  rectangle  is  perpendicular  to 
the  plane  of  the  picture.  If  the  line  is  inclined  in  both  directions  inclose  it  in 
a  parallelepiped  and  project  the  reflection  of  the  solid. 

To  find  the  Perspective  Projection  of  Shadows  (Fig.  1805). — Let  the  con- 
struction points  and  lines  of  the  picture  be  plotted.  Let  A  be  the  perspective 
projection  of  a  cube  placed  against  another  block,  of  which  the  face  is  parallel 
to  the  plane  of  the  picture ;  to  find  the  shadow  upon  the  block  and  upon  the 
ground  plane,  supposing  the  light  to  come  at  such  an  angle  as  to  cause  the 
projections  of  it  (both  vertical  and  horizontal)  to  make  an  angle  of  45°  with 
the  ground  line.  Since  the  angle  of  light  is  the  diagonal  of  a  cube,  construct 
another  cube  similar  to  A,  and  adjacent  to  the  face  bcg\  draw  the  diagonal 
b  k,  it  will  be  the  direction  of  the  ray  of  light,  and  k  will  be  the  shadow  of  b ; 
connect  fk  and  c  k,fk  must  be  the  shadow  of  the  line  J/,  and  c  k  of  b  c ;  the 
one  upon  the  horizontal  plane  and  the  other  in  a  vertical  one :  the  former  will 
have  its  direction,  being  a  diagonal,  toward  the  point  of  distance  D',  the  other 
being  a  diagonal  in  a  plane  parallel  to  that  of  the  picture,  will  be  always  pro- 
jected upon  this  plane  in  a  parallel  direction. 

Let  B  be  a  cube  similar  to  A  ;  to  find  its  projection  upon  a  horizontal  plane, 
the  shadow  of  the  point  b'  may  be  determined  as  in  the  preceding  example,  but 
the  shadow  of  the  point  ^',  instead  of  falling  upon  a  plane  parallel  to  the  pic- 
ture, falls  upon  a  horizontal  one;  its  position  must  be  determined  as  before 
by  b.  Construct  the  cube  and  draw  the  diagonal  c'  I ;  in  the  same  way  deter- 
mine the  point  m  the  shadow  of  d' ;  connect  c  k'  I  m  n,  and  for  the  shadow  of 
the  cube  in  perspective  on  a  horizontal  plane. 

On  examination  of  these  projected  shadows,  it  will  be  found  that  as  the 
rays  of  light  fall  in  a  parallel  direction  to  the  diagonal  of  the  cube,  the  vanish- 
ing point  of  these  rays  will  be  in  one  point  V  on  the  line  D'  L,  prolonged,  at 
a  distance  below  D'  equal  V  D' ;  and  since  the  shadows  of  vertical  lines  upon  a 
horizontal  plane  are  always  directed  toward  the  point  of  distance,  the  extent  of 
the  shadow  of  a  vertical  line  may  be  determined  by  the  intersection  of  the 
shadow  of  the  ground  point  of  the  line  by  the  line  of  light,  from  the  other  ex- 
tremity. Thus,  the  point  &,  cube  A,  is  the  intersection  of  /D'  by  b  V ;  the 
points  &',  I,  m  are  the  intersections  of  c  D',  o  D',  M  D'  by  V  V,  c'V  d'\'. 
Similarly  on  planes  parallel  to  that  of  the  picture,  k,  cube  A  is  intersection  of 
the  diagonal  c  k,  by  the  ray  of  light  b  V. 

Applying  this  rule  to  the  frame  C,  from  r,  s,  p,  draw  lines  to  D' ;  from  r', 
s', ;/,  draw  rays  to  V ;  their  intersections  define  the  outline  of  the  shadow  of 
the  post.  To  draw  the  shadow  of  the  projection,  the  shadow  upon  the  post 
47 


722 


PERSPECTIVE  DRAWING. 


PERSPECTIVE  DRAWING. 


723 


\ 


UNIVERSITY 


724 


PERSPECTIVE  DRAWING. 


from  t  will  follow  the  direction  of  the  diagonal  c  k.  Project  u  and  v  upon  the 
ground  plane  at  u'  and  v' ;  from  t  u'  v'  and  p  draw  lines  to  D' ;  from  t',  u,  v,  w, 
and  x  draw  rays  to  V,  and  the  intersection  of  these  lines  with  their  corre- 
sponding lines  from  their  bases  will  give  the  outline  required ;  as  v  and  w  are 
on  the  same  perpendicular,  their  rays  will  intersect  the  same  line  v'  V. 

With  reference  to  the  intensity  of  "  shade  and  shadow,"  and  the  necessary 
manipulation  to  produce  the  required  effect,  the  reader  is  referred  to  the  article 
on  this  subject. 

In  treating  of  Perspective  it  has  been  considered  not  from  an  artistic  point, 
as  enabling  a  person  to  draw  from  Nature,  but  rather  as  a  useful  art  to  assist 
the  architect  or  engineer  to  complete  his  designs,  by  exhibiting  them  in  a 
view  such  as  they  would  have  to  the  eye  of  a  spectator  when  constructed.  Our 
examples,  owing  to  size  of  the  page,  have  been  limited  in  the  scale  of  the 
figures,  and  in  the  distance  of  the  point  of  view,  or  distance  of  the  eye  from 
the  plane  of  the  picture,  unimportant  to  the  mathematical  demonstration.  It 
is  unnecessary  in  these  particular  points  that  the  examples  should  be  copied. 
The  most  agreeable  perspective  representations  are  generally  considered  to  be 
produced  by  fixing  the  angle  of  vision  at  from  45°  to  50°,  and  the  distance  of 
the  horizon  above  the  ground-line  at  about  one  third  the  height  of  the  picture. 

In  the  early  edition  of  this  work  there  were  illustrations  of  machinery  on 


FIG.  1807. 

sale  in  a  kind  of  perspective,  of  which  two,  Figs.  1806  and  1807,  specimens  of 
ship  work,  a  windlass  and  centreboard  winch,  are  reproduced.  They  are 
graphic  and  natural  in  appearance,  and  similar  illustrations  will  be  found  in 
the  collection  of  "  Scraps." 

With  the  introduction  of  photography  and  the  ready  transfer  of  the  nega- 
tives to  the  positive  and  permanent  condition  of  prints  and  plates,  one  is 
enabled  to  judge  of  sizes  and  dimensions  from  their  surroundings,  or  by  the 
introduction  into  the  view  of  appropriate  marks  or  bounds  of  known  distance 


PERSPECTIVE  DRAWING. 


725 


affording  lines  for  measures.  In  fact,  photography  has  been  applied  to  surveys 
with  records  of  angles  and  topographical  views  of  lines.  Views  of  buildings, 
circulars  of  machinery,  and  objects  on  sale  or  of  interest  are  illustrated  by  the 
aid  of  photography.  The  figure  below  represents  the  office  of  the  publishers 
of  this  work  taken  by  photography,  printed  on  plain  salted  paper.  The  pen- 
work  is  done  in  water-proof  ink  on  the  photograph ;  the  print  is  then  washed 
in  a  chemical  solution,  removing  the  photographed  lines  and  leaving  those  in 
ink.  (See  Free-Hand  Drawing.) 


FREE-HAND  DRAWING. 

A  DRAUGHTSMAN,  who  has  made  himself  conversant  with  the  rules  of  pro-, 
jection  as  laid  down  in  the  preceding  pages,  and  has  applied  these  rules  to  prac- 
tice, will  be  capable  of  representing  correctly  such  objects  as  have  been  illus- 
trated, or  make  up  similar  combinations  of  his  own  invention  and  design  for 
the  comprehension  of  others.  But  natural  objects,  as  animals,  trees,  rocks, 
clouds,  etc.,  can  not  be  imitated  on  paper  with  the  aid  of  drawing  instruments ; 
outlines  so  varied  can  not  be  copied  in  this  mechanical  way  ;  it  can  only  be  done 
by  hand  drawing,  an  educated  eye  that  can  recognise  proportion  and  position,  and 
an  educated  hand  that  can  execute  and  portray  naturally  things  recognised  by 
the  eye,  with  the  aid  of  pencil,  pen,  crayon,  brush,  or  the  various  tools  that  now 
obtain  with  draughtsmen.  But  it  is  by  education  that  one  acquires  the  .facili- 
ties of  such  an  eye  and  hand.  As  the  writer  acquires  facilities  by  the  copying 
of  pothooks,  letters,  and  nourishes  which  may  develop  into  a  valuable  distinct- 
ive hand,  so  the  draughtsman  by  the  study  of  examples,  first  of  drawings  and 
copying,  the  learning  of  proportions,  comparison  of  the  works  of  different  art- 
ists, observations  of  effect  in  drawing  and  nature,  will  commence  an  education 
which  will  produce  pleasant  and  successful  pictures  distinctive  of  the  educated 
artist,  appreciated  by  the  public  and  of  mercantile  value. 

An  educated  free  hand  adds  largely  to  the  effect  on  most  drawings,  where 
close  measures  are  not  requisite,  giving  grace  and  beauty  to  mechanical  designs, 
and  is  especially  applicable  to  architectural  ornaments  and  accessories.  It  will 
be  found  impossible  to  draw  many  of  these  in  any  other  way,  and  there  are  few 
drawings  that  do  not  require  some  patching  by  hand — short  curves,  which  can 
be  thus  done  much  more  readily,  and  connections  of  lines,  which  can  not  be 
done  by  drawing  instruments. 

The  pencil  or  pen  should  be  held  by  the  thumb  and  first  finger,  and  sup- 
ported and  guided  by  the  second.  The  two  fingers  touching  the  pencil  should 
be  placed  firmly  on  it,  and  be  perfectly  straight,  the  end  of  the  middle  finger 
at  least  one  inch  above  the  point  of  the  pencil.  In  drawing,  it  is  well  to  com- 
mence, as  in  writing,  with  straight  lines.  Lines  vertical,  horizontal,  and  in- 
clined, parallel  to  each  other  and  at  angles,  light  and  strong — short  and  long 
lines,  straight  and  curved,  with  pen,  pencil,  or  crayon  on  paper,  or  chalk  on 
a  board.  Dot  points,  and  draw  lines  between  them,  at  a  single  movement, 
without  going  over  them  a  second  time,  and  without  patching.  Besides 
direction,  lines  have  a  definite  length,  and  the  draughtsman  must  practise 
himself  in  drawing  lines  of  equal  lengths,  or  in  certain  proportions  to  each 
other. 

726 


FREE-HAND   DRAWING.  Y27 

Lines  equal  to  each  other  : 


Lines  twice  another  line  : 


Divide  a  line  into  any  number  of  equal  parts  : 


The  accuracy  of  these  divisions  may  be  tested  by  a  strip  of  paper  applied 
along  the  line,  marking  off  the  divisions  upon  it,  and  then  slipping  it  along 
one  division,  and  noting  if  the  divisions  on  the  paper  and  line  still  agree.  By 
practice,  the  eye  will  be  able  to  make  these  divisions  almost  accurately.  Having 
acquired  this  skill,  apply  it  to  the  construction  of  the  Geometrical  Problems,  in 
the  earlier  part  of  the  book,  in  their  proper  proportions,  both  in  straight  and 
curved  lines.  The  construction  should  be  dependent  entirely  on  eye  and  hand  ; 
but  it  will  be  found,  whether  the  draughtsman  draws  from  copy  or  nature,  that  it 
is  almost  impossible  to  get  along  well  without  defining  positions  by  some  points 
in  the  pictures,  and  sketching  in  some  defined  lines  which  may  serve  as  guides. 

Following  this  practice  of  guide  lines,  it  will  be  well  to  copy  the  outlines  of 
architectural  mouldings,  of  which  most  of  the  ornaments  are  conventional  rep- 
resentations of  natural  objects. 

At  page  60  will  be  found  an  application  to  the  drawing  of  acanthus  leaves 
within  the  guiding  lines  of  squares  and  the  designing  for  calicoes  and  woven 
goods,  oilcloths,  ceiling,  and  wall  ornamentation  based  on  geometrical  figures. 

In  such  designs  "  a  true  artistic  end  has  been  accomplished  when  well-ob- 
served features  of  natural  objects  have  been  chronicled  within  the  convention- 
alized limits  of  a  few  geometric  rules  that  include  proportion,  symmetry,  and 
a  proper  subordination  of  one  part  to  another." 

To  acquire  still  further  readiness  in  free  hand,  extend  the  practice  to  "  let- 
tering." 

MATERIAL. 

Paper. — The  different  papers  manufactured  by  Whatman  are  excellent  for 
sketching  purposes,  and  can  be  purchased  either  in  sheets  or  in  pads  of  various 
sizes.  Any  toothed  paper  answers  the  purpose  very  well,  such  as  common  news- 
paper ;  a  sketching  paper  with  either  a  rough  grain  or  a  canvas  grain  may  be 
made  by  pinning  a  sheet  of  thin  typewriting  paper  over  a  piece  of  sandpaper 
or  a  canvas  book  in  the  same  manner. 

For  pen-and-ink  work  a  hard,  unyielding  surface  is  needed ;  nothing  an- 
swers the  purpose  as  well  as  the  best  quality  of  Bristol  board,  although  excel- 
lent results  are  obtained  on  Whatman's  H.  P.  (Hot  Pressed)  paper. 

Pencils. — Faber's  or  Dixon's  pencils  of  medium  hardness  are  best  for  sketch- 
ing, but  for  drawing  on  Bristol  board  the  harder  grades  are  better. 

Lithographic  chalks  are  now  coming  into  use ;  they  are  much  superior  to 
the  ordinary  chalks,  crayons,  and  charcoal  in  their  not  being  readily  smeared. 
They  find  their  best  medium  in  Whatman's  paper,  either  H.  P.  or  "  not,"  and 
in  grained  scratch-out  cardboards  they  give  greater  intensity  than  lead  pencil, 
and  reproduce  with  more  certainty.  Of  course  they  can  not  be  used  where 
much  detail  is  required,  but  for  generalities  they  are  excellent. 

Pens. — The  use  and  selection  of  pens  must  be  left  largely  to  the  draughts- 
man's own  judgment.  The  ordinary  school  pen  is  excellent ;  Gillott's  303,  or 


728 


PEEE-HAND  DRAWING. 


the  same  maker's  mapping  pens,  are  also  good.  The  amateur  is  cautioned 
against  the  diminutive  crow  quill  and  lithographic  pens;  the  pen  is  merely  a 
secondary  matter,  some  illustrators  doing  excellent  work  with  a  brush  used  as 
a  pen,  a  reed  pen,  a  toothpick,  or,  indeed,  with  anything  that  happens  to  be 
at  hand. 

Ink. — The  best  ink  for  reproductive  purposes  is  India  ink  ;  that  which  has 
a  dull  appearance  when  dry  is  the  best  for  this  purpose ;  India  ink  can  be  pur- 
chased in  the  stick  and  ground  down  with  water  or  ready  prepared  in  bottles, 
either  waterproof  or  otherwise. 

The  first  step  in  free-hand  drawing  is  its  application  to  simple  objects,  of 
which  one  must  learn  to  determine  the  relative  proportion  of  their  parts  and  to 
lay  them  down  on  paper  in  their  proper  position  and  this  entirely  by  eye.  Hav- 
ing thus  drawn  one  object,  one  proceeds  to  increase  the  group  of  objects.  As 
has  been  shown  in  "  Perspective,"  objects  appear  smaller  as  they  are  more  re- 
mote from  the  spectator,  who  must  know  how  much  the  relative  scale  is  changed, 
not  only  in  objects  remote  from  each  other,  but  also  as  to  what  parts  of  objects 
can  be  seen  and  how  they  are  seen.  The  rules  of  perspective  give  an  idea  of 
what  can  be  seen  and  the  proportions,  and  serve  to  make  the  eye  intelligent  in 
its  observations  to  be  confirmed  and  strengthened  by  practice. 

In  drawings  of  the  human  frame  there  are  numerous  charts  and  rules  which 
may  be  said  to  be  established  which  may  assist  the  learner  in  fixing  the  form 
and  proportions  of  parts  within  certain  classical  or  normal  limits.  Outlines 
from  these  charts  may  be  traced  for  a  brief  time  by  the  learner  to  acquire  ideas 
of  the  forms,  proportions,  and  positions  when  at  rest ;  but  when  in  action  limbs 
are  moved,  muscles  increase  under  action,  and  the  parts  present  different  lines 
of  sight  which  must  be  studied  by  themselves.  Although  the  length  of  limbs 
is  not  increased,  it  may  be  more  or  less  foreshortened. 

"  Proportions  of  the  Human  Frame"     By  Joseph  Bonomi. 

The  following,  with  the  illustrations,  are  taken  from  the  above  work  : 

"  The  human  frame  is  (Figs.  1808  and  1809)  divided  into  four  equal 
measures,  by  very  distinctly  marked  divisions  on  its  structure  and  outward 
form  : 

"  1.  From  the  crown  of  the  head  to  a  line  drawn  across  the  nipples. 

"  2.  From  the  nipples  to  the  pubes. 

"  3.  From  the  pubes  to  the  bottom  of  the  patella  (knee-pan). 

"  4.  From  the  bottom  of  the  patella  to  the  sole  of  the  foot. 

"  Again,  four  measures,  equal  in  themselves,  and  equal  to  those  just  de- 
scribed, and  as  well  marked  in  the  structure  of  the  human  body,  are  seen  when 
the  arms  are  extended  horizontally.  They  are  the  following  : 

"  From  the  tip  of  the  middle  or  longest  finger  to  the  bend  of  the  arm  is 
one  fourth  of  the  height  of  the  person. 

"  From  the  bend  of  the  arm  to  the  pit  of  the  neck  is  another  fourth. 

"  These  two  measures,  taken  together,  make  the  half  of  the  man's  height, 
and  with  those  of  the  opposite  side  equal  the  entire  height. 

"  In  the  figures,  the  differences  in  width  between  the  male  and  female  figures 
are  given  from  the  tables  of  the  Count  de  Clarac  of  the  Apollino  and  the  Venus 
de  Medici.  The  male  figure  is  in  thicker  line  than  the  female,  and  the  measure- 


FREE-HAND   DRAWING. 


729 


ments  referring  to  it  are  on  your  right  hand,  and  those  referring  to  the  female 
on  your  left. 

"  The  measurements  of  length,  according  to  Vitruvius  and  Leonardo  da 
Vinci,  are  the  same  in  both  sexes,  and  expressed  in  long  horizontal  lines  run- 
ning through  both  the  front  and  profile  figures. 


"  Almost  innumerable  are  the  varieties  of  character  to  be  obtained  by  the 
alterations  of  widths,  without  making  any  change  in  the  measurements  of 
length  ;  nevertheless,  some  ancient  statues  differ  slightly  in  these  measurements 
of  length. 

"  No  measurement  is  given  in  the  figure  of  the  width  of  the  foot ;  its  normal 


730 


FREE-HAND   DRAWING. 


proportion  should  be  one  sixteenth  of  the  height.     The  views  of  the  foot  are 
those  of  the  female. 

"  The  scale,  V,  used  is  8  heads  to  the  height ;  parts,  |  of  a  head  ;  and  min- 
utes, jV  of  a  part. 


"  The  whole  height  is  usually  taken  at  8  heads,  but  there  are  slight  differ- 
ences in  the  classic  statues  ;  the  height  of  the  Venus  de  Medici  is  equal  to  7 


FREE-HAND  DRAWING.  7-3 1 

heads,  3  parts,  10  minutes,  that,  of  the  Apollino  of  Florence,  7  heads,  3  parts,  6 
minutes. 

"  When  the  student  is  acquainted  with  the  forms  of  the  body  and  limbs  in 
two  aspects — viz.,  the  front  and  side  views — and  the  normal  proportions  they 
bear  to  each  other,  then  will  follow  the  study  of  the  characteristic  features  of 
childhood,  youth,  and  mature  age,  and  those  niceties  of  character  that  the 
ancients  invariably  observed  in  the  statues  of  their  divinities,  so  that  in  most 
cases  a  mere  fragment  of  a  statue  could  be  identified  as  belonging  to  this  or 
that  divinity — as,  for  instance,  the  almost  feminine  roundness  of  the  limbs  of 
the  youthful  Bacchus,  the  less  round  and  distinctly  marked  muscles  of  the 
Mercury,  and  of  the  statues  of  the  Athletae." 

Fig.  1811  is  a  half-tone  reproduction  of  a  photograph  showing  three  views 
of  a  plaster  model,  ecorche — i.  e.,  the  body  with  the  skin  removed,  showing  the 
muscles.  In  the  half-tone  process  a  ruled  screen  of  glass  is  interposed  between 
the  drawing  or  object  to  be  photographed  and  the  negative.  The  screen  of 
glass  is  closely  ruled  with  lines  crossing  at  right  angles  and  etched  with  hy- 
drofluoric acid ;  into  the  grooves  thus  produced  printing  ink  is  rubbed.  It  is 
these  lines  which  produce  the  crisscross  appearance  seen  in  the  resulting  pic- 
ture. This  process  is  commonly  used  in  reproducing  wash  drawings  and  pho- 
tographs. 

Figs.  1812,  1813,  and  1814  are  three  views  of  the  above  figure  drawn  in  line. 
A  large  negative  was  taken  and  the  print  made  on  "  plain  salted  paper  " — that 
is,  paper  prepared  without  albumen,  which  gives  to  the  ordinary  print  its  glossy 
appearance.  This  paper  is  made  by  being  soaked  in  a  solution  of 

Chlorate  of  ammonia 100  grains  ; 

Gelatin 10      " 

Water 10  ounces. 

The  figures  thus  made  may  now  be  drawn  in  with  pen  and  water-proof  India 
ink.  The  pen  work  should  not  attempt  the  fulness  of  detail  given  in  the  pho- 
tograph. When  the  drawing  has  been  finished  it  may  be  immersed  in  a  solution 
composed  of  1  ounce  of  bichloride  of  mercury  dissolved  in  8  ounces  of  water, 
which  removes  all  trace  of  the  photograph,  leaving  the  drawing  uninjured  on 
white  paper.  Omissions  may  now  be  supplied,  but  if  there  are  any  conspicuous, 
the  photograph  may  again  be  brought  out  by  immersing  in  a  solution  of  hypo- 
sulphite of  soda  in  water. 

A  readier  way  is  to  draw  with  water-proof  ink  upon  photographs  printed  on 
ferro-prussiate  paper  or  blue  print  paper,  the  directions  for  making  which  will 
be  found  on  page  52,  or  it  can  be  purchased.  It  can  then  be  sent  for  reproduc- 
tion as  it  is,  as  the  blue  will  not  photograph,  or  the  blue  may  be  bleached  by 
immersing  the  print  in  a  dish  of  water  in  which  a  small  piece  of  washing  soda 
has  been  dissolved ;  then  wash  the  print  in  clean  water. 

Both  pen  drawing  and  opaque  water  colour  can  be  used  on  the  ordinary  pho- 
tograph by  mixing  a  small  piece  of  ox  gall  with  the  liquid. 

Figs.  1815  and  1816  are  two  views  of  Sandow  taken  from  his  photographs, 
the  pen  work  being  executed  as  above  and  the  photograph  washed  out. 

In  the  "  Dictionnaire  Eaisonne  de  PArchitecture  "  of  M.  Viollet-le-Duc 


732 


FREE-HAND   DRAWING. 


are  given  drawings  from  an  album  of  the  middle  of  the  thirteenth  century.  Cer- 
tain mechanical  processes  are  given  to  facilitate  the  composition  and  design  of 
figures.  According  to  these  sketches,  geometry  is  the  generator  of  movements 


of  the  human  body,,  and  that  of  animals,  and  serves  to  establish  certain  relative 
proportions  of  the  figures.  The  pen  sketch  (Fig.  1817)  is  an  example  of  this 
practical  process.  In  comparing  this  mode  of  drawing  with  figures  in  the  vi- 
gnettes of  manuscripts,  with  designs  on  glass,  and  even  with  statues  and  bas-reliefs, 
we  must  recognise  the  general  employment  in  the  thirteenth  and  fourteenth 
centuries  of  these  geometrical  means,  suited  to  give  figures  not  only  their  pro- 
portions but  also  the  justness  of  their  movement  and  bearing.  Rectifying 


FREE-HAND   DRAWING. 


733 


the  canon  of  Yillard  in  its  proportions  by  comparison  with  the  best  statues, 
notably  those  in  the  interior  of  the  western  facade  of  the  Cathedral  of  Reims, 
we  obtain  the  Fig.  1818.  The  line  A  B,  the  height  of  the  human  figure,  is  di- 


FIG.  1815. 


734: 


FREE-HAND   DRAWING. 


FIG.  1816. 


vided  into  seven  equal  parts.  The  upper  division  is  from  the  top  of  the  head 
to  the  shoulders.  Let  C  D  be  the  axis  of  the  figure,  the  line  at  the  breadth  of 
the  shoulders  is  f  of  the  whole  height  A  B.  The  point  E  is  the  centre  of  the 


FREE-HAND   DRAWING. 


735 


line  C  D  ;  draw  through  this  point  two  lines,  af  and  b  e,  and  from  the  point  g 
two  other  lines,  g  e  and  gf.     The  line  b  h  is  the  length  of  the  humerus,  and 


FIG.  1817. 


FIG.  1818. 


the  line  of  the  knee-pan  is  on  i  k.  The  length  of  the  foot  is  f  of  a  division,  A 1. 
Having  established  these  proportions,  it  will  be  seen  by  the  following  cuts  how 
the  artisan  gave  movements  to  these  figures  when  the  movements  were  not  in 
absolute  profile. 

Suppose  the  weight  of  the  figure  to  be  borne  upon  one  leg  (Fig.  1819),  the 
line  g  e  becomes  perpendicular,  and  the  axis  op  of  the  figure  is  inclined.  The 
movement  of  the  shoulders  and  trunk  follow  this  inflection  ;  the  axis  of  the 
head  and  the  right  heel  are  in  the  same  vertical  line. 

In  stepping  up  (Fig.  1820),  the  axis  of  the  figure  is  vertical,  and  the  right 
heel  raised  is  on  the  inclined  line  s  £,  while  the  line  of  the  neck  is  on  the  line 
Im,  and  the  trunk  is  vertical, 

In  Fig.  1821  it  will  be  seen  how  a  figure  can  be  submitted  to  a  violent  move- 
ment and  yet  preserve  the  same  geometrical  trace.  The  figure  is  fallen,  sup- 
ported on  one  knee  and  one  arm,  while  the  other  wards  off  a  blow  ;  the  head 
is  vertical. 

In  Fig.  1822,  the  left  thigh  being  in  the  line  a/,  to  determine  the  position 
of  the  heel  c  on  the  ground,  supposed  to  be  level,  an  arc  is  to  be  described  from 
the  knee-pan  ;  the  line  ef  is  horizontal. 

It  is  clear  that,  in  adopting  these  practical  methods,  all  the  limbs  can  be 
developed  geometrically  without  shortening.  The  above  will  supply  to  many  a 


736 


FREE-HAND   DRAWING. 


ready  means  of  sketching  the  human  figure  in  various  attitudes,  naked,  or  in 
the  close-fitting  dresses  of  the  present  fashion ;  but  in  the  arrangement  of 


FIG.  1819. 


FIG.  1820. 


drapery  upon  a  figure,  care  must  be  taken  that  the  drapery  should  fall  in  grace- 
ful folds.  "  It  is  necessary  to  give  the  body  certain  inflections  which  would  be 
ridiculous  in  a  person  walking  naked.  The  walk  should  be  from  the  hips,  with 


FIG.  1821. 


FREE-HAND  DRAWING.  737 

wide-spread  legs,  and,  by  the  movements  of  the  trunk,  make  the  drapery  cling 
on  certain  parts  and  float  on  others." 

In  figures  in  repose,  their  centres  of  gravity  must  fall  within  the  points  of 
support,  but  the  body  can  be  sustained  by  muscular  exertion,  and  this  should 
be  expressed  in  such  cases  by  the  tension  of  the  muscles  on  which  the  position 
depends.  In  the  act  of  running,  the  body  inclines  forward,  its  weight  assists 
the  movement,  and  the  motions  prevent  its  falling. 

In  drawing  figures  it  will  be  understood  that  the  part  that  lies  behind  an- 
other can  not  be  seen,  and  that  one  side  of  a  limb  or  of  the  body  can  not  be 
turned  toward  you  without  turning  the  other  from  you,  and  that  the  length  of 
a  body  or  limb  can  only  be  shown  in  its  full  length  and  proportion  when  it  is 


e  — 


FIG.  1822. 

perpendicular  to  the  line  of  sight — that  is,  if  the  arm,  for  instance,  is  directed 
toward  the  eye,  the  hand  will  be  the  prominent  object  in  view,  that  the  arm  will 
only  be  shown  by  the  portions  prominent  beyond  the  outlines  of  the  hand,  that 
limbs  or  portions  more  or  less  inclined  to  the  line  of  sight  will  be  more  or  less 
foreshortened  or  show  less  than  their  natural  length. 

It  is  very  common  in  the  drawing  of  figures  to  indicate  merely  the  centre 
lines  of  the  various  portions  and  then  clothe  them  as  shown  in  several  of  the 
figures. 

It  is  very  common  with  modern  draughtsmen  to  adopt  a  somewhat  similar 
form  of  sketching  as  given  in  the  "  Dictionnaire  Raisonne  de  1'Architecture  "- 
a  framework  of  bones  in  positions  of  action — and  then  clothing  them  with  flesh 
or  drapery ;  or  manikins  and  lay  figures  in  which  the  limbs  can  be  set  or  fixed 
as  desired,  and  then  drawn  from  as  models.  Figs.  1823  and  1824  are  illustra- 
tions from  Dr.  Eimmer's  "  Elements  of  Design  "  of  skeleton  lines  and  of  manikins. 

Fig.  1825  is  taken  from  photographs  of  a  manikin  in  our  office,  which,  al- 
though maimed  as  to  its  hands,  is  one  of  the  best  forms  of  these  jointed  figures, 
of  which  the  limbs  and  body  can  be  set  in  any  required  position ;  but  the  sug- 
gestion is  obvious  that  by  the  salted-paper  or  blue-print  process,  nude  figures 
can  be  used  instead  of  manikins,  and  photographs  promptly  secured  without 
fatigue  to  the  model  and  in  positions  of  motion  impossible  in  sketching.  As  a 
further  illustration  of  this  process,  a  pen  drawing  is  given  of  the  Venus  de  Milo 
(Figs.  1826-1827)  from  two  points  of  view,  taken  from  a  plaster  model,  and  a 
portrait  of  Alexandre  Dumas  (Fig.  1858)  from  a  photograph. 
48 


738 


FREE-HAND   DRAWING. 


FIG.  1823. 


FIG.  1824. 


FIG.  1825. 


FREE-HAND   DRAWING. 


Y39 


Artists  object  that  photography  is  too  exact  a  reproduction,  but  it  is  well 
that  they  should  understand  what  is  an  exact  reproduction.  Tint  and  colour 
may  produce  pleasant  impressions  without  conformity  to  laws  of  perspective,  but 
if  the  picture  is  to  be  taken  as  whole  it  should  be  natural,  and  with  the  present 
processes  of  photography  it  is  well  to  throw  the  mechanical  drudgery  on  it. 


FIG.  1826. 


FIG.  1827 


Figs.  1828-1831  are  drawings  of  male  hands,  Figs.  1832-1838  of  legs  and 
feet,  with  guide-lines  to  assist  the  draughtsman. 

Figs.  1839-1841  are  drawings  of  female  hands  and  arms. 

Figs.  1842-1845  are  hands  and  feet  of  children. 

Figs.  1846  and  1847  are  illustrations  of  the  human  head  and  face. 


FIG.  1828. 


FIG.  1829. 


FIG.  1830. 


FIG.  1831. 


740 


FREE-HAND   DRAWING. 


FIQ.  1837. 


FIG.  1838. 


FIG.  1839. 


Fia.  1840. 


FIG.  1841. 


FREE-HAND   DRAWING. 


FIG.  1846. 


FIG.  1847. 


742 


FREE-HAND   DRAWING. 


ELECTIONEER. 

The  Forms  of  Animals. — The  bodies  of  most  quadrupeds  can  be  included 
in  rectangles  as  guide-lines,  which  may  be  drawn  around  the  illustration  of  the 
cow  and  horse  (Figs.  1848  and  1849).  The  action  of  the  limbs  of  quadrupeds  is 
chiefly  directly  forward  or  directly  backward,  the  -power  of  lateral  motion  being 
limited.  The  hinder  limbs  always  commence  progressive  motion,  as  in  the  first 
position  of  the  walk,  the  fore  foot  of  the  same  side  advances  next,  then  the 
hind  foot  of  the  opposite  side,  and  lastly  the  fore  foot  on  that  side,  and  so  on. 
In  the  trot,  the  hinder  leg  of  one  side  and  the  fore  leg  of  the  other  are  raised 
together.  In  the  canter  or  gallop,  both  fore  legs  and  one  hind  leg  are  raised 
together ;  when  rapidly  moving,  the  two  fore  legs  and  two  hind  legs  appear  to 
advance  together.  In  fact,  all  the  movements  are  rather  resultants,  as  they 
appear  to  us,  but  when  instantaneously  photographed  the  legs  are  wonderfully 
mixed. 


FIG.  1848. 


FREE-HAND   DRAWING. 


743 


FIG.  1849. 


Fig.  1850  is  one  of  Landseer's  sketches. 

The  forms  of  feet  range  under  two  great  divisions — hoofs  (Fig.  1851)  and 
paws  (Fig.  1852).  All  hoofs,  whether  whole  or  cloven,  approximate  to  a  right- 
angled  triangle,  and  all  paws  to  a  rhomboid. 


744 


FREE-HAND   DRAWING. 


The  J\!oses  of  Animals. — Fig.  1853  represents  that  of  the  horse  ;  Fig.  1854, 
that  of  the  ox  and  deer  tribe;  Fig.  1855,  those  of  the  carnivori;  Fig.  1856, 
those  of  the  camel,  sheep,  and  goat  tribes ;  and  Fig.  1857,  those  of  the  hog 
tribes.  The  muzzles  of  nearly  all  quadrupeds  will  be  found  to  range  under 
one  or  other  of  these  classes,  with  minute  variations  to  characterize  the  differ- 
ent species  and  individuals. 


FIG.  1853. 


FIG.  1854. 


FIG.  1857. 


In  looking  over  the  many  sketches  and  engravings  of  Landseer  which  have 
been  published,  it  will  be  noticed  in  how  varied  a  manner  they  were  executed. 
Sometimes  in  mere  outline  with  lead-pencil,  sometimes  with  a  camel's-hair 
pencil  charged  with  India  ink  or  sepia  for  the  outlines,  giving  effect  to  the 
subject  by  slight  tints  or  washes  of  the  same  colour ;  in  others,  pen  and  ink 
have  been  alone  employed ;  some  are  in  oils,  others  in  water-colours  ;  fre- 
quently chalks,  both  black  and  coloured.  "  As  we  look  at  some  of  these,  we  are 
tempted  to  believe  that,  of  all  the  instruments  that  can  be  used  by  the  artist, 
there  is  none  quite  so  wonderful  as  the  pen.  A  simple  sketch  with  a  pen  or 
lead-pencil  is  naked,  unadorned  truth,  bearing  witness  to  the  skill  or  its  oppo- 
site of  the  hand  which  produced  it." 

Strength  and  boldness  in  outline  are  acquired  by  large  scale  in  drawing ; 
and  in  copying,  if  suitable  originals  can  be  obtained,  copy  them,  but  if  you  are 
confined  to  the  illustration  of  books  and  periodicals,  recollect  that  they  have 
usually  been  reproduced  on  a  reduced  scale,  and  make  your  drawings  two  or 
three  times  their  lineal  dimensions. 

The  directions  and  illustrations  already  given  may  be  considered  copying, 
which  is  absolutely  necessary  as  an  introduction  to  free-hand  drawing,  and  ex- 
amples have  been  selected  from  figure  drawing  to  give  the  draughtsman  a 
strong  bold  hand  and  an  education  in  proportions. 


FREE-HAND   DRAWING. 


745 


Sketching  from  Nature. — It  is  useless  to  give  detailed  rules  for  sketching, 
as  each  has  his  own  way  and  perhaps  equally  good  though  dissimilar.  If  one  is 
inside  the  house,  what  one  sees  through  a  window  is  a  picture,  and  it  may  be 
transferred  to  paper  if  the  eye  is  kept  in  a  single  position  by  a  sight  fastened 
to  the  sash  at  a  convenient  distance ;  and  if  the  pane  of  glass  be  prepared  in 
squares,  as  described  on  page  60,  the  location  of  different  points  can  be  readily 
established.  A  simple  plan  to  begin  with  is  to  set  out  carefully  the  most  con- 
spicuous outline  and  draw  the  others  with  reference  to  it.  If  doubtful  as  to 
the  distances  and  length  of  lines,  stretch  out  your  arm,  holding  your  pencil 
vertically,  horizontally,  or  aslant,  as  the  case  may  be,  and  shutting  one  eye, 
mark  off  the  measure  from  the  end  of  the  pencil  by  placing  your  thumb  on  the 
spot ;  then  compare  that  line  or  space  with  any  other  needed.  By  noting  the 
relative  position  of  one  object  with  reference  to  another,  all  will  fall  into  place 
almost  without  thought.  Thus  you  have  sketched  a  house,  notice  the  next  ob- 
ject and  observe  where  it  is  projected  against  the  building,  as  at  such  a  window 
or  door,  and  draw  it  in.  Every  artist  has  his  own  method  of  handling  the 
sketch,  of  using  his  pen  or  pencil,  charcoal  or  brush  ;  the  aim  of  each  should 
be  to  express  what  he  sees  by  cross-lines  and  hatching  if  the  pen  is  used,  or  by 
scribbling  if  the  work  is  in  pencil  or  charcoal.  A  general  rule  is  to  adapt  your 
strokes  as  far  as  possible  to  the  modelling  of  the  subjects  you  are  drawing. 
Thus  if  you  are  representing  water,  it  is  natural  to  do  it  with  horizontal  lines. 
If  the  water  is  in  motion,  the  lines,  though  still  horizontal,  will  be  broken  and 
irregular.  The  reflections  which  in  still  water  will  be  represented  by  vertical 
lines,  in  running  water  are  indicated  by  horizontal  lines  with  closer  shading  to 
give  depth  of  tone. 

In  drawing  the  trunk  of  a  tree  the  characteristics  of  the  bark  must  be  ob- 
served. The  trunk  of  an  oak  is  rough  and  broken,  while  that  of  the  birch 
requires  curved  lines  across  the  thickness  of  the  tree.  Nature  sufficiently  indi- 
cates the  treatment.  In  many  cases  one  must  not  be  content  with  an  exact 
reproduction.  The  scene  must  be  interpreted. 


746 


FREE-HAND   DRAWING. 


FREE-HAND   DRAWING. 


747 


In  all  sketching  from  Nature-  the  lines  must  be  crisply  and  unhesitatingly 
drawn,  the  forms  clearly  denned,  and  the  masses  decisively  indicated.  In  rapid 
work  a  mere  outline  must  suffice,  but  it  must  be  clearly  and  cleanly  pencilled 
in.  When  an  elaborate  drawing  is  required,  begin  by  indicating  the  general 
arrangement,  and  then  fill  in  as  much  detail  as  may  be  necessary ;  but  it  is  to 
be  remembered  that  the  simplest  expression  is  the  best  and  at  the  same  time 
the  most  difficult,  the  effort  being  to  concentrate  the  effect  on  the  object  to  be 
emphasized,  all  others  being  subordinate  to  it. 

When  a  sketch  has  been  faithfully  made  from  Nature,  as  a  general  rule  it  is 
better  not  to  try  to  improve  it  afterward,  as  one  is  apt  to  lose  the  crispness  and 
vigour  of  the  original.  It  is  better  to  modify  or  amplify  the  first  notes  on  an- 
other sheet  of  paper.  Neither  should  there  be  many  erasures,  as  they  impart 
to  the  paper  a  dingy  appearance  and  the  sketch  loses  its  sharpness. 

The  depth  of  tone  of  shaded  portions,  as  clouds,  in  some  hasty  sketches  is 
indicated  by  numerals  or  letters,  1  or  A  representing  the  lightest;  but  it  is 
better  if  time  is  afforded  to  put  the  shading  in  the  sketch.  In  sketches  of 
landscapes  not  intended  for  reproduction  the  addition  of  colour  often  adds  very 
much  to  the  effect  and  value  of  the  sketch,  but  the  colour  must  be  light  and 
transparent. 

The  foregoing  applies  chiefly  to  landscape  sketching.     If  you  desire  to 


FIG.  1861. 


748 


FREE-HAND  DRAWING. 


sketch  figures  or  animals,  the  character  of  the  individual  is  what  you  must  try 
to  seize ;  if  an  animal  in  motion,  one  must  work  quickly  and  await  the  repeti- 
tion of  the  action  or  particular  movement  you  are  sketching.  Meanwhile  em- 


ploy your  pencil  on  those  portions  that  remain  longer  in  one  position,  except- 
ing to  work  on  the  moving  limb  the  instant  it  has  regained  the  required 
position.  The  sketching  of  animals  in  rapid  motion  is  still  more  difficult  and 
is  to  a  great  extent  a  matter  of  careful  observation  and  memory,  for  the  limbs 
are  not  the  only  parts  that  change  their  position ;  the  whole  attitude  of  the 
body  is  changed.  In  addition  to  memorizing  all  possible  of  the  movement, 


FREE-HAND   DRAWING. 


T49 


considerable  aid  may  be  obtained  in  observing  the  animal  at  rest,  which  will 
enable  you  to  understand  the  details  of  the  structure. 

All  sketches  made  should  be  preserved  for  future  use,  as  they  furnish  the 
best  material  for  original  work  that  one  can  have.  Sketches  made  in  pencil  or 
other  materials  which  smear  may  be  fixed  with  a  solution  composed  of  one  part 
of  gum  mastic  and  seven  parts  of  methylated  spirits  of  wine,  and  is  best  applied 
with  an  atomizer. 

In  transferring  your  sketches  to  the  paper  on  which  the  pen  drawing  is  to 
be  made,  commence  by  making  a  careful  drawing  with  a  hard  pencil  in  outlines, 
confining  yourself  to  those  of  shadows  as  much  as  possible,  to  save  the  surface 
of  the  paper,  as  rubbing  spoils  it  and  grays  the  ink ;  or  make  the  drawing  on 
another  sheet  of  paper  and  transfer  it  by  means  of  graphite  paper  to  the  fair 
sheet,  then  ink  in. 

If  you  want  a  clean,  sharp  line,  the  ink  must  be  perfectly  black  and  must 
stand  out  alone  on  the  paper.  If  you  want  a  gray  line,  it  will  not  be  obtained 
by  using  light  ink,  but  by  making  thin  lines.  A  single  thin  line  will  come  out 
in  the  reproduction  much  blacker  than  is  the  intention,  for  though  a  number 
of  lines  will  stand  together,  a  single  one  will  have  to  be  thickened  in  the  type 
metal  by  the  photo-engraver. 


Fm.  1851). 


FIG.  1S58. 

Fig.  1858,  portrait  of  Alexander  Dumas.  For  description  of  process  see 
page  738. 

Fig.  1859  is  a  portrait  of  Erik  Werenskiold,  the  artist,  drawn  by  himself  on 
Whatman's  paper. 

Wash  drawings  are  made  with  a  brush  on  either  Bristol  board  or  water-colour 
paper,  the  wash  consisting  of  India  ink  and  water,  of  various  degrees  of  inten- 
sity. A  number  of  illustrations  are  given  of  this  method  on  page  750,  by  Paul 
de  Longpre,  and  reproduced  in  half  tone. 

Fig.  1860  is  a  design  for  a  small  pumping  station,  drawn  Avith  India  ink 
and  a  toothpick,  after  W.  R.  Emerson,  in  the  "  Technology  Architectural  Re- 
view." 


750 


FREE-HAND   DRAWING. 


FREE-HAND    DRAWING.  75} 

There  are  many  devices  which  may  be  used  with  effect  in  pen-and-ink  draw- 
ing, such  as  splatter  work,  which"  is  done  by  using  a  small  stiff  bristle  brush  (a 
toothbrush  answers  the  purpose  very  well),  inking  it,  and  holding  the  bristles 
downward  and  inclining  toward  the  drawing  and  stroking  the  bristles  toward 
one  with  a  match  stick.  All  parts  not  intended  to  be  splattered  should  be  cov- 
ered with  paper  masks,  and  even  then  a  waterproof  ink  must  be  used  in  case  it 
is  necessary  to  paint  out  some  portions  with  Chinese  white.  The  lower  portion 
of  Fig.  1860  is  in  splatter.  An  inked  thumb  is  also  a  novel  and  effective  means 
of  representing  a  background  or  an  imitation  of  velvet,  the  lines  on  the  skin 
being  marked  on  the  paper  and  reproduced  excellently. 

An  invention  of  recent  years  is  known  among  artists  as  stipple  paper  or 
clay  board.  The  surfaces  of  these  cardboards  are  of  various  kinds,  but  are  all 
prepared  with  a  surface  of  china  clay.  The  simplest  variety  is  that  prepared 
with  a  plain  white  surface,  upon  w.hich  the  drawing  is  executed  with  pen  and 
ink  or  brush  ;  the  lights  are  taken  out  with  a  sharp  ink  eraser.  It  is  usual  to 
work  upon  these  boards  with  a  pigmental  ink,  such  as  lampblack,  ivory  black, 
or  India  ink.  More  liquid  inks  have  a  tendency  to  soak  through  the  prepared 
surface  rather  than  rest  upon  it,  rendering  the  board  useless  for  scratch-out 
purposes ;  other  kinds  of  boards  are  impressed  with  a  grain  or  with  plain  in- 
dented lines,  which  are  used  similar  to  the  above.  Scratch-out  boards  are  diffi- 
cult of  manipulation  and  are  not  to  be  recommended  to  the  amateur. 

Fig.  1861,  a  portrait  of  Salvini,  is  an  example  of  the  use  of  stipple  paper. 
The  background  or  middle  tone  shows  the  board  in  its  natural  state.  The 
high  lights  and  shadows  are  obtained  respectively  by  erasing  and  adding  India 
ink. 

Fig.  1862,  "  A  Venetian  Fete  on  the  Seine,"  is  another  specimen  of  work  on 
clay  board.  In  this  case  the  board  was  entirely  black,  the  various  tones  being 
obtained  by  various  degrees  of  erasing. 

The  appearance  a  drawing  will  present  when  reduced  may  be  approximate- 
ly judged  by  the  use  of  a  "  diminishing  glass  " — that  is,  a  concave  glass. 

To  remove  blots  or  make  erasures,  use  an  ink  eraser  or  simply  paste  a  piece 
of  paper  over  and  join  the  lines  at  the  edges ;  or  a  neater  way,  cut  out  the 
blotted  part  and  paste  a  piece  of  paper  underneath. 

To  clean  pen-and-ink  drawings  use  bread  one  or  two  days  old  and  not  rubber. 

Aerial  perspective,  or  the  tones  of  lights  and  shadows  according  to  their 
distance  from  the  observer  and  the  sources  of  the  light,  will  be  acquired  by 
studies  of  pictures  and  observations  of  Nature.  The  rule  in  drawing  from 
Nature  is  to  draw  only  what  you  see  and  express  it  in  the  most  truthful  form. 


"52 


FREE-HAND   DRAWING. 


After  a  Pen-and-ink  Design,  by  FORTUNT. 


FREE-BAND   DRAWING. 


753 


G.  L.  SEYMOUR. 


49 


754 


FREE-HAND   DRAWING. 


FREE-HAND   DRAWING. 


755 


756 


FREE-HAND    DRAWING. 


Study  of  Oak- Trees',      R.  LANDSEER. 


FREE-HAXD    DRAWING. 


757 


Morniny.     II.  W.   ROBBINS. 


T58 


FREE-HAND   DRAWING. 


Cattle  going  Home.    JAMES  M.  HART. 


FREE-HAND   DRAWING. 


759 


760 


FREE-HAND   DRAWING. 


The  Lady  of  the  Woods, 


FREE-HAND   DRAWING. 


761 


762 


FREE-HAND   DRAWING. 


rKsV,— -.:  — ;-;.  J     i      f    ', 

!W,-    VtvX^'-i!'-1  -'•'/'••:  ;       I        '       .1 


'""*Jt<;>'V\  ' ,  V'V  si\         i  k'\J.  r:*-1 '•*-"• 

C*S?^^%B     '     '4'      ^    '  -^"H^^ 

•^^apK'  ^JKiH'V.i'lS 

: 


FREE-HAND   DRAWING. 


763 


764 


FREE-HAND   DRAWING. 


PL.  I. 


Rg.12. 


Fig.ll.  I 


Fig.W. 


Fig.  9 


Fig.8. 


Fig.  7. 


Fig.  6. 


a    c 


T/          V 


PL.  I. 


Fig.  4-. 


Rg.3. 


Fig  2. 


Fig.l. 


a  _         C 


Fig.5. 


0,2 


pL.nr. 


PL.IV: 


FIG.4. 


FIG.8 


FIG.7. 


PL.Y 


Ill 


*  « 
I  * 

r~--r  -_---T:J 

!'i!i!ii    '   '    !          'ilnfj  '  'i   'i'l  ! 
I'i'i'i     1   i             '  'n"  '  'i   i'ii 

ijljijij  i  i         [{ijjjj  i  v  j|i]  ; 

I'lil'ii    !    i               •'ill'l  '  ill  'I'1'! 
ii      « 

>  i) 

...;ft< 

*  C* 

i  c» 
;*  i> 

IIJ           ' 

j 

A 

STATE  N  ISLAND 

CONTOURS  20  FT.  APART. 


IX. 


PLX. 
GEOLOGICAL  MAP  OF 

NEW  JERSEY 

GEORGE .  H.C  OOK,  STATE  GE  O  LO  GIST . 


PL.  XII. 


"Topographical   Map  of  Massachusetts" 


PL.XIII. 


PLXY 


PL.XVI. 


PLXVII. 


APPENDIX. 

PATENT-OFFICE   DRAWINGS 

must  be  made  upon  pure  white  paper,  of  a  thickness  corresponding  to  three-sheet  Bristol 
board,  with  surface  calendered  and  smooth.  India  ink  alone  must  be  used. 

The  size  of  the  sheet  must  be  exactly  10  by  15  inches.  1"  from  its  edges  single  mar- 
ginal lines  are  to  be  drawn,  leaving  the  "sight  "  precisely  8"  by  13".  Within  this  mar- 
gin all  work  must  be  included.  Measuring  downward  from  the  marginal  line  of  one  of 
the  shorter  sides,  a  space  of  not  less  than  1J  inch  is  to  be  left  blank  for  the  heading  of 
title,  name,  number,  and  date. 

All  drawings  must  be  made  with  the  pen  only.  All  lines  and  letters  must  be  abso- 
lutely black,  clean,  sharp,  and  solid,  and  not  too  fine  or  crowded.  Surface  shading 
should  be  open,  and  used  only  on  convex  and  concave  surfaces  sparingly.  Sectional 
shading  should  be  made  by  oblique  parallel  lines,  which  may  be  about  •£-§"  apart. 

Drawings  should  be  made  with  the  fewest  lines  possible  consistent  with  clearness. 
The  plane  upon  sectional  views  should  be  indicated  on  the  general  view  by  broken  or 
dotted  lines.  Heavy  lines  on  the  shade  sides  of  objects  should  be  used,  except  where 
they  tend  to  thicken  the  work  and  obscure  letters  of  reference :  light  to  come  from  the 
upper  left-hand  corner,  at  an  angle  of  45°. 

The  scale  of  the  drawing  to  be  large  enough  to  show  the  mechanism  without  crowd- 
ing; but  the  number  of  sheets  must  never  be  increased  unless  it  is  absolutely  neaessary. 

Letters  and  figures  of  reference  must  be  carefully  formed,  and,  if  possible,  measure  at 
least  \"  in  height,  and  so  placed  as  not  to  interfere  with  a  thorough  comprehension  of  the 
drawing,  and  therefore  should  rarely  cross  the  lines.  Upon  shaded  surfaces  a  blank  space 
must  be  left  in  the  shading  for  the  letter.  The  same  part  of  an  invention  must  always 
be  represented  by  the  same  character,  and  the  same  character  must  never  be  used  to 
designate  different  parts. 

The  signature  of  the  inventor,  by  himself  or  by  his  attorney,  is  to  be  placed  at  the 
lower  right-hand  corner  of  the  sheet,  and  the  signature  of  two  witnesses  at  the  lower  left- 
hand  corner,  all  within  the  marginal  line.  The  title  is  to  be  written  with  pencil  on  the 
back  of  the  sheet.  The  permanent  names  and  title  will  be  supplied  subsequently  by  the 
office  in  uniform  style. 

Drawings  should  not  be  folded  for  transmission  to  the  office. 


REGISTRATION   OF   PRINTS   AND  LABELS. 

A  label  is  a  device  or  representation  borne  by  an  article  of  manufacture  or  vendible 
commodity.  A  print  is  a  device  or  representation  not  borne  by  an  article  of  manufac- 
ture or  vendible  commodity,  but  in  some  fashion  pertaining  thereto.  A  label  can  not 
be  registered  if  it  bear  a  device  capable  of  sequestration  as  a  trade-mark  until  after  such 
device  is  registered  as  a  trade-mark.  Both  labels  and  prints,  in  order  to  be  entitled  to 
registry,  must  be  intellectual  productions  in  the  degree  required  by  the  copyright  law. 


765 


766  APPENDIX. 

MENSURATION. 

The  principles  of  measurement  have  been  quite  fully  explained  under  the  heads  of  the 
Construction  of  Geometrical  Problems  and  Plotting,  but  for  ready  reference  there  are 
many  rules  which  are  of  general  application  and  very  necessary  in  designing  and  calcula- 
tion, and  are  given  briefly  as  follows : 
To  find 

The  area  of  a  parallelogram.  Multiply  the  length  by  the  height  or  perpendicular  by 
the  breadth.  Multiply  the  product  of  two  contiguous  sides  by  the  natural  sine  of  the 
included  angle.  (See  Appendix,  Table  of  Natural  Sines.) 

The  area  of  a  triangle.  Multiply  the  base  by  the  perpendicular  height  and  take  half 
the  product.  Multiply  half  the  product  of  two  contiguous  sides  by  the  natural  sine  of 
the  included  angle. 

The  area  of  a  trapezoid.  Multiply  half  the  sum  of  the  parallel  sides  by  the  perpen- 
dicular distance  between  them. 

The  area  of  any  quadrilateral  figure.  Divide  the  quadrilateral  into  two  triangles ;  the 
sum  of  the  areas  of  the  triangles  is  the  area. 

The  area  of  any  polygon.  Divide  the  polygon  into  triangles  and  take  the  sum  of  their 
areas. 

The  circumference  of  a  circle.     Multiply  the  diameter  by  3'1416  =  TT. 

The  diameter  of  a  circle.     Multiply  the  circumference  by  the  reciprocal  of  TT. 

The  area  of  a  circle.  Multiply  the  square  of  the  diameter  by  '7854,  or  the  circumfer- 
ence by  one  fourth  of  the  diameter. 

The  length  of  an  arc  of  a  circle.  Multiply  the  number  of  degrees  in  the  arc  by  the 
radius,  and  by  '01745. 

NOTE.  — The  length  of  an  arc  of  one  degree  =  radius  x  '017453. 

"       "   "     "     "     "  minute  =       "      x  '000291. 

"         "       "  "    "    "    "   second  =       "      x  '000005. 

The  area  of  a  sector  of  a  circle.  Multiply  the  length  of  the  arc  of  the  sector  by  half 
the  radius. 

The  area  of  a  segment  of  a  circle.  From  the  area  of  a  sector  subtract  the  area  of  the 
triangle  formed  by  the  radial  sides  of  the  sector  and  its  chord.  The  area  of  this  triangle 
is  the  product  of  the  natural  sine  and  cosine  by  the  square  of  the  radial  side. 

The  area  of  regular  polygons.  Find  the  area  of  one  triangle,  and  multiply  by  the 
number  of  triangles  composing  the  polygon : 

Or,  multiply  the  total  of  cosines  for  the  periphery  by  one  half  the  sine,  by  the  square 
of  the  radius  for  the  area. 

No.  of    Verti- 
4  Chord.    Sides.       cal.        Product. 

Pentagon -5878  x    5  x  -8090  -  2-3776 

Hexagon -5000  x    (i  x  '8660  =  2-5980 

Heptagon -4357  x    7  x  -9032  =  2-7478 

Octagon -3827  x    8  x  -9238  =  2-8284 

Nonagon -3420  x    9  x  '9396  =  2-8925 

Decagon -3090  x  10  x  -9510  =  2-9389 

Undecagon -2817  x  11  x  -9594  =  2-9739 

Dodecagon -2588  x  12  x  -9660  =  3-0000 

Circle =  TT  =  3-1416 

To  find 

The  area  of  the  cycloid.     Multiply  the  area  of  the  generating  circle  by  3. 
To  find 

The  area  of  the  parabola.  Multiply  the  base  by  the  height;  two  thirds  of  the  product 
is  the  area. 


APPENDIX.  767 

The  circumference  of  an  ellipse.  Multiply  the  square  root  of  half  the  sum  of  the 
squares  of  the  two  axes  by  3-1416. 

The  area  of  an  ellipse.     Multiply  the  product  of  the  two  axes  by  -7854  =  J  TT. 

NOTE. — The  area  of  an  ellipse  is  equal  to  the  area  of  a  circle  of  which  the  diameter  is  a 
mean  proportional  between  the  two  axes. 

To  find  the  area  of  any  curvilineal  figure,  bounded  at  the  ends  by  parallel  straight 
lines  (Fig.  198).  Divide  the  length  of  the  figure  into  any  number  of  equal  parts  and  draw 
ordinates  through  the  points  of  division,  to  touch  the  boundary  lines.  Or,  add  together 
the  first  and  last  ordinates,  making  the  sum  A ;  and  add  together  all  the  intermediate 
ordinates,  making  the  sum  B.  Let  L  =  the  length  of  the  figure,  and  n  =  the  number  of 
divisions,  then 

A  +  2B 

— = x  L  =  area  of  figure. 

That  is  to  say,  twice  the  sum  of  the  intermediate  ordinates,  plus  the  first  and  last  ordi- 
nates, divided  by  twice  the  number  of  divisions,  and  multiplied  by  the  length,  is  equal 
to  the  area  of  the  figure.     This  method  is  sufficiently  exact  for  most  purposes. 
To  find 

The  surface  of  a  prism  or  cylinder.  To  the  product  of  the  perimeter  of  the  end  by 
the  height,  add  twice  the  area  of  an  end. 

The  cubic  contents  of  a  prism  or  a  cylinder.  Multiply  the  area  of  the  base  by  the 
height. 

The  surface  of  a  pyramid  or  cone.  Multiply  the  perimeter  of  the  base  by  half  the 
slant  height,  and  add  the  area  of  the  base. 

The  cubic  contents  of  a  pyramid  or  a  cone.  Multiply  the  area  of  the  base  by  one  third 
of  the  perpendicular  height. 

The  surface  of  a  frustum  of  a  pyramid  or  a  cone.  Multiply  the  sum  of  the  perime- 
ters of  the  ends  by  half  the  slant  height,  and  add  the  areas  of  the  ends. 

The  cubic  contents  of  the  frustum  of  a  pyramid  or  a  cone.  Add  together  the  areas 
of  the  two  ends  and  the  mean  proportional  between  them  (that  is,  the  square  root  of  their 
product)  and  multiply  the  sum  by  one  third  of  the  perpendicular  height. 

The  cubic  contents  of  a  wedge.  To  twice  the  length  of  the  base  add  the  length  of 
the  edge ;  multiply  the  sum  by  the  breadth  of  the  base,  and  by  one  sixth  of  the  height. 

The  cubic  contents  of  a  prismoid  (a  solid  of  which  the  two  ends  are  unequal  but  par- 
allel plane  figures  of  the  same  number  of  sides).  To  the  sum  of  the  area  of  the  two  ends 
add  four  times  the  area  of  a  section  parallel  to  and  equally  distant  from  both  ends ;  and 
multiply  the  sum  by  one  sixth  of  the  length. 

The  surface  of  a  sphere.     Multiply  the  square  of  the  diameter  by  3 '1416. 

The  surface  of  a  sphere  is  equal  to  four  times  the  area  of  one  of  its  great  circles. 

The  surface  of  a  sphere  is  equal  to  the  convex  surface  of  its  circumscribing  cylinder. 

The  surfaces  of  spheres  are  to  one  another  as  the  squares  of  their  diameters. 

The  curve  surface  of  any  segment  or  zone  of  a  sphere.  Multiply  the  diameter  of  the 
sphere  by  the  height  of  the  zone  or  segment,  and  by  3 '1416. 

The  cubic  contents  of  a  sphere.     Multiply  the  cube  of  the  diameter  by  -5236  =  £  IT. 

The  cubic  contents  of  the  segment  of  a  sphere.  From  three  times  the  diameter  of  the 
sphere  subtract  twice  the  height  of  the  segment ;  multiply  the  difference  by  the  square  of 
the  height,  and  by  -5236. 

The  cubic  contents  of  a  frustum  or  zone  of  a  sphere.  To  the  sum  of  the  squares  of 
the  radii  of  the  ends  add  £  of  the  square  of  the  height;  multiply  the  sum  by  the  height 
and  by  1'5708  =  \  TT. 

The  cubic  contents  of  a  spheroid.  (A  solid  body  generated  by  the  revolution  of  an 
ellipse  around  one  of  its  axes.)  Multiply  the  square  of  the  revolving  axis  by  the  fixed 
axis  and  by  '5236. 


708 


APPENDIX. 


LINEAL  MEASUEE. 


Inches. 

1  - 

12  = 

36  = 

72  = 

7-92  = 

198  = 

792  = 

7920  = 

63360  = 

39-3685  = 


Feet. 


•08333 
1 
3 
6 

0-66 

16  J 

66 

660 

5280 

6086-07 

3-2807 


Yards. 

Fath- 
oms. 

Links. 

Rods. 

Chains. 

Furlongs 

Statute 
miles. 

Nautical 
miles. 

Metres. 

•02778 

•0139 

•126 

•005 

•00126 

•000126 

•000016 

•0254 

•333 

•1667 

1-515 

•0606 

•0151 

•00151 

•00019 

.... 

0-3048 

1 

•5 

4-545 

•182 

•0454 

•00454 

•00057 

0-9144 

2 

1 

9-1 

•364 

•091 

•0091 

•00114 

1-8289 

•22 

•11 

1 

•04 

•01 

•001 

•000125 

•2012 

5^ 

2f 

25 

1 

•25 

•025 

•003125 

5-0294 

22\ 

11 

100 

4 

1 

•10 

•0125 

20-118 

220 

\  110 

1000 

40 

10 

1 

•125 

201-18 

1760 

E80 

8000 

320 

80 

8 

] 

0-86755 

1609-41 

2028-69 

1-1527 

1 

1855-11 

1-0936 

•5468 

0-000621 

1 

Latin  prefixes,  as  milli-,  centi-,  deci-,  to  the  French  units  of  length  (metre),  surface  (are),  weight 
(gramme),  or  volume  (litre),  signify  YIOOO,  l/ioo,  or  '/io  of  the  unit ;  as,  millimetre,  '/iooo  of  a  metre, 
decigramme,  '/ID  of  a  gramme.  Greek  prefixes,  as  kilo,  hekto,  deka,  multiples  of  the  unit  by  1,000. 
100,  or  10,  as  kilometre  =  1000  metres. 

r 

MEASUEES  OF  SURFACE. 


j.  inches. 

8q.  feet. 

Sq.  yards. 

Sq.  rods. 

Roods. 

Acres. 

Sq.  miles. 

Sq.  metres. 

Ares. 

1  = 

•00894 

144  = 

1 

•Ill 

•0037 

•0929 

•0009 

1296  = 

9 

1 

•033 

•8361 

•0084 

.... 

272i 

30J 

1 

•025 

•00625 

25-293 

0-253 

10890 

1210 

40 

1 

•25 

43560 

4840 

160 

4 

1 

•00156 

4046-86 

40-47 

27878400 

3097600 

.... 

640 

1 

25899 

549-8  = 

10-763 

1-196 

•0395 

•0009 

•000247 

1 

•01 

.... 

1076-31 

119-60 

•02471 

100 

1 

BOARD   AND   TIMBER   MEASURE. 

In  board  measure  boards  are  assumed  at  one  inch  in  thickness.  To  obtain  the  num- 
ber of  feet,  board  measure  (B.  M.),  of  a  board  or  stick  of  square  timber,  multiply  to- 
gether the  length  in  feet,  the  breadth  in  feet,  and  the  thickness  in  inches. 

To  Compute  the  Volume  of  Round  Timber. — When  all  dimensions  are  in  feet,  multiply 
the  length  by  one  quarter  of  the  product  of  the  mean  girth  and  diameter,  and  the  prod- 
uct will  give  the  measurement  in  cubic  feet. 

For  Square  Timber. — When  all  dimensions  are  in  feet,  multiply  together  the  length, 
breadth,  and  depth :  the  product  will  be  the  volume  in  cubic  feet.  When  one  dimen- 
sion is  given  in  inches,  divide  by  12;  when  two  dimensions  are  given  in  inches,  divide 
by  144;  when  all  three  dimensions  are  given  in  inches,  divide  by  1728. 


APPENDIX. 

MEASURES  OF  CAPACITY. 
LIQUID  MEASURE. 


769 


Gills. 

Pints. 

Quarts. 

Gallons. 

Imp.  gallons. 

Litres. 

Cubic  feet 

Cubic  in. 

Lbs.  water 
at  62°. 

•I     

0-25 

0-125 

•03125 

•026 

•1183 

•0042 

7-219 

•26 

4  = 

1 

0-5 

0-125 

•1041 

•4731 

•01671 

28-875 

1-0412 

Bss 

2 

1 

0-25 

•2083 

0-9463 

•03342 

57-75 

2-0825 

32  = 

8 

4 

1 

0-8331 

3-7852 

0-1337 

231 

8-33 

38-4096  = 

9-6024 

4-8012 

1-2003 

1 

4-5435 

0-1605 

277-27 

10-00 

8-4534  = 

2-1133 

1-0567 

0-26417 

0-2201 

1 

0-0353 

61-0279 

2-2007 

239-36  = 

59-84 

29-92 

7-48 

6-232 

28-320 

1 

1728 

62-321 

•138528  = 

•034632 

•017316 

•004329 

•0036 

0-01639 

0-000579 

1 

•03606 

•01604 

27-727 

1 

1  barrel  =  31J  gallons.     Reciprocal  =  -03175. 


DRY  MEASURE. 


Pints. 

Quarts. 

Gallons. 

Pecks. 

Bushels. 

1  = 

0-50 

0-125 

•0625 

0-01562 

2  = 

1 

0-25 

0-125 

0-0312 

8  = 

4 

1 

0-50 

0-125 

16  = 

8 

2 

1 

0-^5 

64  = 

32 

8 

4 

i 

The  standard  bushel  contains  2150-42  cubic  inches. 


WEIGHTS. 


APOTHECARIES'. 


Grains. 

Scruples. 

Drachms. 

Ounces. 

Pounds. 

1  = 

•05 

•0167 

•0021 

•00018 

20  = 

1 

•333 

•042 

•0035 

60  = 

3 

1 

•125 

•0104 

480  = 

24 

8 

1 

•083 

5760  = 

288 

96 

12 

1 

TROY. 


Grains. 

Pennyweights. 

Ounces. 

Pounds. 

1  = 

•042 

•0021 

•00018 

24  = 

1 

•05 

•0042 

480  = 

20 

1 

•083 

5760  = 

240 

12 

1 

AVOIRDUPOIS. 


Drachms. 

Ounces. 

Pounds. 

Hundred-weights. 

Tons. 

French  grammes. 

1  = 

•0625 

•0039 

•000035 

•00000174 

1-771836 

16  = 

1 

•0625 

•000558 

•000028 

28-34938 

256  = 

16 

1 

•00893 

•000446 

453-59 

28672  = 

1792 

112 

1 

•05 

50802- 

673440  = 

35840 

2240 

20 

1 

1016041-6 

It  is  common  usage  here  to  omit  hundred-weights  (cwt.)  and  rate  tons  at  2,000  pounds  as 
net,  and  2240  Ibs.  as  gross ;  7,000  troy  or  apothecaries'  weight  equal  1  pound  avoirdupois. 
50 


770 


APPENDIX. 


COMPAKISON  OF  WEIGHT. 


DYNAMIC  TABLE. 


Pounds 
apothecaries1. 

Pounds 
Troy. 

Pounds 
avoirdupois. 

Kilo- 
gramme. 

1  = 

1 

0-8229 

0-37324 

1  = 

1 

0-8229 

0-37324 

1-2153  = 

1-2153 

1 

0-4536 

2-6792  = 

2-6792 

2-2046 

1 

Pounds, 
feet. 

Kilogramme- 
metre. 

Horse- 
power. 

French 
horse-  power. 

1  = 

0-13825 

•00003 

•000031 

7-2331  = 

1 

•000219 

•000222 

Per  min. 

33-000  = 

4562-3 

1 

1-01386 

32548-9  = 

4500 

0-98633 

1 

CUBIC  OK  SOLID  MEASURE. 


Cubic  inches. 

Cubic  feet 

Cubic  yards. 

Cubic  metres. 

United  States  gallon. 

1  = 

•00058 

•000021 

•000016 

•004329 

1728  = 

1 

0-037 

0-0283 

7-48 

46656  = 

27 

1 

0-7646 

201-97 

61016  = 

35-31 

1-3078 

1 

264-141 

231  = 

0-1337 

•00495 

•00379 

1 

SHIPPING   MEASURE. 


Register  Ton. — For  register  tonnage  or  for  measurement  of  the  entire  internal  capacity 


of  a  vessel : 

100  cubic  feet  =  1  register  ton. 
Shipping  Ton. — For  the  measurement  of  cargo : 

|  1  U.  S.  shipping  ton. 

40  cubic  feet  =  -(  31 '16  Imp.  bushels.  42  cubic  feet  = 

32-143  U.  S.    " 


1  British  shipping  ton. 
32-719  Imp.  bushels. 
33-75  U.  S.        " 


Carpenter 's  Rule. — Weight  a  vessel  will  carry  =  length  of  keel  x  breadth  at  main 
beam  x  depth  of  hold  in  feet  -j-  95  (the  cu.  ft.  per  ton).  The  result  will  be  the  tonnage. 
For  a  double-decker,  instead  of  the  depth  of  the  hold  take  half  the  breadth  of  the  beam. 


TABLE  OF  INCHES   AND  SIXTEENTHS  IN  DECIMALS  OF  A  FOOT. 


Inches. 

iV 

A 

A 

iV 

A 

A 

A 

A 

A. 

tt 

H 

H 

H 

H 

H 

0  

•000 

•005 

•010 

•016 

•021 

•026 

•031 

•036 

•042 

•047 

•062 

•057 

•062 

•068 

•073 

•078 

1  

•083 

•089 

•094 

•099 

•104 

•109 

•115 

•120 

•125 

•130 

•135 

•141 

•146 

•151 

•156 

•161 

2  

•167 

•172 

•177 

•182 

•187 

•193 

•198 

•203 

•208 

•214 

•219 

•224 

•229 

•234 

•240 

•245 

3  

•250 

•255 

•260 

•266 

•271 

•276 

•281 

•286 

•292 

•297 

•302 

•307 

•312 

•318 

•323 

•328 

4  

•333 

•339 

•344 

•349 

•354 

•359 

•365 

•370 

•375 

•380 

•385 

•391 

•396 

•401 

•406 

•411 

5  

•417 

•422 

•427 

•432 

•437 

•443 

•448 

•453 

•458 

•464 

•469 

•474 

•479 

•484 

•490 

•495 

6  

•500 

•505 

•510 

•516 

•521 

•526 

•531 

•536 

•542 

•547 

•552 

•557 

•562 

•568 

•573 

•578 

7.... 

•583 

•589 

•594 

•599 

•604 

•609 

•615 

•620 

•625 

•630 

•635 

•641 

•646 

•651 

•656 

•661 

8  

•667 

•672 

•677 

•682 

•687 

•693 

•698 

•703 

•708 

•714 

•719 

•724 

•729 

•734 

•740 

•745 

9  

•750 

•756 

•760 

•766 

•771 

•776 

•781 

•786 

•792 

•797 

•802 

•807 

•812 

•818 

•823 

•828 

10  

•833 

•839 

•844 

•849 

•854 

•859 

•865 

•870 

•875 

•880 

•885 

•891 

•896 

•901 

•906 

•911 

11  

•917 

•922 

•927 

•932 

•937 

•943 

•948 

•953 

•958 

•964 

•969 

•974 

•979 

•984 

•990 

•995 

APPENDIX.  771 


ELECTRICAL   UNITS. 

C.  G.  S. 

Unit  of  space,  1  centimetre,  C.  ;  of  mass,  1  gramme,  G.  ;  of  time,  1  second,  S. 

The  definitions  of  units  as  adopted  at  the  International  Electrical  Congress  at  Chicago 
in  1893,  established  by  Act  of  Congress  of  the  United  States,  July  12,  1894,  are  as  follows: 

The  ohm  (the  unit  of  resistance,  represented  by  R)  is  equal  to  10*  (or  1,000,000,000) 
units  of  resistance  of  the  C.  G.  S.  system,  and  is  represented  by  the  resistance  offered  to 
an  unvarying  electrical  current  by  a  column  of  mercury  at  32°  Fahr.  (14-4521  grammes 
in  mass)  of  a  constant  cross-sectional  area,  and  of  the  length  of  106 '3  centimetres. 

The  ampere  (the  unit  of  current  strength,  or  rate  of  flow,  represented  by  C)  is  one  tenth 
of  the  unit  of  current  of  the  C.  G.  S.  system,  and  is  the  equivalent  of  the  unvarying  cur- 
rent which,  when  passed  through  a  solution  of  nitrate  of  silver  in  water  in  accordance 
with  standard  specifications,  deposits  silver  at  the  rate  of  -001118  gramme  per  second. 

The  volt  (the  unit  of  electro-motive  force,  or  difference  of  potential,  represented  by  E) 
is  the  electro-motive  force  that,  steadily  applied  to  a  conductor  whose  resistance  is  1 
ohm,  will  produce  a  current  of  one  ampere,  and  is  equivalent  to  -fj  ££•  (or  -6974)  of  the 
electro-motive  force  between  the  poles  or  electrodes  of  a  Clark's  cell  at  a  temperature 
of  15°  C.,  and  prepared  in  the  manner  described  in  the  standard  specifications. 

The  coulomb  (or  ampere-second,  the  unit  of  quantity,  Q)  is  the  quantity  of  electricity 
transferred  by  a  current  of  one  ampere  in  one  second. 

The  farad  (the  unit  of  capacity  represented  by  K)  is  the  capacity  of  a  condenser 
charged  to  a  potential  of  one  volt  by  one  coulomb  of  electricity. 

The  joule  (volt-coulomb,  the  unit  of  energy  or  work,  W)  is  equal  to  10,000,000  units 
of  work  in  the  C.  G.  S.  system,  and  is  practically  equivalent  to  the  energy  expended  in 
one  second  by  an  ampere  in  one  ohm. 

The  watt,  or  ampere-volt  (the  unit  of  power,  P),  is  equal  to  10,000,000  units  of  power 
in  the  C.  G.  S.  system,  and  is  practically  equivalent  to  the  work  done  at  the  rate  of  one 
joule  per  second ;  746  watts  =  1  H.  P. 

The  henry  (the  unit  of  induction)  is  the  induction  in  a  circuit  when  the  electro-motive 
force  induced  in  this  circuit  is  one  volt,  while  the  inducing  current  varies  at  the  rate  of 
one  ampere  per  second. 

The  ohm.  volt,  etc.,  as  above  defined,  are  called  the  "  international "  ohm,  volt,  etc., 
to  distinguish  them  from  the  "  legal  "  ohm,  B.  A.  unit,  etc. 

The  value  of  the  ohm,  determined  by  a  committee  of  the  British  Association  in  1863, 
called  the  B.  A.  unit,  was  the  resistance  of  a  certain  piece  of  copper  wire  preserved  in 
London.  The  so-called  "  legal  "  ohm  as  adopted  by  the  International  Congress  of  Elec- 
tricians in  Paris  in  1884,  was  a  correction  of  the  B.  A.  unit,  and  was  defined  as  the  re- 
sistance of  a  column  of  mercury  1  square  millimetre  in  section  and  106  centimetres  long, 
at  a  temperature  of  32°  F. 

1  legal  ohm  =  1-0112  B.  A.  units,  1  B.  A.  unit  =  0-9889  legal  ohm. 

1  international  ohm  =  1-0136     "         "       1     "         "    =  0-9866  int.       " 
1  "  "     =  1  -0023  legal  ohm,     1  legal  ohm  =  0-9977  "          " 

UNIT   OF   HEAT. 

The  British  Thermal  Unit  (B.  T.  U.)  is  that  quantity  of  heat  required  to  raise  the 
temp,  of  1  pound  of  pure  water  1°  F.  at  or  near  39-1°  F.,  the  maximum  density- of  water. 

The  French  thermal  unit,  or  calorie,  is  that  quantity  of  heat  which  is  required  to  raise 
the  temperature  of  1  kilogramme  of  pure  water  1°  C.,  at  or  about  4°  C.,  which  is 
equivalent  to  39'1°  F. 

1  French  calorie  =  3'968  British  thermal  units,  1  B.  T.  U.  =  '252  calorie. 


772 


APPENDIX. 


FIFTH   POWERS,    TABLE   OF. 


Fifth  Power. 

Fifth  Power. 

Fifth  Power. 

Fifth  Power. 

11 

1  61051 

33 

391  35393 

55 

5032  84375 

77 

27067  84157 

12 

248832 

34 

454  35424 

56 

5507  31776 

78 

28871  74368 

13 

3  71293 

35 

525  21875 

57 

6016  92057 

79 

30770  56399 

14 

5  37824 

36 

604  66176 

58 

6563  56768 

80 

32768  00000 

15 

7  59375 

37 

693  43957 

59 

7149  24299 

81 

34867  84401 

16 

10  48576 

38 

792  35168 

60 

7776  00000 

82 

37073  98439 

17 

14  19857 

39 

902  24199 

61 

8445  96301 

83 

39390  40643 

18 

18  89568 

40 

1024  00000 

62 

9161  32832 

:  84 

41821  19424 

19 

24  76099 

41 

1158  56201 

63 

9924  36543 

1  85 

44370  53125 

20 

32  00000 

42 

1306  91232 

64 

10737  41824 

86 

47042  70176 

21 

40  84101 

43 

1470  08443 

65 

11602  90625 

87 

49842  09207 

22 

51  53632 

44 

1649  16224 

66 

12523  32576 

88 

52773  19168 

23 

64  36343 

45 

1845  28125 

67 

13501  25107 

89 

55840  59449 

24 

79  62624 

46 

2059  62976 

68 

14539  33568 

90 

59049  00000 

25 

97  65625 

47 

2293  45007 

69 

15640  31349 

91 

62403  21451 

26 

11881376 

48 

2548  03968 

70 

16807  00000 

92 

65908  15232 

27 

143  48907 

49 

2824  75249 

71 

18042  29351 

93 

69568  83693 

28 

172  10368 

50 

3125  00000 

72 

19349  17632 

94 

73390  40224 

29 

205  11149 

51 

3450  25251 

73 

20730  71593 

95 

77378  09375 

30 

243  00000 

52 

3802  04032 

74 

22190  06624 

96 

81537  26976 

31 

286  29151 

53 

4181  95493 

75 

23730  46875 

97 

85873  40257 

32 

335  54432 

54 

4591  65024 

76 

25355  25376 

99 

95099  00499 

CAST-IRON  BALLS,    VOLUME   AND   WEIGHT   OF. 


Diameter. 

Volume. 

Weight. 

Diameter. 

Volume. 

Weight. 

Diameter. 

Volume. 

Weight. 

Inches. 

Cu.  inches. 

Pounds. 

Inches. 

Cu.  inches. 

Pounds. 

Inches. 

Cu.  inches. 

Pounds. 

2 

4-19 

1-09 

«H 

87-1 

22-7 

9 

381-7 

99-4 

2i 

8-18 

2-13 

6 

113-1 

29-5 

9| 

448  9 

116-9 

3 

14-1 

3-68 

6i 

143-8 

37-5 

10 

523-6 

136-4 

3* 

22-5 

5-85 

7 

179-6 

46-8 

11 

696-9 

181-8 

4 

33-5 

8-73 

7* 

220-9 

57-5 

12 

904-8 

235-9 

4| 

47-7 

12-4 

8 

268-1 

69-8 

13 

1150-3 

299-6 

5 

65-5 

17-0 

8* 

321-5 

83-7 

14 

1436-8 

374-6 

Weight  for  other  metals  vary  as  their  specific  gravities  and  for  diameters  as  their  cubes. 
CAST-IRON  PIPES,   STANDARD   WEIGHTS   OF. 


a.S 

«d 

2  a 

g.  . 

•2S 

°"t  • 

5S.& 

o 

i§3 

0,^-42 

gg 

15 

D' 

Id 

1 

rtj2ji 

ssl 

£H         O 

-—  '  CM 

^  o 

E 

5-5 

H  D 

*o 

*0  <D  M 

*°<N  M 

®  S^l 

^5 

^ 

•s 

S 

S     to 

•££•3 

i,wi 

1  E^  j 

i2  p 

•3 

S 

A 

•SP  a5  H 

.Sf    s 

•-^5 

.S<w<M  £ 

11 

a. 

• 

H 

>>  oP" 

«  o  o.ts 

a  co 

09 

^ 

* 

^~ 

O 

O 

Inches. 

Inches. 

Pounds. 

Pounds. 

Pounds. 

Pounds. 

Pounds. 

U.  S.  gal. 

4 

0-40 

17-27 

18-75 

225 

3600 

720 

•6528 

6 

0-42 

26-46 

28-92 

347 

2515 

503 

1-469 

8 

0-45 

37-33 

40-50 

486 

2025 

405 

2-611 

10 

0-50 

51-54 

56-17 

673 

1800 

360 

4-081 

12 

0-55 

67-76 

73-75 

885 

1650 

330 

5-876 

14 

0-58 

83-02 

90-67 

1088 

1490 

298 

7-997 

16 

0-60 

97-78 

106-75 

1281 

1350 

270 

10-440 

18 

0-64 

117-11 

126-67 

1520 

1280 

256 

13-22 

20 

0-70 

142-25 

153-43 

1841 

1260 

252 

16-32 

24 

0-80 

194-77 

210-33 

2524 

1200 

240 

23-50 

30 

0-90 

273-00 

285-33 

3524 

1080 

216 

36-72 

36 

1-00 

363-22 

390-50 

4686 

1000 

200 

52-88 

From  "  Water  Works,"  by  Howland  and  Ellis. 


APPENDIX. 


773 


rH 

£ 
ft 

CM 

8 

a 

go- 
o-is 

Tf  •* 

0 

oot— 

GO-*  rH 

•CO-* 
COb-0 
COCO  •* 

OS 

i 

CM 
CM 

(M  OtO 

rH-*b- 

o  CO  te 

00 

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774  APPENDIX. 

WEIGHTS  OF  WROUGHT-IRON  AND  BRASS  PLATES  AND  WIRE,  SOFT  ROLLED. 


BIRMINGHAM  UAUGE. 

No.  of 

gauge. 

AMERICAN    GAUGE   (BROWN    A   8HAEPE). 

Plate  iron. 

Thickness  of 
each  number. 

Thickness 
of  each 
number. 

PLATES   PER   SQUARE   FOOT. 

WIRE   PER    LINEAL   TOOT. 

Wrought 
iron. 

Brass. 

Wrought 
iron. 

Brass. 

Lbs. 
17-025 

Inch. 
•454 

0000 

Inch. 
•46 

Lbs. 
17-25 

Lbs. 
19-68 

Lbs. 
•5607 

Lbs. 
•6051 

15-9375 

•425 

000 

•4096 

15-361 

17-53 

•4447 

•4799 

14-25 

•38 

00 

•3648 

13-68 

15-61 

•3527 

•3806 

12-75 

•34 

0 

•3248 

12-182 

13-90 

•2797 

•3018 

11-25 

•3 

1 

•2893 

10-848 

12-38 

•2218 

•2393 

10-65 

•284 

2 

•2576 

9-661 

11-02 

•1759 

•1898 

9-7125 

•269 

3 

•2294 

8-603 

9-81 

•1395 

•1505 

8-925 

•238 

4 

•2043 

7-661 

8-74 

•1106 

•1193 

8-25 
7-6125 

•22 
•203 

5 
6 

•1819 
•1620 

6-822 
6-075 

7-78 
6-93 

•0877 
•0695 

•0946 
•0750 

6-75 

•18 

7 

•1442 

5-410 

6-17 

•0551 

•0595 

6-1875 

•165 

8 

•1284 

4-818 

5-49 

•0437 

•0472 

5-55 

•148 

9 

•1144 

4-291 

4-89 

•0347 

•0374 

5-025 

•134 

10 

•1018 

3-820 

4-36 

•0275 

•0296 

4-5 

•12 

11 

•0907 

3-402 

3-88 

•0218 

•0235 

4-0875 

•109 

12 

•0808 

3-030 

3-45 

•0173 

•0186  . 

3-5625 

•095 

13 

•0719 

2-698 

3-07 

•0137 

•0148 

3-1125 

•083 

14 

•0640 

2-403 

2-74 

•0109 

•0117 

2-7 

•072 

15 

•0570 

2-140 

2-44 

•00863 

•00931 

2-4375 

•065 

16 

•0508 

1-905 

2-17 

•00684 

•00758 

2-175 

•058 

17 

•0452 

1-697 

1-93 

•00542 

•00585 

1-8375 

•049 

18 

•0403 

1-511 

1-72 

•00430 

•00464 

1-575 

•042 

19 

•0358 

1-345 

1-53 

•00341 

•00368 

1-3125 

•035 

20 

•(319 

1-198 

1-36 

•00271 

•00292 

1-2 

•032 

21 

•0284 

1-067 

1-21 

•00215 

•00231 

1-05 

•028 

22 

•0253 

•9505 

1-08 

•00170 

•00183 

•9375 

•025 

23 

•0225 

•8464 

•9660 

•00135 

•00145 

•826 

•022 

24 

•0201 

•7537 

•8602 

•00107 

•00115 

•75 

•02 

25 

•0179 

•6712 

•7661 

•00085 

•000916 

•675 

•018 

26 

•0159 

•5977 

•6822 

•000673 

•000726 

•6 

•016 

27 

•0141 

•5323 

•6075 

•000534 

•000576 

•525 

•014 

28 

•0126 

•4740 

•5410 

•000423 

•000457 

•4875 

•013 

29 

•0112 

•4221 

•4818 

•000336 

•000362 

•45 

•012 

30 

•0100 

•3759 

•4290 

•000266 

•000287 

•375 

•01 

31 

•0089 

•3348 

•3821 

•000211 

•000228 

•3375 

•009 

32 

•0079 

•2981 

•3402 

•000167 

•000180 

•3 

•008 

33 

•00708 

•2655 

•3030 

•000132 

•000143 

•2625 

•007 

34 

•00630 

•2364 

•2698 

•000105 

•000113 

•1875 

•005 

35 

•00561 

•2105 

•2402 

•0000836 

•00009015 

•15 

•004 

36 

•005 

•1875 

•214 

•0000662 

•0000715 

37 

•00445 

•1669 

•1905 

•0000525 

•00005671 

38 

•00396 

•1486 

•1697 

•0000416 

•00004496 

39 

•00353 

•1324 

•1511 

•0000330 

•00003566 

40 

•00314 

•1179 

•1345 

•0000262 

•00002827 

Copper  is  about  5  per  cent  heavier  than  brass.  Lead  is  about  47  per  cent  heavier  than  wrought 
iron.  Zinc  is  about  7  per  cent  lighter  than  wrought  iron.  Sheet  copper  is  rated  by  weight  at  so 
many  ounces  per  square  foot,  and  sheet  lead  at  so  many  pounds  per  square  foot. 


APPENDIX. 


775 


TABLE  OF  DIMENSIONS  AND  WEIGHT  OF  WEOUGHT-1RON  WELDED  TUBES. 


Nominal 
diameter. 

External 
diameter. 

Thick- 
ness. 

Internal 
diameter. 

Internal 
circum- 
ference. 

External 
circum- 
ference. 

Length  of 
pipe  per 
square 
toot  of 
internal 
surface. 

Length  of 
pipe  per 
square 
foot  of 
external 
surface. 

Internal 
area. 

Weight 
per  foot. 

No.  of 

threads 
per 
inch  of 
screw. 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

Feet. 

Feet. 

Inches. 

Lbs. 

Yi 

•40 

•068 

•27 

•85 

1-27 

14-15 

944 

•057 

•24 

27 

»/« 

•54 

•088 

•36 

ri4 

1-7 

10-5 

7-075 

•104 

•42 

18 

3/8 

•67 

•091 

•49 

1-55 

2-12 

7-67 

5-657 

•192 

•56 

18 

V. 

•84 

.109 

•62 

1-96 

2-65 

6-13 

4-502 

•305 

•84 

14 

3/4 

1-05 

.113 

•82 

2-59 

3'3 

4-64 

3-637 

•533 

1-13 

14 

1 

1-31 

•134 

1-05 

3-29 

4-13 

3-66 

2-903 

•863 

1-67 

ll1/* 

l'/4 

1-66 

•14 

1-38 

4-33 

5-21 

2-77 

2-301 

1-496 

2-26 

117* 

!«/• 

1-9 

•145 

1-61 

5-06 

5-97 

2-37 

2-01 

2-038 

2-69 

nv« 

2 

2-37 

•154 

2-07 

6-49 

7-46 

1-85 

1-611 

3-355 

3-67 

"V. 

2/2 

2-87 

•204 

2-47 

7-75 

9-03 

1-55 

1-328 

4-783 

5-77 

8 

3 

3-5 

•217 

3-07 

9-64 

11- 

1-24 

1-091 

7-388 

7-55 

8 

•»/• 

4- 

•226 

3-55 

11-15 

12-57 

1-08 

0-955 

9-887 

9-05 

8 

4 

4-5 

•237 

4-07 

12-69 

14-14 

•95 

0-849 

12-73 

10-73 

8 

«*/• 

5- 

•247 

4-51 

14-15 

15-71 

•85 

0-765 

15-939 

12-49 

8 

5 

5-56 

•259 

5-04 

15-85 

17-47 

•78 

0-629 

19-99 

14-56 

8 

6 

6-62 

•28 

6-06 

19-Q5 

20-81 

•63 

0-577 

28-889 

18-77 

8 

7 

7-62 

•301 

7-02 

22-06 

23-95 

•54 

0-505 

38-737 

23-41 

8 

8 

8-62 

•322 

7-98 

25-08 

27-1 

•48 

0-444 

50-039 

28-35 

8 

9 

9-69 

•344 

9- 

28-28 

30-43 

•42 

0-394 

63-633 

34-08 

8 

10 

10-75 

•366 

10-02 

31-47 

33-77 

•38 

0-355 

78-838 

40-64 

8 

Nominal 
diameter. 

Thickness, 
extra  strong. 

Thickness,  double 
extra  strong. 

Actual  inside  diameter. 
Extra  strong. 

Actual  inside  diameter. 
Double  extra  strong. 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

'/• 

o-ioo 



0-205 

.  .  •  •  • 

l/4 

0-123 

0-294 

..... 

3/8 

0-127 



0-421 

...    . 

'/• 

0-149 

0-298 

0-542 

0-244 

3/4 

0-157 

0-314 

0-736 

0-422 

1 

0-182 

0-364 

0-951 

0-587 

W4 

0-194 

0-388 

1-272 

0-884 

l'/2 

0-203 

0-406           * 

1-494 

1-088 

2 

0-221 

0-442 

1-933 

1-491 

f/» 

0-280 

0-560 

2-315 

.   1-755 

3 

0-304 

0-608 

2-892 

2-284 

S'/« 

0-321 

0-642 

3-358 

2-716 

4 

0-341 

0-682 

3-818 

3-136 

BOILER  TUBES. 

External 

Thickness, 

Average 

External 

Thickness, 

Average 

diameter. 

wire  gauge. 

weight. 

diameter. 

wire  gauge. 

Weight. 

Inches. 

No. 

Lbs.  per  foot. 

Inches. 

No. 

Lbs.  per  foot 

W4 

16 

1- 

3 

11 

3-5 

!*/• 

15   ' 

1-16 

8'/4 

11 

4' 

W4 

14 

1-63 

4 

8 

6'4 

2 

13 

2- 

5 

7 

9-1 

2Y4 

12 

2-16 

6 

6 

12'3 

272 

12 

2-56 

7 

6 

15-2 

•*VH 

11 

2-2 

8 

6 

16- 

776 


APPENDIX. 


HEAVY  PIPE  FOE  DRIVEN  WELLS. 
Tested  at  1200  pounds  hydraulic  pressure.     Furnished  in  five-foot  lengths. 


Size  (inches)  

li 

1| 

2 

2£ 

3 

3* 

4 

Weight  per  foot,  Ibs  

3'62 

2-75 

3-75 

6-00 

7'75 

9-25 

11-00 

HEAVY  WROUGHT  GALVANIZED  IKON  SPIRAL  K1VETED  PIPES, 

WITH  FLANGED  CONNECTIONS. 
Tested  at  150  pounds  hydraulic  pressure.     Regalvanized  after  riveting. 


Inside  diameter  (inches  )  .  .    . 

3 

4 

5 

6 

7 

8 

9 

10 

11 

19, 

Wire  gauge,  Nos  

20 

20 

20 

18 

18 

18 

18 

16 

16 

16 

Nominal  weight  per  foot,  Ibs.  .  . 

H 

4 

5 

6 

7 

8 

9 

12 

13 

14 

Manufactured  lengths,  20  feet  or  less.     Elbows  and  other  fittings,  cast  iron. 
LIGHT  PIPE,  SUITABLE  FOB  HOUSE  LEADERS,  VENTILATING,  AIR,  AND  BLOWER  PIPES,  ETC. 


2 

21 

3 

3* 

4 

4* 

5 

5$ 

6 

Nominal  weight  per  foot,  Ibs  

1 

i 

i 

1 

H 

If 

1* 

If 

1* 

TABLE  OF  COPPER  AND  BRASS  RODS  ONE  FOOT  IN  LENGTH. 

To  find  the  weight  of  copper  or  brass  pipe,  take  the  weight  of  the  exterior  diameter  from  the 
table,  and  subtract  from  it  the  weight  of  a  rod  equal  to  that  of  the  interior  diameter,  or  bore.     . 


Diamet'r 
in 
inches. 

Copper. 

Brass. 

Diamet'r 
in 
inches. 

Copper. 

Brass. 

Diamet'r 
in 
inches. 

Copper. 

Brass. 

v« 

•047 

•045 

I'/* 

7-993 

7-593 

4'A 

55-62 

52-27 

'/.• 

•106 

•101 

I11/!. 

8-630 

8-198 

43/8 

58-94 

5539 

'A 

•189 

•179 

!3/4 

9-270 

8-806 

4'A 

62-36 

58-60 

'A- 

•296 

•281 

lls/» 

9-950 

9-452 

4'/8 

65-87 

61-90 

'/• 

•426 

•405 

i'/i 

10-642 

10-110 

4% 

69-48 

6 

v« 

•579 

•550 

i»/i. 

11-370 

10-801 

*'/• 

73-19 

68-77 

'/• 

•757 

•719 

2 

12-108 

11-503 

5 

77-43 

72-76 

•A. 

•958 

•910 

i'/a 

13-668 

12-985 

5'/8 

80-89 

76-00 

5/8 

1-182 

1-123 

2'A 

15-325 

14-559 

5'/4 

84-88 

79-76 

"A. 

1-431 

1-360 

23/8 

17-075 

16-221 

58/8 

88-97 

83-60 

% 

1-703 

1-618 

2'A 

18-916 

17-970 

5'A 

93-15 

87-53 

'•/.• 

1-998 

1-898 

25A 

20-856 

19-808 

56/8 

97-44 

91-56 

V« 

2-318 

2-202 

23A 

22-891 

21-746 

53/4 

101-81 

95-68 

16Ae 

2-660 

2-527 

27/8 

25-019 

23-768 

5'/8 

106-29 

99-88 

1 

3-027 

2-876 

3 

27-243 

25-881 

6 

110-85 

104-15 

I1/" 

3-417 

3-246 

3'/8 

29-559 

28-081 

6>/4 

12030 

113-04 

1'A 

3-831 

3-639 

3'A 

31-972 

30-373 

6'A 

130-10 

122-26 

l»/>e 

4-269 

4-056 

33/8 

34-481 

32-757 

63/4 

140-32 

131-85 

*v« 

4-723 

4-487 

31/* 

37-081 

35-227 

7 

150-86 

141-76 

!•/!• 

5-214 

4-953 

36/8 

39-777 

37-788 

VV4 

161-87 

152-10 

!3/8 

5-723 

5-437 

3«/4 

42-568 

40-440 

»'/• 

173-22 

162-77 

l'/M 

6-255 

5-943 

3'/8 

45-455 

43-182 

73/4 

184-97 

173-81 

W. 

6-811 

6-470 

4 

48-433 

46-000 

8 

197-03 

185-14 

!9/ie 

7-390 

7-020 

4V8 

52-40 

49-24 

APPENDIX. 


NUMBER  OF  BURDEN'S  RIVETS  IN  ONE  HUNDRED  POUNDS. 


Lengths. 

DIAMETER. 

Lengths. 

3S.B. 

i 

1 

H 

i 

1 

1,092 

665 

.... 

5 

90 

i 

1,027 

597 

«* 

85 

1 

940 

538 

450 

.... 

6 

80 

H 

840 

512 

415 

6} 

75 

H 

797 

487 

389 

356 

7 

70 

if 

760 

460 

370 

329 

n 

67 

1* 

730 

440 

357 

280 

8 

65 

if 

711 

420 

340 

271 

H 

61 

if 

693 

390 

325 

262 

9 

67 

*i 

648 

375 

312 

257 

H 

54 

2 

608 

360 

297 

243 

10 

61 

2i 

573 

354 

.... 

10$ 

47 

H 

555 

347 

280 

232 

H 

525 

335 

260 

220 

2f 

500 

312 

242 

208 

3 

460 

290 

224 

197 

3* 

433 

267 

212 

180 

»i 

413 

248 

201 

169 

Si 

395 

241 

192 

160 

4 

230 

184 

158 

4i 

.... 

220 

177 

150 

H 



210 

171 

146 

4f 

200 

166 

138 

5 

190 

161 

135 

6* 

180 

156 

130 

H 

.... 

172 

151 

124 

5f 

164 

145 

120 

6 

.... 

157 

140 

115 

6* 

.... 

150 

138 

111 

64 

.... 

146 

134 

107 

H 

.... 

143 

129 

104 

7 

.... 

140 

125 

100 

WEOUGHT  SPIKES  — NUMBER  TO  A  KEG  OF  ONE  HUNDRED  AND  FIFTY  POUNDS. 


LENGTH. 

i" 

A" 

1" 

TV 

i" 

Inches 
3 

2  250 

3|  

1,890 

1,208 

4  

1,650 

1,135 

44  . 

1,464 

1,064 

5  

1,380 

930 

742 

6  

1,292 

868 

570 

7  . 

1,161 

662 

482 

445 

806 

8  

635 

455 

384 

256 

9  

573 

424 

300 

240 

10  

391 

270 

222 

11  

249 

203 

12  

236 

180 

778  APPENDIX. 

LENGTHS   OF  CUT  NAILS  AND  SPIKES,   AND  NUMBER   IN  A  POUND. 


Size. 

Length. 

No. 

Size. 

Length.    . 

No. 

Size. 

Length. 

No. 

Inches. 

Inches. 

Inches. 

3d. 

1± 

420 

8d. 

2i 

100 

SOd. 

4 

24 

4 

1* 

270 

10 

3 

65 

40 

*i 

20 

5 

If 

220 

12 

H 

52 

60 

6 

2 

175 

20 

H 

28 

APPROXIMATE  NUMBER  OF   WIRE   NAILS  PER  POUND. 


LENGTH,  INCHES. 


B.  W.  G. 

X 

% 

X 

K 

% 

1 

1* 

IX 

IX 

2 

2* 

3 

3X 

4 

4# 

5 

6 

7 

00... 

33 
34 

45 
52 
60 
72 
85 
99 
120 
137 
165 
198 
251 
329 
429 
568 
701 
913 
1246 
1655 
2133 
3000 

27 
29 

38 
44 
50 
60 
71 
82 
100 
115 
138 
165 
209 
274 
357 
473 
584 
761 
1038 
1379 
1778 

23 
25 
32 
37 
43 
51 
60 
71 
85 
98 
118 
142 
179 
235 
306 
406 
500 
653 
890 
1182 

20 
21 
28 
32 
38 
45 
53 
62 
75 
86 
103 
124 
157 
204 
268 
350 
438 
571 
779 

16 
17 
23 
26 
30 
36 
42 
50 
60 
69 
82 
99 
125 
164 
214 
284 
350 

14 

15 
19 
22 
25 
30 
35 
41 
50 
57 
69 
83 
105 
137 
178 
236 

12 
13 
16 
19 
22 
26 
30 
35 
43 
49 
59 
71 
90 
117 
153 

10 
11 
14 
16 
19 
23 
26 
31 
37 
43 
52 
62 
79 
103 

9 
10 
13 
14 
17 
20 
24 
28 
33 
39 
46 
55 
70 

8 
9 
11 
13 
15 
18 
21 
25 
30 
35 
41 
50 

7 
8 
10 
11 
13 
15 
18 
21 
25 
29 

6 

8 
9 
11 
13 
15 
18 

o 

1  

57 
65 

76 
90 
106 
123 
149 
172 
207 
248 
314 
411 
536 
710 
876 
1143 
1558 
2069 
2667 
3750 
4444 

2  

3 

100 
120 
141 
164 
200 
229 
276 
333 
418 
548 
714 
947 
1168 
1523 
2077 
2758 
.3556 
5000 
5926 
7618 

4  

5  

211 

247 
299 
345 
414 
496 
628 
822 
1072 
1420 
1752 
2280 
3116 
4138 
5334 
7500 
8888 
11428 

169 
197 
239 
275 
331 
397 
502 
658 
857 
1136 
1402 
1828 
2495 
3310 
4267 
6000 
7111 
9143 

6  

7  

8  

9  

10  . 

663 
837 
1096 
1429 
1893 
2336 
3048 
4156 
5517 
7112 
10000 
11850 
15237 

11  

13 

13  

14  

2840 
3504 
4571 
6233 
8276 
10668 
15000 
17777 
;>v>H5(i 

15  
16  

B.  W.  G. 

8 

9 

10 

11 

12 

~3K 
3% 
W 
5# 

17... 

0  

5 
5^ 
7 
8 
10 
11 

W 
5 

6 

7 
8 
10 

4 
4K 
5% 
?,% 
T# 
9 

3% 
4 
5 
6 

18 

1 

19... 

2  

20  
21  .. 

3  

4  

22... 

5... 

TESTS  OF  TELEGRAPH  WIRE. 

The  following  data  are  taken  from  a  table  given  by  Mr.  Prescott  relating  to  tests  of  E.  B. 
B.  galvanized  wire  furnished  the  Western  Union  Telegraph  Company : 


Size 
of 
Wire. 

Diameter 
Parts  of 
One  Inch. 

WEIGHT. 

Length, 
Feet  per 
Pound. 

RESISTANCE. 
TEMP.,  75-8°  FAHB. 

Ratio  of 
Breaking 
Weight  to 
Weight  per 
Mile. 

Grains,  per 
Foot. 

Pounds  per 
Mile. 

Feet  per 
Ohm. 

Ohms  per 
Mile. 

4 

•238 

1043-2 

886-6 

6-00 

958 

5-51 

5 

•220 

891-3 

673-0 

7-85 

727 

7-26 

6 

•203 

758-9 

572-2 

9-20 

618 

8-54 

3-05 

7 

•180 

596-7 

449-9 

11-70 

578 

10-86 

3-40 

8 

•165 

501-4 

378-1 

14-00 

409 

12-92 

3-07 

9 

•148 

403-4 

304-2 

17-4 

328 

16-10 

3-38 

10 

•134 

330-7 

249-4 

21-2 

269 

19-00 

3-37 

11 

•120 

265-2 

200-0 

26-4 

216 

24-42 

2-97 

12 

•109 

218-8 

165-0 

32-0 

179 

29-60 

3-43 

14 

•083 

126-9 

95-7 

55-2 

104 

51-00 

3-05 

SIZES    OF   GALVANIZED   WIRE   USED    IN    TELEGRAPH   AND   TELEPHONE 

LINES. 

No.  4.  Now  used  on  important  lines  where  the  multiplex  systems  are  applied.  No. 
5.  Little  used.  No.  6.  Used  for  important  circuits  between  cities.  No.  8.  Medium  size 
for  circuits  of  400  miles  or  less.  No.  9.  For  similar  locations  to  No.  8,  but  on  somewhat 


APPENDIX.  Y79 

shorter  circuits  ;  until  lately  was  the  size  most  largely  used  in  this  country.  Nos.  10,  11. 
For  shorter  circuits,  railway  telegraphs,  private  lines,  police  and  fire-alarm  lines,  etc. 
No.  12.  For  telephone  lines,  police  and  fire-alarm  lines,  etc.  Nos.  13,  14.  For  telephone 
lines  and  short  private  lines  :  steel  wire  is  used  most  generally  in  these  sizes. 

The  grades  of  line  wire  are  generally  known  to  the  trade  as  "Extra  Best  Best  "  (E. 
B.  B.),  "Best  Best"  (B.  B.),  and  "Steel." 


STANDARD  I  BEAMS. 


Depth 

Min.  wt. 

WEIGHT  PER  FOOT. 

Increase 
of  b  and  t 

of 
beam. 

per 
foot. 

Min. 
b. 

Min. 
t. 

z. 

s. 

P- 

y- 

Intermediate. 

for  each 
Ib.  inc.  of 
weight. 

Max. 

24" 

80-00 

7-00 

•50 

3-250 

•60 

•542 

1-142 

Vary  by  5  Ibs. 

•0123 

100-00 

20" 

64-00 

6-25 

•50 

2-875 

•55 

•479 

1-029 

65  Ibs.  then  by  5  Ibs. 

•015 

75-00 

15" 

42-00 

5-50 

•41 

2-545 

•41 

•424 

0-834 

45   "           "      5    " 

•020 

55-00 

12" 

31-50 

5-00 

•35 

2-325 

•35 

•388 

0-738 

•025 

35-00 

10" 

25-00 

4-66 

•31 

2-175 

•31 

•363 

0-673 

Vary  by  5  Ibs. 

•029 

40-00 

9" 

21-00 

4-33 

•29 

2-020 

•29 

•337 

0-627 

25  Ibs.  then  by  5  Ibs. 

•033 

35-00 

8" 

18-00 

4-00 

•27 

1«865 

•27 

•311 

0-581 

Vary  by  2£  Ibs. 

•037 

25-50 

7" 

15-00 

3-66 

•25 

1-705 

•25 

•284 

0-534 

"      "  2|    " 

•042 

20-00 

6" 

12-25 

3-33 

•23 

1-550 

•23 

•258 

0-488 

«      «   2i    " 

•049 

17-25 

5" 

9-75 

3-00 

•21 

1-395 

•21 

•233 

0-443 

»      "   2i    " 

•059 

14-75 

4" 

7-50 

2-66 

•19 

1-235 

•19 

•206 

0-396 

"      "   1    Ib. 

•074 

10-50 

3" 

5-50 

2-33 

•17 

1-080 

•17 

•180 

0-350 

"      "   1     " 

•098 

7-50 

STANDARD   CHANNELS. 


WEIGHT  PER  FOOT. 

Increase 

Depth 

Min    wt 

of  b  and  t 

of 
chan- 

per 
foot. 

Min. 
b. 

Min. 

t. 

z. 

s. 

P- 

y- 

Intermediate. 

for  each 
Ib.  inc.  of 

Max. 

nel. 

weight. 

15" 

33-00 

3-40 

•40 

3-00 

•40 

•500 

•900 

35  Ibs.  then  by  5  Ibs. 

•020 

55-00 

12" 

20-50 

2-94 

•28 

2-66 

•28 

•443 

•723 

25   "            "      5    " 

•025 

40-00 

10" 

15-00 

2-60 

•24 

2-36 

•24 

•393 

•633 

Vary  by  5  Ibs. 

•029 

35-00 

9" 

13-25 

2-43 

•23 

2-20 

•23 

•367 

•597 

15  Ibs.  then  bv  5  Ibs. 

•033 

25-00 

8" 

11-25 

2-26 

•22 

2-04 

•22 

•340 

•560 

Vary  by  2i  Ibs. 

•037 

21-25 

7" 

9-75 

2-09 

•21 

1-88 

•21 

•313 

•523 

2£    " 

•042 

19-75 

6" 

8-00 

1-92 

•20 

1-72 

•20 

•287 

•487 

2|    «'• 

•049 

15-50 

5" 

6-50 

1-75 

•19 

1-56 

•19 

•260 

•450 

2i    " 

•059 

11-50 

4" 

5-25 

1-58 

•18 

1-40 

•18 

•233 

•413 

1    Ib. 

•074 

7-25 

3" 

4-00 

1-41 

•17 

1-24 

•17 

•207 

•377 

1     " 

•098 

6-00 

During  the  preparation  of  this  work  the  Association  of  American  Steel  Manufacturers 
has  been  formed,  from  whose  circular  the  above  table,  has  been  extracted. 

GRADES   OF   STEEL. 

Rivet  Steel.—  Ultimate  strength,  48,000  to  58,000  pounds  per  square  inch. 
Elongation,  26  per  cent. 


780 


APPENDIX. 


Soft  Steel.—  Ultimate  strength,  52,000  to  62,000  pounds  per  square  inch. 
Elongation,  25  per  cent. 

Medium  Steel.— Ultimate  strength,  60,000  to  70,000  pounds  per  square  inch. 
Elongation,  22  per  cent. 

Elastic  limit,  not  less  than  one  half  the  ultimate  strength. 

Bending  test,  180  degrees  flat  on  itself,  or  equal  to  thickness  of  piece  tested,  without 
fracture  on  outside  of  bent  portion. 


WEIGHTS  OF  LEAD   PIPE  PEE  FOOT  IN  LENGTH. 


Caliber. 


i 

I 

i 

f 
I 

1 

u 


if 

2 


MARK. 

AAA 

AA 

A 

B 

C 

D 

E 

Lbs.  oz. 

Lbs.  oz. 

Lbs.  oz. 

Lbs  oz. 

Lbs.  oz. 

Lbs.  oz. 

Lbs.  oz. 

Lbs.  oz. 
0  2 

0  10 

0  9i 

0  2 

1  12 

1   5 

1   2 

1   0 

0  14 

0  7 

3  .. 
2   8 
3   8 

2   0 

1  10 

1   3 

1  0 

0  10 
0  12 
1  4 

0  12 

2  12 

2   8 

2   0 

1  7 

4  14 

3   3 

3   0 

2   3 

1  12 

1  3 

1  0 

6  .. 

4   8 

4   0 

3   4 

2  8 

2  4 

2  0 

1  8 

6  12 

5  12 

4  11 

3  11 

3  0 

2  8 

2  0 

.  .  .  . 

8   0 

7   0 

6   4 

5   0 

4  4 

3  8 
3  0 
3  10 

2  0 

.  .  .  . 

8   8 

6   7 

5   0 

4  0 

10  11 

8  14 

7   0 

6   0 

5  0 

4  0 

.  . 

.  .  .  . 

.  . 

.  . 

.  . 

3  0 

THICKNESS. 

WASTE. 

1 

A 

i 

A 

16  11 

13  10 

10  10 

7   3 

6  0 

4  0 

19   9 
22   8 
25   6 

16   0 
18   7 
20  14 

12   9 
14   8 
16   7 

9   4 
10  12 
12   2 

5  0 

3  8 

..  .. 

8  0 

6  0 

.  .  .  . 

.  .   .  . 

.. 

18   6 

13   9 

10  8 

7  6 

31   3 

..   .. 

20   5 

15   0 

..  .. 

10  8 
12  0 

.  .  .  . 

TABLE  OF  THE  WEIGHT  OF  A  CUBIC  FOOT  OF  WATER  AT  DIFFERENT  TEM- 
PERATURES. 


Fahren- 
heit. 

Centi- 
grade. 

Weight  in 
pounds. 

Fahren- 
heit. 

Centi- 
grade. 

Weight  in 
pounds. 

Fahren- 
heit. 

Centi- 
grade. 

Weight  in 
pounds. 

Degrees. 
32 

Degrees. 
0 

62-42 

Degrees. 
95 

Degrees. 
35 

62-06 

Degrees. 
167 

Degrees. 

75 

60-87 

39 

4 

62-42 

104 

40 

61-95 

176 

80 

60-68 

41 

5 

62-42 

113 

45 

61-83 

185 

85 

60-48 

50 

10 

62-41 

122 

50 

61-69 

194 

90 

60-27 

59 

15 

62-37 

131 

55 

61-55 

203 

95 

60-04 

68 

20 

62-32 

140 

60 

61-39 

212 

100 

59-83 

77 

26 

62-25 

149 

65 

61-23 

86 

30 

62-16 

158 

70 

61-06 

APPENDIX. 


T81 


FIG.  1863. 


THE  FLOW   OF   WATER. 

With  the  increased  consumption  of  water  by  the  mills  at  Lowell,  Mass.,  there  was 
found  a  necessity  for  the  accurate  gauging  of  the  quantities  severally  used,  and,  as  at 
times  the  total  was  beyond  the  flow  of  the  stream,  that  it  should  be  properly  distributed 
and  that  none  should  be  wasted.  At  this  time  the  late  James  B.  Francis  was  the  engi- 
neer of  the  Locks  and  Canals  Company,  to  whom  the  charge  of  the  canals  and  water  dis- 
tribution was  committed.  He  decided  that  the  weir  was 
the  form  in  which  the  water  from  the  several  wheels 
should  be  measured  as  most  economical  in  application  and 
accurate  in  results. 

Figs.  1863  and  1864  are  the  sectional  elevation  and 
plan  of  the  common  form  of  weir,  in  which  the  lower 
edges,  bottom,  and  sides  are  chamfered  off,  with  edges 
about  i"  wide,  making  a  perfect  rectangle.  In  his  ex- 
periments Mr.  Francis  made  the  bottom  plate  of  cast  iron 
with  the  upper  edge  planed  and  set  accurately  horizontal 
and  the  sides  planed  for  the  vertical  edges  and  for  the 
joints  with  the  bottom  plate.  The  iron  rectangle  could 
be  accurately  measured,  but  it  was  necessary  to  deter- 
mine the  wetted  rectangle  from  the  height  of  the  water 
above  the  bottom  edge.  This  was  done  by  the  hook 
gauge,  in  which  the  hook  was  stbmerged  in  the  water 
and  gradually  raised  by  a  micrometer  screw  till  it  showed 
the  sign  of  a  rising  at  the  surface  of  the  water  (Fig.  1865). 
The  0  of  the  scale  of  the  gauge  was  accurately  referred 
to  the  edge  of  the  weir.  It  was  necessary  that  the  surface 
of  the  water  at  the  hook  be  kept  perfectly  still.  It  was 
therefore  submerged  in  a  tight  box  which  had  communi- 
cation with  the  water  in  the  flume  by  a  very  small  hole  or 
by  a  small  pipe  on  the  bottom  of  the  flume,  across  it  par- 
allel to  the  weir  and  at  a  slight  distance  from  it.  In  this 
pipe  at  equal  intervals  in  the  width  of  the  weir  small  holes 
were  drilled.  The  effect  of  this  pipe  was  to  give  an  aver- 
age water  level  in  the  gauge  box. 

The  general  formula  established  by  the  experiments, 
on  which  the  following  table  is  calculated,  is  Q  =  3'33 
(I  —  -2A)  AJ,  in  which  Qis  the  discharge  in  cubic  feet  per 
second,  I  the  length  of  the  weir,  and  h  the  height  of  water 
above  the  crest  of  the  weir,  both  in  feet. 

For  complete  end  contractions  the  side  of  the  weir 
should  be  at  least  equal  to  the  depth  of  the  water  on  it 
from  the  side  of  the  canal.  The  bottom  contraction,  also 
complete,  is  shown  by  a  body  of  air  below  the  crest  of 
the  weir.  Where  there  is  no  end  contraction,  provision 
should  be  made  for  introducing  and  maintaining  free 
communications  of  the  air  beneath  the  water  sheet.  For 
large  velocities  of  approach  to  the  weir,  divide  the  area  of  a 

water  section  above  it  by  its  discharge  from  the  table  for  »,  in  the  equation  h'  =  — ,  and 
add  h'  to  previous  depth  for  corrected  discharge. 

In  the  table,  the  discharge  is  given  for  one  foot  in  length ;  but  as  in  weirs  there  are 
usually  two  end  contractions,  virtually  reducing  the  length,  and  met  in  the  formula  above 
by  —  -%h,  a  column  of  correction  has  been  added,  which  is  to  be  subtracted  from  the 
product  of  discharge,  as  shown  in  example. 


FIG.  1864. 


.       I 

~  C-t-J-C  —  ~  ~  +.— 1 


FICJ.  1805. 


782 


APPENDIX. 


DISCHAKGE,  IN  CUBIC  FEET  PEE    SECOND,  OF  A  WETE  ONE  FOOT   LONG,  WITH- 
OUT CONTRACTION  AT  THE  ENDS  ;    FOE  DEPTHS  FEOM  0-200  TO  0-999  FEET. 


Correction 
for  con- 
tractions. 

Depth. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

•012 

0-20 

0-298 

0-300 

0-302 

0-305 

0-307 

0-309 

0-311 

0-314 

0-316 

0-318 

•013 

•21 

0-320 

0-323 

0-325 

0-327 

0-330 

0-332 

0-334 

0-337 

0-339 

0-341 

•015 

•22 

0-344 

0-346 

0-348 

0-351 

0-353 

0-355 

0-358 

0-360 

0-362 

0-365 

•017 

•23 

0-367 

0-370 

0-372 

0-374 

0-377 

0-379 

0-382 

0-384 

0-387 

0-389 

•019 

•24 

0-391 

0-394 

0-396 

0-399 

0-401 

0-404 

0-406 

0-409 

0-411 

0-414 

•021 

•25 

0-416 

0-419 

0-421 

0-424 

0-426 

0-429 

0-431 

0-434 

0-436 

0-439 

•023 

•26 

0-441 

0-444 

0-447 

0-449 

0-452 

0-454 

0-457 

0-459 

0-462 

0-465 

•025 

•27 

0-467 

0-470 

0-472 

0-475 

0-478 

0-480 

0-483 

0-485 

0-488 

0-491 

•028 

•28 

0-493 

0-496 

0-499 

0-501 

0-504 

0-507 

0-509 

0-512 

0-515 

0-517 

•030 

•29 

0-520 

0-523 

0-525 

0-528 

0-531 

0-534 

0-536 

0-539 

0-542 

0-544 

•033 

0-30 

0-547 

0-550 

0-553 

0-555 

0-558 

0-561 

0-564 

0-566 

0-569 

0-572 

•036 

•31 

0-575 

0-577 

0-580 

0-583 

0-586 

0-589 

0-591 

0-594 

0-597 

0-600 

•039 

•32 

0-603 

0-606 

0-608 

0-611 

0-614 

0-617 

0-620 

0-623 

0-625 

0-628 

•042 

•33 

0-631 

0-634 

0-637 

0-640 

0-643 

0-646 

0-649 

0-651 

0-654 

0-657 

•045 

•34 

0-660 

0-663 

0-666 

0-669 

0-672 

0-675 

0-678 

0-681 

0-684 

0-687 

•048 

•35 

0-689 

0-692 

0-695 

0-698 

0-701 

0-704 

0-707 

0-710 

0-713 

0-716 

•052 

•36 

0-719 

0-722 

0-725 

0-728 

0-731 

0-734 

0-737 

0-740 

0-743 

0-746 

•056 

•37 

0-749 

0-752 

0-755 

0-759 

0-762 

0-765 

0-768 

0-771 

0-774 

0-777 

•059 

•38 

0-780 

0-783 

0-786 

0-789 

0-792 

0-795 

0-799 

0-802 

0-805 

0-808 

•063 

•39 

0-811 

0-814 

0-817 

0-820 

0-823 

-'0-827 

0-830 

0-833 

0-836 

0-839 

•067 

0-40 

0-842 

0-846 

0-849 

0-852 

0-855 

0-858 

0-861 

0-865 

0-868 

0-871 

•072 

•41 

0-874 

0-877 

0-881 

0-884 

0-887 

0-890 

0-893 

0-897 

0-900 

o'gos 

•076 

•42 

0-906 

0-910 

0-913 

0-916 

0-919 

0-923 

0-926 

0-929 

0-932 

0-936 

•081 

•43 

0-939 

0-942 

0-945 

0-949 

0-952 

0-955 

0-959 

0-962 

0-965 

0-969 

•085 

•44 

0-972 

0-975 

0-978 

0-982 

0-985 

0-988 

0-992 

0-995 

0-998 

1-002 

•090 

•45 

1-005 

1-009 

1-012 

1-015 

1-019 

1-022 

1-025 

1-029 

1-032 

1-035 

•095 

•46 

1-039 

1-042 

1-046 

1-049 

1-052 

1-056 

1-059 

1-063 

1-066 

1-070 

•100 

•47 

1-073 

1-076 

1-080 

1-083 

1-087 

1-090 

1-094 

1-097 

1-100 

1-104 

•106 

•48 

1-107 

1-111 

1-114 

1-118 

1-121 

1-125 

1-128 

1-132 

1-135 

1-139 

•111 

•49 

1-142 

1-146 

1-149 

1-153 

1-156 

1-160 

1-163 

1-167 

1-170 

1-174 

•118 

0-50 

1-177 

1-181 

1-184 

1-188 

1-191 

1-195 

1-199 

1-202 

1-206 

1-209 

•124 

•51 

1-213 

1-216 

1-220 

1-223 

1-227 

1-231 

1-234 

1-238 

1-241 

1-245 

•130 

•52 

1-249 

1-252 

1-256 

1-259 

1-263 

1-267 

1-270 

1-274 

1-278 

1-281 

•136 

•53 

1-285 

1-288 

1-292 

1-296 

1-299 

1-303 

1-307 

1-310 

1-314 

1-318 

•143 

•54 

1-321 

1-325 

1-329 

1-332 

1-336 

1-340 

1-343 

1-347 

1-351 

1-355 

•150 

•55 

1-358 

1-362 

1-366 

1-369 

1-373 

1-377 

1-381 

1-384 

1-388 

1-392 

•157 

•56 

1-395 

1-399 

1-403 

1-407 

1-410 

1-414 

1-418 

1-422 

1-425 

1-429 

•164 

•57 

1-433 

1-437 

1-441 

1-444 

1-448 

1-452 

1-456 

1-459 

1-463 

1-467 

•171 

•58 

1-471 

1-475 

1-478 

1-482 

1-486 

1-490 

1-494 

1-498 

1-501 

1-505 

•178 

•59 

1-509 

1-513 

1-517 

1-521 

1-524 

1-528 

1-532 

1-536 

1-540 

1-544 

•186 

0-60 

1-548 

1-551 

1-555 

1-559 

1-563 

1-567 

1-571 

1-575 

1-579 

1-583 

•194 

•61 

1-586 

1-590 

1-594 

1-598 

1-602 

1-606 

1-610 

1-614 

1-618 

1-622 

•202 

•62 

1-626 

1-630 

1-633 

1-637 

1-641 

1-645 

1-649 

1-653 

1-657 

1-661 

•210 

•63 

1-665 

1-669 

1-673 

1-677 

1-681 

1-685 

1-689 

1-693 

1-697 

1-701 

•218 

•64 

1-705 

1-709 

1-713 

1-717 

1-721 

1-725 

1-729 

1-733 

1-737 

1-741 

•227 

•65 

1-745 

1-749 

1-753 

1-757 

1-761 

1-765 

1-769 

1-773 

1-777 

1-781 

•236 

•66 

1-785 

1-790 

1-794 

1-798 

1-802 

1-806 

1-810 

1-814 

1-818 

1-822 

•245 

•67 

1-826 

1-830 

1-834 

1-838 

1-843 

1-847 

1-851 

1-855 

1-859 

1-863 

•254 

•68 

1-867 

1-871 

1-875 

1-880 

1-884 

1-888 

1-892 

1-896 

1-900 

1-904 

•263 

•69 

1-909 

1-913 

1-917 

1-921 

1-925 

1-929 

1-934 

1-938 

1-942 

1-946 

•273 

0-70 

1-950 

1-954 

1-959 

1-963 

1-967 

1-971 

1-975 

1-980 

1-984 

1-988 

•283 

•71 

1-992 

1-996 

2-001 

2-005 

2-009 

2-013 

2-017 

2-022 

2-026 

2-030 

•293 

•72 

2-034 

2-039 

2-043 

2-047 

2-051 

2-056 

2-060 

2-064 

2-068 

2-073 

•303 

•73 

2-077 

2-081 

2-085 

2-090 

2-094 

2-098 

2-103 

2-107 

2-111 

2-115 

•314 

•74 

2-120 

2-124 

2-128 

2-133 

2-137 

2-141 

2-146 

2-150 

2-154 

2-159 

•324 

•75 

2-163 

2-167 

2-172 

2-176 

2-180 

2-185 

2-189 

2-193 

2-198 

2-202 

APPENDIX. 


783 


DISCHAKGE,   IN   CUBIC  FEET  PEE  SECOND,   OF  A   WE1K  ONE  FOOT  LONG,   WITH- 
OUT  CONTKACTION  AT   THE   ENDS;FOK   DEPTHS   FKOM   0-200  TO   0-999    FEET. 

(Continued.) 


Correction 
for  con- 
tractions. 

Depth. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

•335 

•76 

2-206 

2-211 

2-215 

2-219 

2-224 

2-228 

2-232 

2-237 

2-241 

2-246 

•346 

•77 

2-250 

2-254 

2-259 

2-263 

3-267 

2-272 

2-276 

2-281 

2-285 

2-290 

•358 

•78 

2-294 

2-298 

2-303 

2-307 

2-312 

2-316 

2-320 

2-325 

2-329 

2-334 

•369 

•79 

2-238 

2-343 

2-347 

2-351 

2-356 

2-360 

2-365 

2-369 

2-374 

2-378 

•381 

0-80 

2-383 

2-387 

2-392 

2-396 

2-401 

2-405 

2-410 

2-414 

2-419 

2-423 

•393 

•81 

2-428 

2-432 

2-437 

2-441 

2-446 

2-450 

2-455 

2-459 

2-464 

2-468 

•406 

•82 

2-473 

2-477 

2-482 

2-486 

2-491 

2-495 

2-500 

2-504 

2-509 

2-513 

•413 

•83 

2-518 

2-523 

4-527 

2-532 

2-536 

2-541 

2-545 

2-550 

2-554 

2-559 

•431 

•84 

2-564 

2-568 

2-573 

2-577 

2-582 

2-587 

2-591 

2-596 

2-600 

2-605 

•444 

•85 

2-610 

2-614 

2-619 

2-623 

2-628 

2-633 

2-637 

2-642 

2-646 

2-651 

•457 

•86 

2-656 

2-660 

2-665 

2-670 

2-674 

2-679 

2-684 

2-688 

2-693 

2-698 

•470 

•87 

7-702 

2-707 

2-712 

2-716 

2-721 

2-726 

2-730 

2-735 

2-740 

2-744 

•484 

•88 

2-749 

2-754 

2-758 

2-763 

2-768 

2-772 

2-777 

2-782 

2-786 

2-791 

•498 

•89 

2-796 

2-801 

2-805 

2-810 

2-815 

2-819 

2-824 

2-829 

2-834 

2-838 

•512 

0-90 

2-843 

2-848 

2-853 

2-857 

2-862 

2-867 

2-872 

2-876 

2-881 

2-886 

•526 

•91 

2-891 

2-895 

2-900 

2-905 

2-910 

2-915 

2-919 

2-924 

2-929 

2-934 

•541 

•92 

2-938 

2-943 

2-948 

2-953 

2-958 

2-963 

2-967 

2-972 

2-977 

2-982 

•555 

•93 

2-986 

2-991 

2-996 

3-001 

3-006 

3-011 

3-015 

3-020 

3-025 

3-030 

•570 

•94 

3-035 

3-040 

3-044 

3-049 

3-054 

3-059 

3-064 

3-069 

3-074 

3-078 

•586 

•95 

3-083 

3-088 

3-093 

3-098 

3-103 

3-108 

3-113 

3-117 

3-122 

3-127 

•601 

•96 

3-132 

3-137 

3-142 

3-147 

3-152 

3-157 

3-162 

3-166 

3-171 

3-176 

•677 

•97 

3-181 

3-186 

3-191 

3-196 

3-201 

3-206 

3-211 

3-216 

3-221 

3-226 

•632 

•98 

3-231 

3-235 

3-240 

3-245 

3-250 

3-255 

3-260 

3-265 

3-270 

3-275 

•648 

•99 

3-280 

3-285 

3-290 

3-295 

3-300 

3-305 

3-310 

3-315 

3-320 

3-325 

Example. — Let  the  weir,  with  end  contractions,  be  5 '3  feet  long,  and  depth  of  water, 
or  h  =  0-612. 

By  table  the  discharge  for  one  foot  in  length  is 1  -594 

5-3 


Correction 


8-4482 
•196 


Discharge  in  cubic  feet  per  second 8'2522 

The  measures  of  the  discharge  of  the  different  wheels  was  accurately  determined;  it 
was  equally  important  to  determine  the  quantities  used  by  the  different  corporations. 
Mr.  Francis's  arrangements  for  this  purpose  were  the  construction  of  rectangular  plank 
flumes  in  the  different  canals  or  feeders,  of  which  the  widths  were  divided  into  feet 
marked  on  the  upstream  faces  of  the  timbers,  extending  above  and  across  the  ends  of  the 
flume,  which  enabled  the  average  thread  of  the  float  in  its  passage  through  the  flume  to 
be  ascertained.  The  depth  of  the  water  in  the  flume  was  measured  by  a  gauge  placed 
centrally  on  one  side  of  the  flume.  The  floats  measuring  the  velocity  of  the  currents 
were  adjusted  to  the  depths  of  water,  having  some  two  inches  clearance  from  the  bottom. 
The  tubes  were  of  two  to  three  inches  diameter,  loaded  at  the  bottom,  and  marked  with 
their  water  line.  They  were  brought  to  the  flume  and  those  of  length  appropriate  to 
its  depth  were  selected.  From  the  notes  thus  taken  the  average  path  of  the  float  was 
determined,  on  which  was  plotted  its  velocity,  as  represented  by  the  different  circles 
(Fig.  182).  Through  the  average  of  these  circles  on  the  lines  of  flow  is  drawn  the  full 
line  of  averages  from  which  the  average  of  the  total  flow  was  determined. 


784 


APPENDIX. 


In  a  similar  way  gaugings  may  be  made  of  natural  streams  where  the  sections  are  ap- 
proximately smaller.  Soundings  are  to  be  made  across  the  stream  and  sections  drawn. 
The  average  velocities  may  be  taken  through  these  sections,  which  multiplied  by  the 
products  of  the  sections  and  nine  tenths  of  their  sum  will  give  approximately  the  flow 
of  the  streams.  For  this  kind  of  measure  I  have  used  two  rubber  balls  connected  by  an 
adjustable  soft  cotton  cord,  the  lower  ball  being  filled  with  water.  A  light  strong  thread 
is  attached  to  the  upper  ball  with  the  ends  in  the  hands  of  the  observers  on  each  side  of 
the  stream,  by  which  the  ball  may  be  guided  in  the  thread  of  its  appropriate  section. 

It  was  customary  to  find  the  average  flow  of  a  stream  from  the  surface  velocities  in 
different  threads  of  it  according  to  the  sections  by  means  of  apples  loaded  with  shingle 
nails  to  nearly  the  specific  gravity  of  the  water,  casting  them  into  the  stream,  and  taking 
the  time  of  transit  between  two  cords  stretched  across  it,  and  taking  as  an  average  about 
eighty  per  cent  that  of  the  whole  observations  by  the  area  of  the  entire  section.  Surface 
velocities  only  to  be  considered  as  loose  approximations,  as  they  are  very  much  influenced 
by  the  direction  and  strength  of  the  wind  and  the  uniformities  of  flow  in  the  different 
sections  and  diversions  or  eddies. 

The  miner's  inch  is  designated  as  the  flow  through  one  square  inch,  but  under  vari- 
ous heads  in  different  states.  P.  J.  Flynn  in  "Irrigation  Canals"  gives  one  cubic  foot 
per  second  as  the  equivalent  flow  through  fifty  miner's  inches  under  a  mean  head  of  four 
inches. 


Fro.  1866. 


FLOW   OF   WATER  IN  PIPES   AND   CONDUITS. 

The  general  formula  for  the  flow  of  water  in  all  channels  is  v  =  c  \/fis,  in  which  ®  is 
the  velocity,  c  a  coefficient  determined  for  the  particular  form  of  channel,  It  the 
hydraulic  mean  depth — that  is,  the  area  of  water  cross-section — divided  by  its  wetted 
perimeter  of  channel ;  s  is  the  slope  of  difference  of  level  or  pressure  in  feet  between  two 
points  divided  by  the  length  in  feet. 

Fig.  1866  is  a  section  of  a  water  pipe  in  which  the  capacities  are  shown  of  its  differ- 
ent sections  from  the  bottom  to  a  full  section  without  any  head.  The  friction  of  the 
sides  of  the  full  pipe  reduces  the  velocity,  and  the  maximum  is  at  about  eighty  per  cent 
of  full,  and  the  maximum  of  the  curve  of  discharge  or  velocity  by  area  of  section  a  little 
above  ninety  per  cent.  It  must  be  observed  that  the  velocity  at  half  section  is  the  same 
as  when  the  pipe  is  full. 

Messrs.  Ganguillet  and  Kutter  have  established  formulae,  of  which  there  is  a  modifi- 
cation according  to  the  character  of  the  surface  of  the  wetted  perimetre. 

The  Kutter  formula,  as  it  is  called,  is  very  complicated,  but  it  has  been  simplified 
graphically  by  Mr.  Rudolph  Hering  and  published  in  the  "  Transactions  of  the  A.  S.  C. 
E.,"  January,  1879,  from  which  the  figures  have  been  redrawn. 


APPENDIX. 


785 


IRON  ;    CEMENT  ;   TERRA   COTTA   PIPES,    WELL-JOINTED   AND   IN  BEST    ORDER  ;    CAREFULLY 

PLASTERED   SURFACE. 

Grades  in  feef  per  hundred  n..o// 

n -/     .?        .4     .6    .8    / £ J.  4.  5.          6. 


51 


786 


APPENDIX. 


OLD    IRON  ;     CEMENT    AND    TERRA     COTTA    PIPES    NOT     WELL-JOINTED    NOR    IN  PERFECT 
ORDER  ;    WELL   LAID   BRICKWORK. 

Grades  in  feel  per  hundred  n  .0/3 

.1     .2       .4     .6    .81-  t  3.  4.  5.        6. 


60 


36D/am 


APPENDIX. 


787 


FOUL  AND  SLIGHTLY  TUBEKCTJLATED  IRON  ;  CEMENT  AND  TERRA  COTTA  PIPES  WITH 
IMPERFECT  JOINTS,  AND  IN  BAD  ORDER  ;  WELL-DRESSED  STONEWORK  AND  SECOND 
CLASS  BRICKWORK. 

Grades  fn  feet  per  hundred         n=  .0/6 

.1      .?       A      .6     .8    /.  2.  3.  4  6.          6. 


788 


APPENDIX. 


IRON  ;     CEMENT  ;     TEKRA   COTTA    PIPES,    WELL-JOINTED    AND    IN   BEST    ORDER. 


.OZ.04.06*  .1 


Grades  in  feet  per  hundred]  /?=  -Oil 

.2      .3     .4    £    .6  .7  .$.3  /.O /.6  2.0          26         3.O 


56X83    5X76          46X6'9 


1'6XZ3 


APPENDIX. 


789 


OLD    IRON  ;    CEMENT 


AND    TERRA     COTTA    PIPES    NOT    WELL-JOINTED    NOR    IN    PERFECT 
ORDER  ;     WELL   LAID    BRICKWORK. 


Grades  m  feef  per  hundred  /?» .0/3 

02.04O6./         .2      .3    .4    .J    6  .7  .8 .3/.O X.v5  2.O  Z5        3.O 


0X9       66X83   6X76  46"X63 


790 


APPENDIX. 


FOTJL  AND  SLIGHTLY  TUBERCULATED  IRON  ;  CEMENT  AND  TERRA  COTTA  PIPES  WITH 
IMPERFECT  JOINTS,  AND  IN  BAD  ORDER  ;  WELL-DRESSED  STONEWORK  AND  SECOND 
CLASS  BRICKWORK. 


Grades  //?  feet  per  hundred 

•         -3     •*   -5    .6  .7.8.9*0  '-5 


n~.OI5 


46X69 


APPENDIX. 


T91 


For  tables  of  the  Kutter  formula  see  "Irrigation  Canals,"  by  P.  J.  Flynn,  C.  E. 

It  will  be  observed  that  n  depends  on  the  condition  of  the  wetted  surface,  and  that 
with  iron  surfaces  it  must  vary  largely  with  the  time  exposure  of  these  surfaces  and  the 
characteristics  of  the  water  passing  through. 

Where  pipes  of  iron  can  not  be  cleaned,  it  is  impossible  for  the  engineer  to  form  re- 
liable judgment  of  their  condition  after  years  of  use.     They  can  be  tested 
by  measuring  flows  through  a  hydrant  which  discharges  from  a  single 
length  of  pipe  and  determining  the  s  in  that  length. 

For  a  main  with  no  available  gate  the  following  is  suggested : 

Let  a  d  be  the  main ;  establish  s  between  a  &  and  cdby  reliable  gauges. 
At  g  put  in  a  branch  controlled  by  a  gate.  After  s  s  are  established  as 
above,  open  the  gate  and  measure  its  discharge  accurately  by  a  weir.  With 
this  factor  see  what  »  is  between  a  and  &  and  check  the  quantities  by  the 
changes  between  c  and  d  and  compare  with  flows  at  different  values  of  n. 

Should  the  values  of  ?&,  as  thus  established  by  experiment,  be  outside 
of  the  limits  of  n  =  'Oil,  '013,  '015,  as  given  by  the  diagrams,  curves 
can  be  established  from  these  values  and  extended  to  include  those  of 
the  experiments,  which  may  answer  as  approximations. 


FLOW   OF   AIR. 

The  flow  of  air  is  subject  to  the  same  laws  as  the  flow  of  water.     The 
preceding  diagrams  may  therefore  be  used  in  finding  the  discharge  of  air  in  cubic  feet 
per  second,  under  the  same  heads  of  water  in  feet,  by  multiplying  by  27'6,  the  square 
root  of  761,  the  difference  in  density  of  a  cubic  foot  of  the  two  fluids. 

The  theoretical  discharge  of  a  pipe  is  as  the  square  root  of  the  fifth  power  of  the 
diameter,  from  which  the  following  table,  derived  from  the  circular  of  the  B.  F.  Sturte- 
vant  Company,  is  based : 


$ 

TABLE  FOE  EQUALIZING  THE  DIAMETER 

OF  PIPES. 

1 

i 

P 

irties  putting  up  blast  pipes 
four  6-inch  pipes  is  the  same 

are  very  liable  to  think,  because  the  combined  area  of 
as  one  12-inch  pipe,  that  the  four  pipes  will  convey  the 

2 

5.7 

2    ] 

3 

1C 

2.7|     3 

4 

32 

5.7      2. 

4 

same  quantity  of  air  with  the  same  ease  and  freedom  that  the  12-inch  will,  where- 

5 

5C 

9.8 

I.I 

1.8|    5 

as  it  actually  does  take  5-7—  almost  six  6-inch 

pipes.     Again, 

16  3-inch  pipes 

6 

88 

1C 

».] 

2.3|   1.6|    6 

have  the  combined  area  of  one  12-inch  pipe,  but  in  actual  practice  it  takes 

7 

129 

23j     8.3 

4.1 

2.3|   1.5 

7 

just  32  3-inch  pipes  to  do  the  work  of  one  12-inch. 

8 

180 

32  |     12 

.'..7 

3.2|  2.1|   1.4 

8 
1.1 

T" 

Thi 

s  is 
the 

lue 
sin 
Th 

to  t 

lllp 

el* 

an 

he  < 
ipos 
•Kc 
icte 
Tl 

xee 

OV( 

Iffn 

rs  ii 
le  fi 
til 

SS  0 

r  th 
-es  f 
inc 
_nm 
le  \ 
0 

"•fri 
at  i 
t,  tl 
lies 
s  a 
•ith 
pes 
O 

ctio 
n  th 

e  to 

oft 
the 
the 
|0f 

f  til 

4 

1 

1   fc 
o  la 

po 
he  I 
in 
ve 
the 
100 
:ipa 

r  every  cubic  foot  of  ai. 
rge. 
f  each  column  give  the 
run  c'li  pipes, 
ersection  of  the  horizo 
rtical  give  the  numbe 
diameter  given  at  the 
umn,  that  will  be  equa 
city  for  conveying  aii 
one  given  opposite  in 
first  column. 

1 

r  in 
di- 

ntal 
r  of 
top 
1  in 
to 
the 

9 

244 

42 

1C 

7   f 

4.3|  2.8 

1.9 

10 

317 

56 

20 

I.I 

5.7[  S:6|  2.4|  1.7|  1.3 

10 

11 

402 

71 

26 

12 

7.0|  4.5    3.1 

I.I 

1.7 

t.l 

11 

12 

501 

88 

32 

16 

9.0[  5.7)  3.S 

2.8[  2.0)   1.6 

1.1 

12 

13 

613 

107 

.11) 

l» 

11   |  6.9 

4.7 

3.4 

2.5 

I.I 

U 

1.1 

13 

14 
IS 

737 

129 

47 

2.1 

13  |  8.3|  5.7|  4.1 

3.0|  2.3 

I.I 

1..- 

l.i 

14 

16 

026 

180 

6, 

M 

18 

n 

7.9|  5.7 

4.2 

1.9 

2, 

t.l 

1.7 

1.4 

1.2 

16 

17 

4.9[  8.8)  2.9 

1.2(17 

18 

375 

239 

88 

43 

M 

16 

10 

1.1 

5.7 

4.8|  3.4 

2.8|  2.3|   1.9[  1.6 

1.3 

1.2|  18 

19 
20 

580 
797 

275 

no 

411 

23 

18 

12 

M 

8    8 

t.S 

5, 

3.9 

3.2 

I.I 

|J.2|   1.8 

,.:, 
l.T 

1.3 

\.: 

1.2!  19  | 
1.3)  1.1J20 

22 
24 

284 
834 

493 

80 

88 

M 

.12 

18 
22 

1C 

12 

|.| 

7.1 

4.1 

5.7 

3.7|3.1 
4.6|  3.8 

3.2 

2.9 

2.4 

I.I 

1.6 

i.< 

22  | 
|  1.2|24] 

aal 

26 

474 

C05 

19 

1M 

62 

n 

IT 

1* 

14 

11 

8.6 

I1."* 

s,r 

6.8    „.. 

4.1 

4.0|3.4 

2.9    2.5 

2.1 

1.9|   1.5|   1.2|26 

30 

963 

8C4 

11 

IH 

8.8 

56 

.18 

2.8 

20 

1C 

12 

9.9 

8.0|  6.7 

4.8|   4.1 
5.7J  4.7 

4.1 

I.I 

3.» 

2.6|  2.2(    1.7|   1.4 

1.2|3O| 

36 

818 

1361 

n 

243 

139 

M 

w 

43 

32 

2.1 

19  |   16 

13 

11 

8.9 

7.C 

c.;, 

.'..7 

•>•'' 

4.3 

3.4|  2.7[  2.2|1.9|l.C|38| 

48 

989 

2792 

81   |492  |282 

180 

123 

88 

CO 

50 

39 

.12 

26 

22 

18 

16 

13 

12 

10 

8.1. 

7.0|  5.7i  4.7|3.8J3.2|2.1|1.4|48| 

54   | 

i   560 

3753 

08    671    384 

244 

160 

11  'J 

88 

C8 

53  |  43 

.1J 

29 

24 

21 

18 

1C 

15 

12 

9.4|   7.6|  6.25.  2 

4.3;2.8|1.9 

1.3|54 

6O    ]27913 

4879  ] 

81 

872 

499 

.114 

215 

1M 

111 

H 

69 

M 

40 

3f-    32 

27 

23 

20 

18 

10 

12  |  9.9|  8.1 

0.', 

5.7|3.6|2.4|l.8|l.S 

792 


APPENDIX. 


APPENDIX. 


793 


: 


:  : 


tr- 


U5I 


794 


APPENDIX. 


The  foregoing  diagrams  of  the  flow  of  gas  have  been  made  from  the  formula  con- 
tained in  "Practical  Treatise  on  Heat,"  by  Thomas  Box,  and  is  as  follows  : 
Q=  (H  x  (3-7D)5-^L)i, 

in  which  Q  =  discharge  cubic  feet  per  minute;  H  =  pressure  (grade)  in  inches  of  water; 
D  =  diameter  of  pipe  in  inches ;  L  =  length  in  yards.  The  specific  gravity  (G)  of  the 
gas  in  this  formula  is  -42.  

Formula  in  previous  editions  of  this  work  was  Q  =  1350  D24/ ,  and  agrees  very 

closely  with  the  results  from  the  diagrams  given  below. 

The  diagrams  for  the  flows  of  water  (pages  785-790)  in  pipes  are  equally  applicable 
to  the  movement  of  gaseous  fluids,  the  velocities  being  directly  as  the  square  roots  of 
their  specific  gravities.  Thus,  the  water  discharge  of  a  conduit  2  feet  in  diameter  under 
a  grade  of  .0833'  per  100  feet  in  the  diagram  n  =  -015  is  5 '5  cubic  feet  per  second.  By 
Tables  of  the  Weight  of  Water  (page  780)  compared  with  that  of  air  below  it  will  be 
seen  that  at  62°  F.  the  weight  of  a  cubic  foot  of  water  is  to  that  of  air  as  1  to  820. 
5-5  x  1/820  =  5-5  x  28-636  =  157  cubic  feet  per  second. 

As  the  diagrams  for  the  flow  of  water  are  in  feet  per  hundred  and  those  of  air  or  gas 
in  inches,  to  convert  the  grades  of  the  former  into  those  of  the  latter,  multiply  the  dis- 
charge by  the  square  root  of  '0833'  (1")  or  '2889'.  Taking  above  example,  diagram 
under  1: 100  gives  a  discharge  of  19  cubic  feet  per  second,  which  x  '2889  x  28'636  =  157 
cubic  feet  per  second ;  but  as  the  flow  of  air  is  usually  given  in  cubic  feet  per  minute, 
multiply  by  60  and  we  obtain  9,420  cubic  feet  of  air  per  minute. 

In  the  movement  of  compressed  air  by  the  action  of  the  pump  the  air  is  heated,  and  in 
its  passage  through  the  pipe  this  heat  is  gradually  dissipated  with  a  change  of  its  specific 
gravity,  for  which  allowance  is  to  be  made  in  velocity  of  movement.  With  illuminating 
gas  the  specific  gravity  of  '42  adopted  in  the  diagram  is  a  common  one. 

The  products  of  combustion  escaping  into  a  large  chimney  may  be  taken  as  of  the 
same  specific  gravity  as  illuminating  gas  at  '42,  but  the  velocity  in  the  general  rules  is 
much  less  than  that  given  by  the  diagrams.  There  is  no  objection  to  large  chimneys  ex- 
cept in  their  cost  and  back  draughts,  which  last  may  be  met  by  uniformity  of  section 
without  eddies  or  by  a  Venturi  converging  and  diverging  tube,  at  the  bottom. 

Insufficient  draught  in  short  chimneys,  induced  by  positions  or  necessities  of  con- 
struction, is  met  by  fans  discharging  directly  into  a  fire-room  or  ash-pit,  or  by  steam-jet 
blowers,  as  illustrated  on  page  368. 


VOLUME   AND   WEIGHT   OF   DRY  AIR 

At  Different  Temperatures  under  a  Constant  Atmospheric  Pressure  of  29-92  Inches  of  the 
Barometer,  the  Volume  at  32°  F.  being  the  Unit. 


Temp.  F. 

Volume. 

Weight    per 
cub.  ft., 
Pounds. 

Temp.  F. 

Volume. 

Weight    per 
cub.  ft., 
Pounds. 

Temp.  F. 

Volume. 

Weight    per 
cub.  ft., 
Pounds. 

0° 

•935 

•0864 

132° 

1-204 

•0671 

325° 

1-597 

•0506 

12 

•960 

•0842 

142 

1-224 

•0659 

350 

1-648 

•0490 

22 

•980 

•0824 

152 

1-245 

•0649 

375 

1-689 

•0477 

32 

1-000 

•0807 

162 

1-265 

•0638 

400 

1-750 

•0461 

42 

1-020 

•0791 

172 

1-285 

•0628 

450 

1-852 

•0436 

52 

1-041 

•0776 

182 

1-306 

•0618 

500 

1-954 

•0413 

62 

1-061 

•0761 

192 

1-326 

•0609 

550 

2-056 

•0384 

72 

1-082 

•0747 

202 

1-347 

•0600 

600 

2-150 

•0376 

82 

1-102 

•0733 

212 

1-367 

•0591 

650 

2-260 

•0357 

92 

1-122 

•0720 

230 

1-404 

•0575 

700 

2-362 

•0338 

102 

1-143 

•0707 

250 

1-444 

•0559 

800 

2-566 

•0315 

112 

1-163 

•0694 

275 

1-495 

•0540 

900 

2-770 

•0292 

122 

1-184 

•0682 

300 

1-546 

•0522 

1000 

2-974 

•0268 

APPENDIX. 


796 


APPENDIX. 


A  Babcock  and  Wilcox  water  tube  boiler  (Fig.  1867)  is  composed  of  lap-welded 
wrought-iron  tubes  placed  in  an  inclined  position  and  connected  with  each  other  and 
with  a  horizontal  steam  and  water  drum,  by  vertical  passages  at  each  end,  while  a  mud 
drum  is  connected  to  the  rear  and  lowest  point  in  the  boiler. 

The  end  connections  are  in  one  piece  for  each  vertical  row  of  tubes,  and  are  of  such 
form  that  the  tubes  are  staggered.  The  sections  thus  formed  are  connected  with  the 
drum,  and  with  the  mud  drum  also,  by  short  tubes  expanded  into  bored  holes.  The 
openings  for  cleaning,  opposite  the  end  of  each  tube,  are  closed  by  hand-hole  plates. 

To  utilize  waste  heat  heaters  are  set  in  a  chamber  in  connection  with  the  flues  leading 
to  the  chimney.  Fig.  1868  is  an  elevation  of  one  of  these  forms  of  apparatus,  the  Green 
economizer,  consisting  of  ranges  of  vertical  pipes,  connected  at  the  top  and  bottom 
with  horizontal  pipes,  into  which  the  feed  water  is  introduced  at  the  bottom  and  leaves 
at  the  top.  The  whole  is  inclosed  in  a  brick  chamber  with  the  products  of  combustion 
passing  among  the  pipes.  The  outsides  of  the  pipes  are  ckaned  by  automatic  scrapers. 
Where  the  heat  is  necessary  to  insure  draft  in  the  smoke  flue  there  can  be  no  economy  in 
the  apparatus,  but  an  obstruction  to  the  draft. 

In  operation,  the  fire  is  made  under  the  front  and  higher  ends  of  the  tubes,  and  the 
products  of  combustion  pass  up  between  the  tubes  into  a  combustion  chamber  under  the 
steam  and  water  drum ;  from  thence  they  pass  down  between  the  tubes,  then  once  more 
up  through  the  spaces  between  the  tubes  and  off  to  the  chimney.  The  water  inside  the 
tubes,  as  it  is  heated,  tends  to  rise  toward  the  higher  end,  and  as  it  is  converted  into 
steam,  the  mingled  column  of  steam  and  water  rises  through  the  vertical  passages  into 
the  drum  above  the  tubes,  where  the  steam  separates  from  the  water,  and  the  latter  flows 
back  to  the  rear  and  down  again  through  the  tubes  in  a  continuous  circulation. 

The  steam  is  taken  out  at  the  top  of  the  steam  drum,  near  the  back  end  of  the  boiler, 
after  it  has  thoroughly  separated  from  the  water. 


Scale..l  in.=13  ft. 


FIG.  1868. 


APPENDIX. 


797 


L  J 


The  Heine  boiler  (Fig.  1869)  is  composed  of  wrought-iron  tubes  extending  between 
the  inside  of  two  "water  legs,"  or  end  connections,  between  the  tubes  and  a  steam  and 
water  drum  placed  above  them.  These  end  chambers  are  of  approximately  rectangular 
shape,  drawn  in  at  the  top  to  fill  the  curvature  of  the  shells.  Each  is  composed  of  a 
head  plate  and  a  tube  sheet,  flanged  all  around  and  joined  at  bottom  and  sides  by  a  butt 
strap  of  the  same  material,  strongly  riveted  to  both.  They  are  further  stayed  by  hollow- 
stay  bolts  of  hydraulic  tubing  of  large  diameter,  so  placed  that  two  stays  support  each 
tube  and  hand  hole.  The  water  legs  are  joined  to  the  shell  by  flanged  and  riveted  joints, 
and  the  shells  are  cylinders  with  heads  dished.  The  steam  space  in  front  is  about  two 
thirds  the  diameter  of  the  shell,  while  at  the  rear  the  water  occupies  two  thirds  of  the 
shell,  the  whole  contents  being  equally  divided  between  steam  and  water.  On  the  top 
of  the  shell,  near  the  front  end,  is  riveted  a  nozzle  for  a  steam  and  safety  valve.  A  flue, 
or  breeching,  connects  the  furnace  to  the  chimney. 


798 


APPENDIX. 


TABLE   OF   SATURATED   STEAM. 

ENGLISH    UNITS. 

CECIL  H.  PEABODY,  B.  S. 


to    •  \ 

II 

•5 

2 

p 

a 
.0 

OJ 

S 

DENSITY. 

1-8 

ji 

"2 
'3 

j 

6 

S 

DENSITY. 

IS 

-  CO 

o1 

•g 

§ 

•S'o-" 

§M 

jffi 

.S 

"S 

3 

.S"o-« 

O 

P-4   ^ 

5$ 

£3 

•g 

i 

o 

•§ 

PH  d1 

3  ca 

—   ~ 

j»i-j 

jjj 

9 

I 

«f* 

ri 

M  ^ 

Mf 

-*j 

"o 

4) 
03 

B 

g 

o| 

o 

i 

o 

.£?§  §  § 

i  * 

V    QC 

CMP 

? 

44 

1 

"3 

!> 

£ 
1 

rff°  . 

1 

1 

B 
B 

I 

2 

B 

1 

^ff»O« 

PH 

r 

B 

i 

B 

a 

02 

^PnOEn 

P 

< 

Q 

A 

r 

S 

y 

P 

t 

q 

A 

r 

S 

y 

1 

101-99 

70-0 

1113-1 

1043-0 

334-6 

0-00299 

51 

282-10 

251-5 

1168-0 

916-5 

8-259 

0-1211 

2 

126-27 

94-4 

1120-5 

1026-1 

173-6 

0-00576 

52 

283-32 

252-7 

1168-4 

915-7 

8-110 

0-1233 

3 

141-62 

109-8 

1125-1 

1015-3 

118-4 

0-00844 

53 

284-53 

253-9 

1168-7 

914-8 

7-968 

0-1255 

4 

153-09 

121-4 

1128-6 

1007-2 

90-31 

0-01107 

54 

285-72 

255-1 

1169-1 

914-0 

7-829 

0-1277 

5 

162-34 

130-7 

1131-5 

1000-8 

73-22 

0-01366 

55 

286-89 

256-3 

1169-4 

913-1 

7-696 

0-1299 

6 

170-14 

138-6 

1133-8 

995-2 

61-67 

0-01622 

56 

288-05 

257-5 

1169-8 

912-3 

7-568 

0-1321 

7 

176-90 

145-4 

1135-9 

990-5 

53-37 

0-01874 

57 

289-19 

258-6 

1170-1 

911-5 

7-443 

0-1344 

8 

182-92 

151-5 

1137-7 

986-2 

47-07 

0-02125 

58 

290-31 

259-7 

1170-5 

910-8 

7-323 

0-1366 

9 

188-33 

156-9 

1139-4 

982-5 

42-13 

0-02374 

59 

291-42 

260-8 

1170-8 

910-0 

7-208 

0-1387 

10 

193-25 

161-9 

1140-9 

979-0 

38-16 

0-02621 

60 

292-51 

261-9 

1171-2 

909-3 

7-096 

0-1409 

11 

197-78 

166-5 

1142-3 

975-8 

34-88 

0-02866 

61 

293-59 

263-0 

1171-5 

908-5 

6-987 

0-1431 

12 

201-98 

170-7 

1143-6 

972-9 

32-14 

0-03111 

62 

294-65 

264-1 

1171-8 

907-7 

6-882 

0-1453 

13 

205-89 

174-6 

1144-7 

970-1 

29-82 

0-03355 

63 

295-70 

265-2 

1172  1 

906-9 

6-779 

0-1475 

14 

209-57 

178-3 

1145-8 

967-5 

27-79 

0-03600 

64 

296-74 

266-2 

1172-4 

906-2 

6-680 

0-1497 

15 

213-03 

181-8 

1146-9 

965-1 

26-15 

0-03826 

65 

297-77 

267-2 

1172-7 

905-5 

6-583 

0-1519 

16 

216-32 

185-1 

1147-9 

962-8 

24-59 

0-04067 

66 

298-78 

268-3 

1173-0 

904-7 

6-490 

0-1541 

17 

219-44 

188-3 

1148-9 

960-6 

23-22 

0-04307 

67 

299-77 

269-3 

1173-3 

904-0 

6-401 

0-1562 

18 

222-40 

191-3 

1149-8 

958-5 

22-00 

0-04547 

68 

300-76 

270-3 

1173-6 

903-3 

6-314 

0-1584 

19 

225-24 

194-1 

1150-7 

956-6 

20-90 

0-04786 

69 

301-74 

271-2 

1173-9 

902-7 

6-228 

0-1606 

20 

227-95 

196-9 

1151-5 

954-6 

19-91 

0-05023 

70 

302-71 

272-2 

1174-3 

902-1 

6-144 

0-1628 

21 

230-55 

199-5 

1152-3 

952-8 

19-01 

0-05259 

71 

303-66 

273-2 

1174-6 

901-4 

6-063 

0-1649 

22 

233-06 

202-0 

1153-0 

951-0 

18-20 

0-05495 

72 

304-61 

274-1 

1174-9 

900-8 

5-984 

0-1671 

23235-47 

204-5 

1153-7 

949-2 

17-45 

0-05731 

73 

305-54 

275-1 

1175-2 

900-1 

5-908 

0-1693 

24 

237-79 

206-8 

1154-4 

947-6 

16-76 

0-05966 

74 

306-46 

276-0 

1175-4 

899  -i 

5-834 

0-1714 

25 

240  04 

209-1 

1155-1 

946-0 

16-13 

0-06199 

75 

307-38 

276-9 

1175-7 

898-8 

5-762 

0-1736 

26 

242-21 

211-2 

1155-8 

944-6 

15-55 

0-06432 

76 

308-28 

277-8 

1176-0 

898-2 

5-691 

0-1757 

27 

244-32 

213-4 

1156-5 

943-1 

15-00 

0-06666 

77 

309-18 

278-7 

1176-2 

897-5 

5-621 

0-1779 

28 

246-36 

215-4 

1157-1 

941-7 

14-49 

0-06899 

78 

310-06 

279-6 

1176-5 

896-9 

5-554 

0-1801 

29 

248-34 

217-4 

1157-7 

940-3 

14-03 

0-07130 

79 

310-94 

280-5 

1176-8 

896-3 

5-488 

0-1822 

30 

250-27 

219-4 

1158-3 

938-9 

13-59 

0-07360 

80 

311-80 

281-4 

1177-0 

895-6 

5-425 

0-1843 

31 

252-15 

221-3 

1158-8 

937-5 

13-18 

0-07590 

81 

312-66 

282-3 

1177-3 

895-0 

5-362 

0-1865 

32 

253-98 

223-1 

1159-4 

936-3 

12-78 

0-07821 

82 

313-51 

283-2 

1177-6 

894-4 

5-3010-1886 

33 

255-76 

224-9 

1159-9 

935-0 

12-41 

0-08051 

83 

314-36 

284-1 

1177-8 

893-7 

5-2400-1908 

34 

257-50 

226-7 

1160-4 

933-7 

12-07 

0-08280 

84 

315-19 

285-0 

1178-1 

893-1 

5-1820-1930 

35 

259-19 

228-4 

1161-0 

932-6 

11-75 

0-08508 

85 

316-02 

285-8 

1178-3 

892-5 

5-125 

0-1951 

36 

260-85 

230-0 

1161-5 

931-5 

11-45 

0-08736 

86 

316-84 

286-7 

1178-6 

891-9 

5-069 

0-1973 

37 

262-47 

231-7 

1162-0 

930-3 

11-16 

0-08964 

87 

317-65 

287-5 

1178-8 

891-3 

5-014 

0-1994 

38264-06 

233-3 

1162-5 

929-2 

10-88 

0-09191 

88 

318-45 

288-4 

1179-1 

890-7 

4-961 

0-2016 

39265-61 

234-8 

1163-0 

928-2 

10-62 

0-09417 

89 

319-25 

289-2 

1179-3 

890-1 

4-909 

0-2037 

40 

267-13 

236-4 

1163-4 

927-0 

10-37 

0-09644 

90 

320-04 

290-0 

1179-6 

889-6 

4-858 

0-2058 

41 

268-62 

237-9 

1163-9 

926-0 

10-13 

0-09869 

91 

320-83 

290-8 

1179-8 

889-0 

4-808 

0-2080 

42270-08 

239-3 

1164-3 

925-0 

9-906 

0-10090 

92 

321-60 

291-6 

1180-0 

888-4 

4-760 

0-2101 

43271-51 

240-8 

1164-8 

924-0 

9-690 

0-10320 

93 

322-37 

292-4 

1180-3 

887-9 

4-712 

0-2122 

44272-91 

242-2 

1165-2 

923-0 

9-484 

0-10540 

94 

323-14 

293-2 

1180-5 

887-3 

4-665 

0-2144 

45274-29 

243-6 

1165-6 

922-0 

9-287 

0-10770 

95 

323-89 

294-0 

1180-7 

886-7 

4-619 

0-2165 

46275-65 

245-0 

1166-0 

921-0 

9-097 

0-10990 

96 

324-64 

294-8 

1181-0 

886-2 

4-574 

0-2186 

47276-99 

246-3 

1166-4 

920-1 

8-914 

0-11220 

97 

325-38 

295-6 

1181-2 

885-6 

4-5300-2208 

48 

278-30 

247-6 

1166-8 

919-2 

8-740 

0-11440 

98 

326-12 

296-4 

1181-4 

885-0 

4-4860-2229 

49 

279-58 

248-9 

1167-2 

918-3 

8-573 

0-11660 

99 

326-86297-1 

1181-6 

884-5 

4-4440-2250 

50 

280-85 

250-2 

1167-6 

917-4 

8-414 

0-11880 

100 

327-58 

297-9 

1181-9 

884-0 

4-4030-2271 

APPENDIX. 


TABLE  OP  SATURATED  STEAK— Continued. 


f-g 

J3 

2 

g 

S 

DENSITY. 

94 

a 

2 

g 

S 

DENSITY. 

o  M 

fM 

.2* 

l 

a 

.3*8-2 

O  M 

iT83 

a1 

^O 

i 

•S'6-2 

8'? 

3  r. 

®  J 

| 

J 

1 

J3 
,3 

(Eg, 

5  8 

j3 

4 

i 

3 

£. 

1i  Jyn 
I! 

o 
1 

» 

1 

|| 

o 

9 

"3 

• 

Hsl 

II 

ao? 

o 

1 
3 

ll 

o 

<c 
"3 

!§•« 

.2f  o  c  o 

£ 

4) 

B 

H 

£ 

1 

K 

02 

£ 

H 

H 

K 

1 

4> 

I 

02 

SftOfa 

p 

t 

Q 

A 

r 

S 

y 

p 

t 

Q 

* 

r 

8 

V 

101 

328-30 

298-6 

1182-1 

883-5 

4-362 

0-2293 

151 

358-78 

330-5 

1191-4 

860-9 

2-992 

0-3342 

102 

329-02 

299-4 

1182-3 

882-9 

4-322 

0-2314 

152 

359-30 

331-1 

1191-5 

860-4 

2-973 

0-3363 

103 

329-73 

300-1 

1182-5 

882-4 

4-282 

0-2335 

153 

359-82 

331-6 

1191-7 

860-1 

2-955 

0-3384 

104 

330-43 

300-9 

1182-7 

881-8 

4-244 

0-2356 

154 

360-34 

332-2 

1191-8 

859-6 

2-937 

0-3405 

105 

331-13 

301-6 

1182-9 

881-3 

4-206 

0-2378 

155 

360-86 

332-7 

1192-0 

859-3 

2-919 

0-3426 

106 

331-83 

302-3 

1183-1 

880-8 

4-169 

0-2399 

156 

361-37 

333-3 

1192-2 

858-9 

2-901 

0-3447 

107 

332-52 

302-0 

1183-4 

880-4 

4-132 

0-2420 

157 

361-88 

333-8 

1192-3 

858-5 

2-884 

0-3467 

108 

333-20 

303-8 

1183-6 

879-8 

4-096 

0-2441 

158 

362-39 

334-3 

1192-5 

858-2 

2-867 

0-3488 

109 

333-88 

304-5 

1183-8 

879-3 

4-061 

0-2462 

159 

362-90 

334-9 

1192-7 

857-8 

2-850 

0-3509 

110 

334-56 

305-2 

1184-0 

878-8 

4-026 

0-2484 

160 

363-40 

335-4 

1192-8 

857-4 

2-833 

0-3530 

111 

335-23 

305-9 

1184-2 

878-3 

3-992 

0-2505 

161 

363-90 

335-9 

1193-0 

857-1 

2-816 

0-3551 

112 

335-89 

306-6 

1184-4 

877-8 

3-959 

0-2526 

162 

364-40 

336-4 

1193-1 

856-7 

2-799 

0-3572 

113 

336-55 

307-3 

1184-6 

877-3 

3-926 

0  2547 

163 

364-90 

337-0 

1193-3 

856-3 

2-783 

0-3593 

114 

337-20 

308-0 

1184-8 

876-8 

3-894 

0-2568 

164 

365-39 

337-5 

1193-4 

855-9 

2-767 

0-3614 

115 

337-86 

308-7 

1185-0 

876-3 

3-862 

0-2589 

165 

365-88 

338-0 

1193-6 

855-6 

2-751 

0-3635 

116 

338-50 

309-4 

1185-2 

875-8 

3-831 

0-2610 

166 

366-37 

338-5 

1193-7 

855-2 

2-736 

0-3655 

117 

339-14 

310-0 

1185-4 

875-4 

3-801 

0-2631 

167 

366-85 

339-0 

1193-9 

854-9 

2-721 

0-3675 

118 

339-78 

310-7 

1185-6 

874-9 

3-770 

0-2653 

168 

367-33 

339-5 

1194-0 

854-5 

2-706 

0-3695 

119 

340-42 

311-4 

1185-8 

874-4 

3-740 

0-2674 

169 

367-81 

340-0 

1194-2 

854-2 

2-691 

0-3716 

120 

341-05 

312-0 

1186-0 

874-0 

3-711 

0-2695 

170 

368-29 

340-5 

1194-3 

853-8 

2-676 

0-3737 

121 

341-67 

312-7 

1186-2 

873-5 

3-683 

0-2715 

171 

368-77 

341-0 

1194-4 

853-4 

2-661 

0-3758 

122 

342-29 

313-3 

1186-3 

873-0 

3-655 

0-2736 

172 

369-24 

341-5 

1194-6 

853-1 

2-647 

0-3778 

123 

342-91 

314-0 

1186-5 

872-5 

3-627 

0-2757 

173 

369-71 

342-0 

1194-7 

852-7 

2-632 

0-3799 

124 

343-52 

314-6 

1186-7 

872-1 

3-599 

0-2779 

174 

370-18 

342-5 

1194-8 

852-3 

2-618 

0-3820 

125 

344-13 

315-2 

1186-9 

871-7 

3-572 

0-2800 

175 

370-65 

343-0 

1195-0 

852-0 

2-603 

0-3841 

126 

344-73 

315-9 

1187-1 

871-2 

3-546 

0-2820 

176 

371-12 

343-5 

1195-1 

851-6 

2-589 

0-3862 

127 

345-33 

316-5 

1187-3 

870-8 

3-520 

0-2841 

177 

371-59 

344-0 

1195-3 

851-3 

2-575 

0-3883 

128 

345-93 

317-1 

1187-4 

870-3 

3-494 

0-2862 

178 

372-05 

344-4 

1195-4 

851-0 

2-561 

0-3904 

129 

346-53 

318-7 

1187-6 

869-9 

3-469 

0-2883 

179 

372-51 

344-9 

1195-6 

850-7 

2-548 

0-3925 

130 

347-12 

318-4 

1187-8 

869-4 

3-444 

0-2904 

180 

372-97 

345-4 

1195-7 

850-3 

2-535 

0-3945 

131 

347-71 

319-0 

1188-0 

869-0 

3-419 

0-2925 

181 

373-43 

345-9 

1195-9 

850-0 

2-522 

0-3966 

132 

348-29 

319-6 

1188-2 

868-6 

3-395 

0-2946 

182 

373-88 

346-4 

1196-0 

849-6 

2-508 

0-3987 

133 

348-87 

320-2 

1188-4 

868-2 

3-371 

0-2967 

183 

374-33 

346-8 

1196-1 

849-3 

2-495 

0-4008 

134 

349-45 

320-8 

1188-5 

867-7 

3-347 

0-2988 

184 

374-78 

347-3 

1196-2 

848-9 

2-482 

0-4029 

135 

350-03 

321-4 

1188-7 

867-3 

3-3230-3009 

185375-23 

347-8 

1196-4 

848-6 

2-470 

0-4049 

136 

350-60 

322-0 

1188-9 

866-9 

3-3000-3030 

186 

375-68 

348-2 

1196-5 

848-3 

2-457 

0-4070 

137 

351-17 

322-6 

1189-0 

866-4 

3-277 

0-3051 

187 

376-12 

348-7 

1196-6 

847-9 

2-445 

0-4090 

138 

351  •  73 

323-2 

1189-2 

866-0 

3-255 

0  3072 

188 

376-56 

349-2 

1196-8 

847-6 

2-432 

0-4111 

139 

352-29 

323-8 

1189-4 

865-6 

3-234 

0-3092 

189 

377-00 

349-6 

1196-9 

847-3 

2-420 

0-4132 

140 

352-85 

324-4 

1189-5 

865-1 

3-212 

0-3113 

190 

377-44 

350-1 

1197-1 

847-0 

2-408 

0-4153 

141 

353-40 

325-0 

1189-7 

864-7 

3-191 

0-3134 

191 

377-88 

350-5 

1197-2 

846-7 

2-396 

0-4174 

142 

353-95 

325-6 

1189-9 

864-3 

3-170 

0-3155 

192378-32 

351-0 

1197-3 

846-3 

2-385 

0-4194 

143 

354-50 

326-1 

1190-1 

864-0 

3-149 

0-3176 

1931378-75 

351-4 

1197-4 

846-0 

2-373 

0-4215 

144 

355-05 

326-7 

1190-2 

863-5 

3-128 

0-3197 

194379-18 

351-9 

1197-6 

845-7 

2-361 

0-4236 

145 

355-59 

327-2 

1190-4 

863-2 

3-107 

0-3218 

195 

379-61 

352-4 

1197-7 

845-3 

2-349 

0-4257 

146 

356-13 

327-8 

1190-6 

862-8 

3-087 

0-3239 

196 

380-04 

352-8 

1197-8 

845-0 

2-337 

0-4278 

147 

356-67 

328-3 

1190-7 

862-4 

3-068 

0-3259 

197 

380-47 

353-3 

1198-0 

844-7 

2-325 

0-4298 

148 

357-20 

328-9 

1190-9 

862-0 

3-049 

0-3280 

198 

380-89 

353-7 

1198-1 

844-4 

2-314 

0-4318 

149 

357-73 

329-4 

1191-0 

861-6 

3-030 

0-3300 

199 

381-31 

354-1 

1198-2 

844-1 

2-304 

0-4338 

150 

358-26 

330-0 

1191-2 

861-2 

3-011 

0-3321 

200 

381-73 

354-6 

1198-4 

843-8 

2-294 

0-4359 

800 


APPENDIX. 


EXPANSIVE  WORKING  OP  STEAM. 


Cut-off  in 
percentage 
of  stroke. 

Number 
of  expan- 
sions. 

MEAN  ABSOLUTE  PRESSURE, 
IN  DECIMAL  PARTS,  OF 
ABSOLUTE  PRESSURE  OP 
ADMISSION. 

Cut-off  in 
percentage 
of  stroke. 

Number 
of  expan- 
sions. 

MEAN  ABSOLUTE  PRESSURE, 
IN  DECIMAL  PARTS,  OF 
ABSOLUTE  PRESSURE  OF 
ADMISSION. 

Dry  satu- 
rated steam. 

Moderately 
moist  steam. 

Dry  satu- 
rated steam. 

Moderately 
moist  steam. 

•800 

ii 

•9760 

•9784 

•1 

10 

•3145 

•3303 

•667 

14 

•9403 

•9366 

•095 

10J 

•3035 

•3189 

•571 

11 

•8857 

•8910 

•091 

11 

•2933 

•3089 

•500 

2 

•8394 

•8465 

•087 

114 

•2839 

•2991 

•444 

2* 

•7960 

•8050 

•083 

12 

•2751 

•2904 

•400 

24 

•7560 

•7664 

•080 

1S4 

•2669 

•2818 

•364 

2f 

•7200 

•7316 

•077 

13 

•2592 

•2742 

•333 

3 

•6870 

•6997 

•074 

184 

•2520 

•2666 

•308 

3i 

•6570 

•6705 

•071 

14 

•2452 

•2599 

•286 

84 

•6300 

•6437 

•069 

144 

•2388 

•2532 

•267 

8i 

•6051 

•6192 

•067 

15 

•2327 

•2472 

•250 

4 

•5820 

•5965 

•065 

15i 

•2270 

•2411 

•235 

4* 

•5608 

•5757 

•063 

16 

•2216 

•2358 

•222 

4* 

•5410 

•5564 

•061 

1«4 

•2164 

•2303 

•211 

4f 

•5230 

•5386 

•059 

17 

•2115 

•2255 

•200 

5 

•5060 

•5218 

•057 

m 

•2069 

•2205 

•191 

5k 

•4904 

•5063 

•056 

18 

•2024 

•2161 

•182 

6J 

•4760 

•4918 

•054 

184 

•1982 

•2116 

•174 

54 

•4620 

•4781 

•053 

19 

•1942 

•2181 

•167 

6 

•4490 

•4653 

•051 

19| 

•1903 

•2034 

•160 

ej 

•4370 

•4533 

•050 

20 

•1866 

•1998 

•154 

64 

•4250 

•4418 

•048 

21 

•1796 

•1926 

•148 

6f 

•4150 

•4311 

•045 

22 

•1736 

•I860 

•143 

7 

•4046 

•4208 

•043 

23 

•1672 

•1790' 

•138 

71 

•3950 

•4112 

•042 

24 

•1610 

•1741 

•133 

7* 

•3857 

•4020 

•040 

25 

•1566 

•1688 

•129 

7* 

•3770 

•3933 

•038 

26 

•1518 

•1638 

•125 

8 

•3688 

•3849 

•037 

27 

•1474 

•1591 

•121 

8J 

•3608 

•3769 

•036 

28 

•1431 

•1547 

•117 

84 

•3533 

•3694 

•034 

29 

•  1392 

•1506 

•114 

8f 

•3461 

•3622 

•033 

30 

•1355 

•1467 

•111 

9 

•3392 

•3552 

•108 

9* 

•3326 

•3494 

•105 

94 

•3274 

•3422 

•103 

9f 

•3203 

•3359 

TABLE  OF   FACTORS   OF   EVAPORATION. 


Pressure 
Pounds 
per 
Sq.  Inch. 

Boiling 
Point 
T,. 
Fahr. 

INITIAL  TEMPERATURE  OF   FEED  WATER,  T2. 

32° 

50° 

68° 

86° 

104° 

122° 

140° 

158° 

176° 

194° 

212° 

14-70 

212° 

1-19 

1-17 

1-15 

1-13 

1-11 

1-10 

1-08 

1-06 

1-04 

1-02 

1-00 

20-78 

230 

1-20 

1-18 

1-16 

1-14 

1-12 

1-10 

1-08 

1-06 

1-04 

1-02 

1-01 

28-82 

248 

1-20 

1-18 

1-16 

1-14 

1-13 

1-11 

1-09 

1-07 

1-05 

1-03 

1-01 

39-26 

266 

1-21 

1-19 

1-17 

1-15 

1-13 

1-11 

1-09 

1-07 

1-06 

1-04 

1-02 

52-56 

284 

1-21 

1-20 

1-18 

1-16 

1-14 

1-12 

1-10 

1-08 

1-06 

1-04 

1-02 

69-27 

302 

1-22 

1-20 

1-18 

1-16 

1-14 

1-12 

1-11 

1-09 

1-07 

1-05 

1-03 

89-95 

320 

1-22 

1-21 

1-19 

1-17 

1-15 

1-13 

1-11 

1-09 

1-07 

1-05 

1-03 

115-22 

338 

1-23 

1-21 

1-19 

1-17 

1-15 

1-14 

1-12 

1-10 

1-08 

1-06 

1-04 

145-75 

356 

1-23 

1-22 

1-20 

1-18 

1-16 

1-14 

1-12 

1-10 

1-08 

1-06 

1-04 

182-27 

374 

1-24 

1-22 

1-20 

1-18 

1-17 

1-15 

1-13 

1-11 

1-09 

1-07 

1-05 

225-56 

392 

1-24 

1-23 

1-21 

1-19 

1-17 

1-15 

1-13 

1-11 

1-09 

1-07 

1-06 

276-54 

410 

1-25 

1-23 

1-22 

1-20 

1-18 

1-16 

1-14 

1-12 

1-10 

1-08 

1-06 

336-26 

428 

1-25 

1-24 

1-22 

1-20 

1-18 

1-16 

1-14 

1-12 

1-11 

1-09 

1-07 

APPENDIX. 


801 


The  Twenty-eighth  Street  Central  Station  of  the  United  Electric  Light  and  Power 
Company.  By  H.  W.  York,  "Trans.  A.  S.  C.  EM"  March  18,  1896. 

In  this  station  20,000  H.  P.  of  engines,  together  with  the  boilers,  condensing  appa- 
ratus, dynamos,  and  switchboard,  and  storage  for  6,000  tons  of  coal,  are  all  on  a  plot  of 
ground  160  feet  11  inches  by  197  feet  6  inches.  All  machinery,  including  the  boilers,  is 
on  the  ground  floor,  and  yet  there  is  plenty  of  light,  air,  and  ample  space  for  working 
around  all  the  apparatus.  Fig.  1870  is  a  plan  of  the  foundation  walls  and  piers  of  the 


802 


APPENDIX. 


building.  The  entire  front  wall  is  hollow  and  carried  up  above  the  roof  to  prevent  the 
noise  of  the  machinery  annoying  the  patients  in  Bellevue  Hospital,  which  is  directly 
across  the  street.  Fig.  1871  is  a  cross-section  of  the  entire  structure. 

Loop  System. — The  main  steam  and  exhaust  piping  is  shown  in  plan  on  Fig.  1872.  A 
16-inch  header  is  run  the  length  of  the  boiler-room,  and  a  similar  header  is  run  the  length 
of  the  engine  room  between  the  two  rows  of  foundations  and  parallel  to  the  boiler-room 
header.  Each  of  these  headers  are  divided  into  five  sections  by  means  of  four  gate- 


APPENDIX. 


803 


valves,  and  each  section  of  the  boiler-room  header  is  connected  to  the  corresponding  sec- 
tion of  the  engine-room  header  by  a  14-inch  branch  rising  from  the  top  of  one  and  dis- 
charging into  the  top  of  the  other,  a  valve  being  placed  on  each  end  where  a  connection 
is  made  to  the  header.  Each  boiler  lias  an  independent  connection  to  the  boiler-room 
header,  supplied  with  two  stop-valves,  one  in  the  customary  position  just  beyond  the 
safety-valves,  and  the  other  at  the  point  where  the  pipe  enters  the  header.  This  second 
valve  has  its  stem  extended  through  the  wall  into  the  repair  shop,  so  that  in  case  of 
trouble  any  boiler  may  be  cut  out  of  a  room  having  no  communication  with  the  boiler 
house. 

Each  engine  on  the  east  side  of  the  engine  room  is  connected  to  one  of  the   14-inch 


804 


APPENDIX. 


branches  previously  mentioned,  while  outlets  are  left  on  the  engine-room  header  for  con- 
nections to  the  west  row  of  the  engines  as  soon  as  they  are  placed  in  position.  In  case 
any  section  of  the  engine-room  header  is  cut  out,  one  engine  connected  to  this  section 
can  be  fed  directly  from  the  14-inch  branch,  leaving  only  one  which  can  not  be  run,  and 
in  case  any  section  of  the  boiler-room  header  is  cut  out  no  engine  need  be  shut  down,  as 

the  one  connected  to  the  14-inch  branch  can  be 
fed  back  from  the  engine-room  header. 

The  boilers  are  of  the  upright  water-tube 
type  of  the  Clonbrock  pattern,  and  are  in  600 
H.-P.  units,  occupying  little  ground  room 'per 
unit  of  capacity  (Fig.  1873). 

The  conveyer  for  handling  coal  and  ashes 
consists  of  an  endless  chain  of  gravity  buckets, 
which  are  loaded  by  means  of  a  filler  and  can  be 
dumped  at  any  desired  point.  The  driver  is  in 
the  north  end  of  the  ventilator  over  the  coal 
bunker.  The  coal  filler  is  in  a  vault  under  the 
sidewalk,  and  the  coal  is  dumped  into  this  ap- 
paratus through  a  grating  situated  about  the 
street  level.  After  being  deposited  in  the  buck- 
ets the  coal  is  carried  up  into  the  ventilator  over 
the  coal  bunker  and  dumped  into  any  portion 
of  the  bunker  desired.  From  the  hoppers  in 
the  bottom  of  the  bunker  the  coal  is  spouted 
to  the  different  boilers.  The  arrangement  is 
such  that  the  coal  trims  itself  and  will  con- 
tinue running  down  the  spouts  as  required  and 
without  assistance  so  long  as  any  remains  in  the 
bunker. 

Under  each  boiler  is  an  ash  hopper  deliver- 
ing the  ashes  to  a  second  movable  filler,  which 
deposits  them  in  the  buckets  of  the  conveyer 
when  it  is  not  used  for  coal.  The  conveyer 
dumps  the  ashes  at  a  point  from  which  they  are 
spouted  over  to  a  tank  in  the  southeast  corner 
of  the  coal  bunker. 

The  engines  are  Westinghouse  double  acting 
"Columbian  steepled  compounds."  Fig.  1874 
shows  one  of  these  engines  in  section.  The  low 
pressure  is  placed  over  the  high  pressure,  and 
both  pistons  are  connected  to  the  same  rod. 
The  crank  is  inclosed  in  the  same  manner  as 
the  Westinghouse  engines.  The  low-pressure 
valve  is  operated  by  a  fixed  eccentric  placed  in- 
side the  crank  case,  while  the  high-pressure 
valve  receives  its  motion  from  a  shifting  eccen- 
tric outside  the  crank  case,  operated  automati- 
cally by  the  governor,  which  is  placed  on  the 
shaft  outside  of  the  eccentric.  The  low-pressure  valve  is  of  the  slide-valve  type,  while 
that  for  the  high-pressure  cylinder  is  a  hollow  piston  valve,  being  constructed  in  this 
manner  to  allow  the  exhaust  from  the  lower  end  of  the  high-pressure  cylinder  to 
pass  up  through  it.  Diameter  high-pressure  cylinder,  21J  inches  ;  diameter  low- 
pressure  cylinder,  37  inches ;  stroke,  22  inches.  The  speed  is  200  revolutions  -per 


Elevation. 


APPENDIX. 


805 


minute  and  the  rated  horse  power  1,200  when  operating  condensing,  with  150  pounds 
initial  steam  pressure. 

Each  main  engine  is  directly  connected  to  a  600- kilowatt  Westinghouse  ^alternator  by 
a  rigid  coupling,  both  engine  and  generator  being  set  on  a  firm  cast-iron  bedplate.  The 
generator  has  but  one  bearing,  the  armature  being  swung  between  the  engine  and  this 
single  support. 

For  exciting  the  fields  of  the  alternators,  75-kilowatt  direct-current  Westinghouse 
dynamos  of  the  railway  generator  type  are  used. 


FIG.  1874. 


FOUNDATION   FOB   VERTICAL    ENGINES. 


806 


APPENDIX. 


Zoss  j/i  Yo/fs. 


FIG.  1875. 


In  the  "  Universal  "Wiring  Com- 
puter, ''  by  Carl  Hering,  charts  are  giv- 
en which  give  directly,  and  without 
calculation  or  the  use  of  formulae,  'the 
gauge  number  or  cross  section  in  cir- 
cular mils  of  lead  for  any  number  of 
lamps  of  any  make  at  any  distance  or 
for  any  loss.  One  of  these  tables  is 
given  above  as  an  illustration  on 
"graphics." 

Follow  the  general  direction  of 
the  broken  line  and  the  arrows  from 
one  set  of  diagonals  to  the  next. 

Example  :  What  size  wire  is  re- 
quired for  10  lamps  of  '775  amperes 
each,  at  50  feet,  for  a  loss  of  one  volt  ? 

Solution :  Starting  with  the  cur- 
rent for  one  lamp,  -775  amperes  (see 
scale  below  centre),  follow  it  to  the 
left  until  it  intersects  the  diagonal 
representing  one  volt  loss,  thence  up 
to  the  diagonal  representing  10  lamps, 
thence  to  the  right  to  the  diagonal 
representing  50  feet,  and  from  here 
down  to  the  scale  of  the  circular  mils 
or  gauge  numbers,  on  which  the  read- 
ing is  found  to  be  about  8,200  circu- 
lar mils,  or  a  No.  11  B.  S.  wire. 

Fig.  1875  is  an  incandescent  elec- 
tric lamp  socket  of  the  Bryant  Elec- 
tric Company. 

Fig.  1876  is  a  switch  of  the  Hart 
and  Hegeman  Company. 


APPENDIX. 


sor 


All  of  the  above  drawings  are  made  in  a  style  in  which  the  exterior  shell  is  trans- 
parent, showing  the  interior  mechanism,  and  known  as  "ghost  cuts." 


FIG.  1876. 


Area. 

Chms  pr  1000  ft. 

No. 

at  70°  F. 

B.  &  S. 

Diameter, 
Mils. 

Circular 

Current 

Guage. 

Mils  (d2) 

allowed  by 

1  mil  =  -001  in. 

Underwriter's 

Code. 

0000 

460-000 

211600-00 

175 

.000 

409-640 

167805-00 

145 

00 

364-800 

133079  '04 

120 

0 

324-860 

105534-03 

100 

1 

5289-300 

83694-20 

95 

2 

257-630 

66373-00 

70 

3 

229-420 

52633-40 

60 

4 

204-310 

41742-57 

50 

5 

181-940 

33102-00 

45 

6 

162-020 

26250-50 

35 

7 

144-280 

20816-70 

30 

8 

128-490 

16509-00 

25 

9 

114-430 

13094-00 

10 

101  -890 

10381-00 

20 

11 

90-742 

8234-10 

12 

80-808 

6529-90 

15 

13 

71-901 

5178-40 

14 

64-084 

4106-80 

10 

LUNDELL   MOTOR. 


808 


APPENDIX 


TABLE  OP  DENSITY  OP  GASES  AND  VAPOURS,  AIR  AT  THE  SAME  TEM- 
PERATURE AND  PRESSURE  BEING  1-0 ;  ALSO  THE  WEIGHT  OF  A 
CUBIC  FOOT  AT  62°  FAHR.,  UNDER  AN  ATMOSPHERIC  PRESSURE 
OF  29-92  INCHES  OF  MERCURY. 


Density  of 
air. 

Specific 
gravity. 

Weight  of 
cubic  foot 
in  pound. 

Cubic  feet. 

Air  (atmospheric)    

1-00000 

•001221 

•07610 

13-14 

•06926 

•000085 

•00527 

189-70 

Oxygen  ga^                   .           

1-10563 

•001350 

•08414 

11-88 

Nitrogen  gas  

•97137 

•001185 

•07383 

13-54 

Carbonic-acid  gas     

1-52901 

•001870 

•11636 

8-59 

Carbonic-oxide  gas  

•9674 

•00118 

•07364 

13-60 

Vapour  of  water      

•6235 

•000761 

•04745 

21-07 

•'        "  alcohol  

1-589 

•00194 

•  12092 

8-27 

"        "  sulphuric  ether  

2-586 

•00316 

•19680 

5-08 

"        "  oil  of  turpentine  

4-760 

•00581 

•36224 

2-76 

SPECIFIC  GRAVITY  OP  LIQUIDS  AT  60°   FAHR. 


Acid,  muriatic 1-200 

Acid,  nitric 1-217 

Acid,  sulphuric 1*849 

Alcohol,  pure -794 

Ammonia,  27-9  per  cent  -891 

Carbon  disulphide 1-260 


Ether,  sulphuric .     -720 

Oil,  linseed '940 

Oil,  olive -920 

Oil,  petroleum '780- -880 

Oil,  turpentine •  870 


Oil,  whale -920 

Tar 1-000 

Vinegar 1-080 

Water 1-000 

Water,  sea. . . , . .  1-026-1  -030 


SPECIFIC  GRAVITIES  AND  WEIGHTS  OF  EARTHS,  ETC. 


SUBSTANCE. 

Common 
specific 
gravity. 

Average 
weight 
per  cubic 
foot. 

SUBSTANCE. 

Common 
specific 
gravity. 

Average 
weight 
per  cubic 
foot. 

Alabaster  

2-73 
3-57 
1-13 
1-40 
4-0-4-86 
2-74 
1-71 
1-6-1-8 
1-6-2-16 
2-3 
1-28 
•96 
1-93 
1-40 
1-24-1-30 
1-0 
2-08 

171 
192 
70 
87 
250-304 
171 
107 
100-115 
100-125 
140-150 
80 
60 
121 
80-95 
77-81 
62 
120-140 
80-110 
250 
162 
150-200 
160-170 
138 
110 
135 
61 

Gypsum  . 

2-24 

•80 
2-88 
2-4 
2-72 
2-08 
2-08 
2-72 
2-72 
2-24 
2-80 
2-80 
•96 
2-64 
8-96 
1-09 
•95 
2-16 
1-60 
2-32 
2-80 
2-72 
2-03 
1-95 
2-88 

140 
50 
180 
150 
170 
130 
130 
170 
170 
140 
175 
175 
60 
165 
560 
68 
60 
135 
100 
145 
175 
170 
127 
122 
180 

Asbestos  

,7f-       -"••  • 

Lime  quick 

Asphalt,  California  
"        Trinidad  

Limestone  

Magnesia  carbonate  .... 
Marble  . 

Barvtes  

Basalt  

Masonry,  concrete  

"         rubble 

Borax  

Brick,  masonry  

"         granite.   .  .  . 

Bricks  

"         limestone  
"         sandstone  .... 
Mica  

"      fire  

Cement,  Portland  

"        Rosendale  
Clay  

Porphyry  

Coal  

Quartz                            . 

Coal  tar  

Red  lead      . 

Coke  

Concrete  

Rubber  pure 

Earth  

Salt,  common  and  rock  . 
Sund 

Emerv  

4-0 

2-60 

Feldspar  

Glass  

Slate 

Gneiss  and  granite  
Graphite  

2:20 

Soapstone         

Sulphur 

Gravel  

Grindstone  

2-14 
•98 

Trap 

Gutta-percha  

APPENDIX. 


809 


SPECIFIC   GRAVITY  AND   WEIGHT   OF   WOOD. 


WOOD. 

Specific 
gravity. 

Average 
weight 
per  cubic 
foot. 

WOOD. 

Specific 
gravity. 

Average 
weight 
per  cubic 
foot. 

Apple  .  . 

•73-  -80 

47 

Lignum-vitas  

•65-1-33 

62 

Ash   

•60-  -84 

45 

Lime  

•80 

50 

Bamboo  

•31-  -40 

22 

Linden. 

•60 

37 

Beech  

•62-  -85 

46 

Locust  

•73 

46 

Birch  

•56-  -74 

41 

Mahogany  

•56-1-06 

51 

Box  

•91-1-33 

70 

Maple  

•57-  -79 

42 

Butternut  

•38 

24 

Oak,  live  

•96-1-10 

64 

Cedar  

•49-  -75 

39 

"     white  

•69-  -86 

48 

Cherry  

•61-  -72 

41 

"     red  

•73-  -75 

46 

Chestnut  

•46-  -66 

35 

Palmetto  

Cork  

•24 

15 

Pine,  long  leaf  

•70 

44 

Cypress  

•41-  -66 

33 

"     white  

•35-  -55 

25 

Ebony                      .  . 

1-13-1-33 

76 

"     yellow     

•46-  -76 

38 

Elm.            

-  55—  *  78 

38 

Poplar  

•38-  -58 

30 

Fir  

•48-  -70 

37 

Spruce  

•40-  -50 

28 

Gum 

•84-1-00 

57 

Sycamore  

•59-  -62 

37 

Hackmatack    

•59 

37 

Tamarack    

•40 

25 

Hemlock  

•36-  -41 

24 

Teak  

•66-  -98 

51 

Hickory     ...         .... 

•69-  -94 

48 

Walnut  

•50-  -67 

36 

Hornbeam  .  . 

•76 

47 

"       black.  . 

•50 

31 

PROPERTIES  OF  METALS. 


METAL. 

Specific 
gravity. 

Weight  per 
cubic  foot. 

Melting  point, 
degrees  Fahr. 

Tensile  strength, 
pounds  per  square 
inch. 

Expansion 
in  100  ft. 
from  temp. 
32°  to  212°  F. 

Aluminum     

2-63 

166 

1,400 

26,000 

Antimony 

6'76 

421 

842 

•1083 

Bismuth  

9-82 

612 

510 

6,400 

•1392 

Cadmium  

8-65 

539 

Calcium  

1-58 

Chromium  

5-00 

Cobalt  

8-60 

Copper  

8-7to  8-9 

450 

1,930 

20,000  to  30,000 

•1722 

Gold  pure 

19-30 

1215 

1,915 

•1552 

"     22  carats  
"     20      "     
Iron  cast 

17-49 
15-71 
7-20 

450 

2  000  to  2,200 

•1109 

"     wrought  

7-68 

480 

2,700  to  2,900 

46,000  to  48,000 

•1220 

Lead 

11-36 

709 

625 

•2848 

Magnesium  

1-70 

106 

1,200 

Manganese  

8-00 

499 

Mercury,  60°  

13-58 

847 

662 

Nickel  

8'3to  8-9 

537 

3,000 

21-50 

1341 

•0857 

Potassium  

0-86 

144 

Selinium  

4-30 

220 

Silver 

10-50 

655 

1,750 

•1909 

Sodium   

0-97 

Steel  

7-84 

490 

2,500 

IHigh  grade,  70,- 
000  to  80,000. 
Medium      grade, 
(50  000  to  70  000 

1-1079 

Strontium  

2-54 

Soft  grade,  52,000 
to  60,000. 

Tellium       

6-11 

Thallium    

11-85 

Tin.               

7*35 

458 

442 

3,500 

•2173 

Tungsten    

17-00 

18-33 

Zinc  

7-14 

445 

780 

5,000  to  6,000 

•2942 

810 


APPENDIX. 

SOLDERS. 


Copper. 

Tin. 

Lead. 

Zinc. 

Antimony. 

Silver. 

Nickel. 

Lead,  melts  at  441°  
Tin  melts  at  340°  

•• 

33 
67 

67 
33 

Spelter  soft  .         

50 

50 

"       hard  

65 

35 

Steel             

13 

5 

82 

Brass  or  copper  

50 

50 

47 

47 

6 

66 

33 

1 

Copper        ...    

53 

47 

German  silver  .  . 

38 

54 

,    . 

8 

Solders  of  lead  and  tin  are  termed  soft  solders,  in  plumbers'  work  the  joints  are  wiped 
and  the  solder  is  in  a  mass.  In  soldering  cornices,  where  there  is  a  strain,  the  metal 
should  be  riveted  as  well.  Solders  containing  copper  are  used  for  brazing. 

Sheet  lead  for  sulphuric-acid  chambers  is  joined  by  burning  the  sheets  by  a  blowpipe. 
The  welding  of  various  metals  is  now  effected  by  electricity.  In  joining  one  metal  to 
another,  one  must  be  fluid;  and  mercury,  being  usually  fluid,  combines  with  most  metals 
except  iron  and  platinum.  An  amalgam  of  tin  or  cold  solder  can  be  applied  by  friction 
to  polished  iron  and  form  a  surface  which  admits  of  being  soldered. 

Fusible  Alloys. — A  fusible  alloy  composed  of  50  bismuth,  25  tin,  and  25  lead  melts  at 
212°  •,  the  melting  point  may  be  still  further  reduced  by  a  larger  percentage  of  bismuth, 
and  it  is  used  either  as  a  solder  or  a  fusible  plug.  In  automatic  fire  extinguishers  the 
cap  of  the  sprinkler  is  soldered  with  this  alloy,  and  melts  at  about  170°.  For  fusible 
plugs  in  boilers,  the  United  States  supervising  inspectors  specify  Banca  tin,  which  melts 
at  about  445°  F.  The  plug  must  be  at  least  |"  smallest  diameter. 

ALLOYS  AND   COMPOSITIONS. 


Cop- 
per. 

Zinc. 

Tin. 

Nickel. 

Lead. 

Alu- 
mi- 
num. 

Steel. 

Anti- 
mony. 

Tensile 
strength 
per  sq. 
inch. 

Aluminum  bronze 

90-0 
33£ 

10-0 

lumi 
90-0 

75.000- 
90,000 

78,327 

"           brass 

33i 

Add 
10-0 
89-3 

88-9 
81-0 

33i  per 

cent  t 

num  bi 

onze  .  . 

"           composition  . 
Babbitt's  metal,  light  duty 
"            "      for    bear- 
ing's 

1-8 
3-7 



8-9 

7.4 
16-0 

2-0 

1-0 

98-0 

2-0* 

51-1 

31-9 

3-2 

13-8 

42.560 
49,280 
57,000 

Muntz  metal  

6-25 
67-3 

93-75 
13-0 

Manganese  alloy  \  

1-2 

96:75 

18-0^ 

•5|| 

3-25 

Sheathing  metal  

56-0 
66-0 
50-0  - 

61-0 

44-0 

2i:6' 

35-0 

22-0 
29-0 

2-0 

12-0 

it                   « 

Sterrometal  

Iron. 
2-0 

Anti- 

monv. 
25  -0 
12-5 

56-8 

85,120 

Type  metal       

75-0 

87-5 

White    "       

7-4 
69-8 

7.4 

25-8 

28-4 
4-4 

"        "    hard.., 

*  Chromium,  2'0.     f  Twenty-five  per  cent  manganese  to  copper  doubles  its  tensile  strength 
without  diminishing  its  ductility.     \  Manganese,  18'0.     ||  Silicon,  '5. 


APPENDIX. 


811 


TABLES  OF  THE  CIRCUMFEEENCES  OF  CIRCLES  TO  THE  NEAREST  FRACTION  OF 
PRACTICAL  MEASUREMENT  ;'  ALSO,  THE  AREAS  OF  CIRCLES,  IN  INCHES  AND 
DECIMAL  PARTS,  LIKEWISE  OF  FEET  AND  DECIMAL  PARTS. 


Circumfer- 

Diameter 

Area 

Area 

Circumfer- 

Diameter 

Area 

Area 

ence  in  feet 

in 

in  square 

in  square 

ence  in  feet 

in 

in  square 

in  square 

and  inches. 

inches. 

inches. 

feet. 

and  inches. 

inches. 

inches. 

feet. 

1     65 

6 

28-27 

•196 

•20 

iV 

•003 

1     74 

64 

29-46 

•204 

•39 

1 

•012 

1    7f 

64 

30-68 

•212 

•59 

A 

•028 

1     8 

6f 

31-92 

•220 

•78 

| 

•049 

1     8f 

64 

33-18 

•228 

•98 

ft 

•077 

1     8f 

6| 

34-47 

•237 

1-18 

f 

•no 

1     M 

M 

35-78 

•246 

1-37 

TV 

•150 

1     94 

63 

37-12 

•256 

1-57 

| 

•196 

1   10 

7 

38-48 

•267 

1-77 

ft 

•248 

1   lOf 

74 

39-87 

•277 

1-96 

f 

•307 

1   10  J 

H 

41-28 

•287 

2-16 

H 

•371 

i  114 

71 

42-72 

•297 

2-36 

$ 

•442 

i  11* 

» 

44-18 

•307 

2-55 

« 

•518 

i  n4 

7f 

45-66 

•318 

2-75 

f 

•601 

2     Of 

7f 

47-17 

•328 

2-94 

If 

•690 

2     03 

74 

48-71 

•338 

34 

i 

•785 

•0054 

2     14 

8 

50-26 

•349 

H 

i* 

•994 

•0069 

2     14 

84 

51-85 

•360 

35 

14 

1-23 

•0085 

2     15 

84 

53-46 

•371 

44 

if 

1-48 

•0103 

2     2| 

81 

55-09 

•383 

4* 

il 

1-77 

•0123 

2     2f 

84 

56-74 

•394 

4 

M 

2-07 

•0144 

2     3 

8| 

58-43 

•406 

& 

i* 

2-40 

•0167 

2     3f 

8| 

60-13 

•428 

5l 

il 

2-76 

•0192 

2     3j 

85 

61-86 

•430 

64 

2 

3-14 

•0218 

2     44 

9 

63-62 

•442 

«3 

24 

3-55 

•0246 

2     4f 

9£ 

65-40 

•455 

7 

H 

3-98 

•0276 

2     5 

94 

67-20 

•467 

7f 

21 

4-43 

•0307 

2     5| 

9^ 

69-03 

•480 

11 

4 

4-91 

•0341 

2     5j 

94 

70-88 

•493 

if 

25 

5-41 

•0376 

2     64 

9f 

72-76 

•506 

8| 

8* 

5-94 

•0412 

2     6f 

»i 

74-66 

•519 

9 

24 

6-49 

•0450 

2     7 

95 

76-59 

•532 

9| 

3 

7-07 

•0490 

2     7? 

10 

78-54 

•545 

9* 

Si 

7-67 

•0532 

2     7£ 

104 

80-51 

•559 

104 

8* 

829 

•0576 

2     84 

104 

82-52 

•573 

103 

3| 

8-95 

•0621 

2     84 

101 

84-54 

•587 

11 

84 

9-62 

•0668 

2     9 

104 

86-59 

•601 

11? 

8f 

10-32 

•0716 

2     9| 

lOf 

88-66 

•615 

ill 

3j 

11-04 

•0766 

2     9J 

lOf 

90-76 

•630 

124 

33 

11-79 

•0818 

2  104 

io4 

92-88 

•645 

1     04 

4 

12-57 

•087 

2  104 

11 

95-03 

•660 

1    1 

44 

13-36 

•093 

2   10? 

ii4 

97-21 

•675 

1  11 

*i 

14-19 

•099 

2  114 

114 

99-40 

•690 

1  If 

4! 

15-03 

•105 

2   11  J 

ill 

101-62 

•705 

1     24 

4* 

15-90 

•111 

3     04 

114 

103-87 

•720 

1     24 

43 

16-80 

•118 

3     04 

ill 

106-14 

•736 

1     25 

4j 

17-72 

•124 

3     Oj 

11* 

108-43 

•752 

1     34 

«i 

18-66 

•130 

3     14 

ill 

110-75 

•768 

1     3| 

5 

19-63 

•136 

3     If 

12 

113-10 

•785 

1     44 

54 

20-63 

•14S 

3     2 

124 

115-47 

•802 

1     44 

54 

21-65 

•150 

3     24 

124 

117-86 

•819 

1     45 

5« 

22-69 

•157 

3     23 

12f 

120-28 

•836 

1     54 

54 

23-76 

•165 

3     3J: 

124 

122-72 

•853 

1     5f- 

5| 

24-85 

•173 

3     3f 

12* 

125-19 

•870 

1     6 

5f 

25-97 

181 

3     4 

iaf 

127-68 

•887 

1     6f 

6l 

27-11 

•189 

3     4| 

124 

130-19 

•904 

812 


APPENDIX. 


TABLES  OF  THE  CIKCUMFEKENCES  OF  CIECLES,  ETC.— (Continued.) 


Circumfer- 

Diameter 

Area 

Area 

Circumfer- 

Diameter 

Area 

Area 

ence  in  feet 

in 

in  square 

in  square 

ence  in  teet 

in  feet  and 

in  square 

in  square 

and  inches. 

inches. 

inches. 

feet. 

and  inches. 

inches. 

inches. 

feet. 

3     4f 

13 

132-73 

•922 

5     2J 

20 

314-16 

2-182 

3     51 

131 

135-30 

•939 

5     Si- 

201 

318-10 

2-209 

3     5f 

131 

137-89 

•956 

5     3| 

20i 

322-06 

2-237 

3     6 

13f 

140-50 

•974 

5     4 

20f 

326-05 

2-265 

3     6f 

131 

143-14 

•992 

5     4f 

20^ 

330-06 

2-293 

3     6f 

18f 

145-80 

1-011 

5     41 

20| 

334-10 

2-321 

3     71 

18f 

148-49 

1-030 

5     5£ 

20f 

338-16 

2-349 

3     7f 

181 

151-20 

1-050 

5     5| 

201 

342-25 

2-377 

3D 
o 

14 

159-94 

1-069 

5     6 

21 

346-36 

2-405 

3     8f- 

141 

156-70 

1-088 

5     6| 

211 

350-50 

2-434 

3     8f 

141 

159-49 

1-107 

5     6J 

ill 

354-66 

2-463 

3     91 

14? 

162-30 

1-126 

5     7| 

21f 

358-84 

2-492 

3     91 

141 

165-13 

1-146 

5     71 

211 

363-05 

2-521 

3     9| 

14* 

167-99 

1-166 

5     7£ 

21| 

367-28 

2-550 

3  101 

14f 

170-87 

1-186 

5     81 

2li 

871-54 

2-580 

3  lOf 

14i 

173-78 

1-206 

5     8f 

211 

375-83 

2-610 

3  HI 

15 

176-71 

1-227 

5     9J 

22 

380-13 

2-640 

3  111 

151 

179-67 

1-247 

5     9| 

221 

384-46 

2-670 

3  Hi 

1M 

182-65 

1-267 

5     9£ 

221 

388-82 

2-700 

4     01 

155 

185-66 

1-288 

5  10J 

22} 

393-20 

2-730 

4    Of 

151 

188-69 

1-309 

5  lOf 

221 

397-61 

2-761 

4     1 

Iftf 

191-75 

1-330 

5  11 

22f 

402-04 

2-792 

4     11 

I6f 

194-83 

1-352 

5  11J 

22* 

406-49 

2-823' 

4     11 

16* 

197-93 

1-374 

5  11| 

22i 

410-97 

2-854 

4     21 

16 

201-06 

1-396 

6     01 

23 

415-48 

2-885 

4     2f 

161 

204-22 

1-418 

6     Of 

231 

420-00 

2-917 

4     3 

161 

207-39 

1-440 

6     1 

23ir 

424-56 

2-949 

4     33 

l«t 

210-60 

1-462 

6     It 

23| 

429-13 

2-981 

4     S| 

161 

213-82 

1-484 

6     If 

231 

433-74 

3-013 

4     41 

16$ 

217-08 

1-507 

6     2| 

28| 

4S8-36 

3-045 

4     4^ 

16f 

220-35 

1-530 

6     2| 

23| 

443-01 

3-077 

4     5 

16i 

223-65 

1-553 

6     3 

23| 

447-69 

3-109 

4     5| 

17 

226-98 

1-576 

6     8| 

2     0 

45239 

3-142 

4     6J 

171 

230-33 

1-599 

6     4| 

2     01 

461-86 

3-207 

4     61 

171 

233-70 

1-622 

6     4£ 

2     OJ 

471-44 

3-273 

4     6l 

171 

237-10 

1-645 

6     5| 

2     Of 

481-11 

3-341 

4     ft? 

171 

240-53 

1-669 

6     6J 

2     1 

490-87 

3-408 

4     7t 

171 

243-98 

1-693 

6     71 

2     11 

500-74 

3-477 

4     7* 

171 

247-45 

1-718 

6     81 

2     1J 

510-71 

3-547 

4     8l 

IT! 

250-95 

1-743 

6     8| 

2     If 

520-77 

3-617 

4     81 

18 

254-47 

1-767 

6     9| 

2     2 

530-93 

3-687 

4     8| 

18* 

258-02 

1-792 

6   lOt 

2     21 

541-19 

3-758 

4     94 

181 

261-59 

1-817 

6  lli 

2     2£ 

551-55 

3-830 

4     9f 

18f 

265-18 

1-842 

7     0 

2     2f 

562-00 

3-904 

4  101 

181 

268-80 

1-868 

7     0* 

2     3 

572-56 

3-976 

4  101 

18f 

272-45 

1-893 

7     If 

2     3J 

583-21 

4-050 

4  lOi 

18* 

276-12 

1-918 

7     2| 

2     3i 

59396 

4-124 

4  111 

18i 

279-81 

1-943 

7     3£ 

2     8| 

604-81 

4-200 

4  Hf 

19 

283-53 

1-969 

7     3£ 

2     4 

615-75 

4-276 

6    0 

191 

287-27 

1-995 

7    4f 

2     41 

626-80 

4-352 

5     03 

19* 

291-04 

2-021 

7    51 

2     44- 

637-94 

4-430 

5     OJ 

19| 

294-83 

2-047 

7     61 

2     4| 

649-18 

4-508 

6     It 

19i 

298-65 

2-074 

7    7 

2     5 

660-52 

4-586 

5     If 

191 

302-49 

2-101 

7    7* 

2     51 

671-96 

4-666 

5     2 

19* 

306-36 

2-128 

7    81 

2     5} 

683-49 

4-747 

5     2| 

in 

310-25 

2-155 

7     91 

2     5f 

695-13 

4-827 

APPENDIX. 


813 


TABLES   OF  THE   CIECUMFEKENCES  OF  CIRCLES,   ETC.— (Continued.) 


Circumfer- 

Diameter 

Area 

Area 

Circumfer- 

Diameter 

Area 

Area 

ence  in  feet 

in  feet  and 

in  square 

in  square 

ence  in  teet 

in  feet  and 

in  square 

in  square 

and  inches. 

inches. 

inches. 

feet. 

and  inches. 

inches. 

inches. 

feet. 

1   10J 

2     6 

706-86 

4-908 

11     6J 

3     8 

1520-5 

10-56 

7  11 

2     6J 

718-69 

4-990 

11     7 

3     8i 

1537-9 

10-68 

7  11J 

2     64 

730-62 

5-073 

11     7f 

3     8i 

1555-3 

10-80 

8     0| 

2     6f 

742-64 

5-157 

11     8J 

3     8| 

1572-8 

10-92 

8     1| 

2     7 

754-77 

5-241 

11     9| 

3     9 

1590-4 

11-04 

8     2k 

2     7i 

766-99 

5-326 

11   lOfr 

3     9i 

1608-1 

11-17 

8     23- 

2     7£ 

779-31 

5-411 

11   lOJt 

3     9£ 

1626-0 

11-29 

8     3f 

2     7f 

791-73 

5-498 

11  llf 

3     9f 

1643-9 

11-41 

8     4£ 

2     8 

804-25 

5-585 

12     OJ 

3  10 

1661-9 

11-54 

8     5| 

2     Si 

816-86 

5-673 

12     1£ 

3  10J 

1680-0 

11-67 

8     6| 

2     8J 

829-58 

5-761 

12     2 

3  10i 

1698-2 

11-79 

8     6£ 

2     8| 

842-39 

5-849 

12     21 

3   10* 

1716-5 

11-92 

8     7& 

2     9 

855-30 

5-939 

12     3f 

3  11 

1734-9 

12-05 

8     8i 

2     9| 

868-31 

6-029 

12     4| 

3  lit 

1753-4 

12-18 

8     9i 

2     9| 

881-41 

6-120 

12     5i 

3  1H 

1772-0 

12-30 

8  10 

2     9f 

894-62 

6-212 

12     6 

3  llf 

1790-8 

12-43 

8  lOJ 

2  10 

907-92 

6-305 

12     6f 

4     0 

1809-6 

12-57 

8  11£ 

2  10J 

921-32 

6-398 

12     U 

4     OJ 

1828-6 

12-70 

9     Of 

2  10A 

934-82 

6-491 

12     8| 

4     0^ 

1847-4 

12-83 

9     IJ 

2  lOf 

948-42 

6-586 

12     0J- 

4     Of 

1866-5 

12-96 

9     11 

2  11 

962-11 

6-681 

12     91 

4     1 

1885-7 

13-09 

9     2| 

2  11J 

975-91 

6-777 

12  lOf 

4     li 

1905-0 

13-23 

9     3^ 

2  11J 

989-80 

6-874 

12   11J 

4     1* 

1924-4 

13-36 

9     4± 

2   llf 

1003-8 

6-970 

13     0| 

4     14 

1943-9 

13-50 

9     5 

3     0 

1017-9 

7-069 

13     1 

4     2 

1963-5 

13-63 

9     5J 

3     Oi 

1032-1 

7-167 

13     11 

4     2i 

1983-2 

13-77 

9     6| 

3     OJ 

1046-3 

7-266 

13     2| 

4     2* 

2003-0 

13-91 

9     74 

3     Of 

1060-7 

7-366 

13     3f 

4     2f 

2022-8 

14-05 

9     Si 

3     1 

1075-2 

7-466 

13    4| 

4     3 

2042-8 

14-19 

9     9 

3     1J 

1089-8 

7-567 

13     5 

4     8i 

2062-9 

14-32 

9     »J 

3     H 

1104-5 

7-669 

13     5f 

4     3^ 

2083-1 

14-46 

9   10$ 

3     If 

1119-2 

7-772 

13     6i 

4     3f 

210S-3 

14-61 

9  11| 

3     2 

1134-1 

7-876 

13     7f 

4     4 

2123-7 

14-75 

10     Oj- 

3     2* 

1149-1 

7-979 

13     8J- 

4     4J 

2144-2 

14-89 

10     OJ 

3     2£ 

1164-2 

8-085 

18     8| 

4     4^ 

2164-7 

15-03 

10     If 

3     2| 

1179-3 

8-189 

13     9f 

4     4f 

2185-4 

15-18 

10     2* 

3     3 

1194-6 

8-295 

13  10| 

4     5 

2206-2 

15-32 

10     3i 

3     3i 

1:409-9 

8-403 

13   11J 

4     5J 

2227-0 

15-46 

10     4 

3     3k 

1225-4 

8-509 

14     0 

4     5| 

2248-0 

15-61 

10     4£ 

3     3f 

1241-0 

8-617 

14     0£ 

4     5| 

2269-1 

15-76 

10     5| 

3     4 

1256-6 

8-727 

14     1| 

4     6 

2290-2 

15-90 

10     6| 

3     4J 

1272-4 

8-836 

14     2| 

4     6J 

2311-5 

16-05 

10     7i 

3     44 

1288-2 

8-946 

14     3i 

4     6i 

2332-8 

16-20 

10     8 

3     4f 

1304-2 

9056 

14     4 

4     6f 

2354-3 

16-35 

10     8| 

3     5 

1320-2 

9-169 

14     4f 

4     7 

2375-8 

16-50 

10     9* 

3     5\ 

1336-4 

9-211 

14     5J- 

4     7} 

2397-5 

16-65 

10  lOf 

3     5£ 

1352-6 

9-394 

14     6| 

4     74 

2419-2 

16-80 

10  11J 

3     5f 

1369-0 

9-506 

14     7£ 

4     7f 

2441-1 

16-95 

10  111 

3     6 

1385-4 

9-62 

14     7^ 

4     8 

2463-0 

17-10 

11     Of 

3     6i 

1402-0 

9-73  . 

14     8| 

4     8* 

2485-0 

17-26 

11     1J 

3     6J 

1418-6 

9-84 

14     9i 

4     8^ 

2507-2 

17-41 

11     2i 

3     6f 

1435-4 

9-96 

14   lOi 

4     8f 

2529-4 

17-56 

11     3 

3     7 

1452-2 

10-08 

14  11 

4     9 

2551-8 

17-72 

11     8J 

3     7i 

1469-1 

10-20 

14  lls7 

4      9J: 

2574-2 

17-88 

11     4| 

3    7£ 

1486-2 

10-32 

15     Of 

4     9J 

2596-7 

18-03 

11     5fc 

3     7f 

1503-3 

10-44 

15     If 

4     9f 

2619-3 

18-19 

814:  APPENDIX. 

TABLES  OF  THE  CIKCUMFEKENCES  OF  CIRCLES,  ETC.— (Continued.) 


Circumfer- 

Diameter 

Area 

Area 

Circumfer- 

Diameter 

Area 

Area 

ence  in  feet 

in  feet  and 

in  square 

in  square 

ence  in  feet 

in  teet  and 

in  square 

in  square 

and  inches. 

inches. 

inches. 

feet. 

and  inches. 

inches. 

inches. 

feet. 

15  2£ 

4  10 

2642-1 

18-35 

18  10i 

6  0 

4071-5 

28-27 

15  3 

4  10J 

2664-9 

18-51 

18  10£ 

6  OJ 

4099-8 

28-47 

15  3f 

4  10$ 

2687-8 

18-66 

18  llf 

6  Oi 

4128-2 

28-67 

15  4i 

4  lOf 

2710-8 

18-82 

19  0£ 

6  Of 

4156-8 

28-87 

15  r>t 

4  11 

2734-0 

18-98 

19  l| 

6  1 

4185-4 

29-07 

15  6i 

4  Hi 

2757-2 

19-15 

19  2i 

6  1J 

4214-1 

29-27 

15  6£ 

4  iii 

2780-5 

19-31 

19  2} 

6  H 

4242-9 

29-47 

15  7f 

4  llf 

2803-9 

19-47 

19  3£ 

6  l| 

4271-8 

29-67 

15  8i 

5  0 

2827-4 

19-63 

19  4$ 

6  2 

4300-8 

29-87 

15  9J 

5  Oi 

2861-0 

19-80 

19  5J 

6  2i 

4329-9 

30-07 

15  10 

5  0^ 

2874-8 

19-96 

19  6 

6  2i 

4359-2 

30-27 

15  lOf 

5  Of 

2898-6 

20-13 

19  6f 

6  2£ 

4388-5 

30-47 

15  llf. 

5  1 

2922-5 

20-29 

19  7i 

6  3 

4417-9 

30-68 

16  Of 

5  11 

2946-5 

2046 

19  8| 

6  3\ 

4447-4 

30-88 

16  U 

5  if 

2970-6 

20-63 

19  9i 

6  3| 

4477-0 

31-09 

16  2 

5  If 

2994-8 

20-80 

19  9| 

6  3f 

4506-7 

31-30 

16  2f 

5  2 

3019-1 

20-96 

19  lOf 

6  4 

4536-5 

31-50 

16  3* 

6  2* 

3043-5 

21-13 

19  Hi 

6  4J 

4566-4 

31-71 

16  4J 

5  2i 

3068-0 

21-30 

20  01 

6  4^ 

45963 

31-92 

16  &l 

5  2| 

3092-6 

21-48 

20  l| 

6  4f 

4626-4 

32-13 

16  5£ 

5  3 

3117-2 

21-65 

20  11 

6  5 

4656-6 

32-34 

16  6£ 

5  3* 

3142-0 

21-82 

20  2| 

6  5J 

4686-9 

32-55 

16  7£ 

5  3J 

3166-9 

21-99 

20  3J 

6  5J 

4717-3 

82-76' 

16  8i 

5  3f 

3191-9 

22-17 

20  4J 

6  5f 

4747-8 

32-97 

16  9 

5  4 

3217-0 

22-34 

20  5 

6  6 

4778-3 

33-18 

16  9f 

5  4J 

3242-2 

22-51 

20  5| 

6  6£ 

4809-0 

33-40 

16  10| 

5  4\ 

3267-5 

22-69 

20  6£ 

6  6£ 

4839-8 

33-61 

16  llf 

5  4f 

3292-8 

22-87 

^!0  7f 

6  6| 

4S70-7 

33-82 

17  Oi 

5  5 

3318-3 

23-04 

20  8| 

6  7 

4901-6 

34-04 

17  1 

5  5J. 

3343-9 

23-22 

20  8| 

6  7J 

4932-7 

34-25 

17  If 

5  5| 

3369-6 

23-40 

20  9| 

6  7^ 

4963-9 

34-47 

17  2£ 

5  5f 

3395-3 

23-58 

20  10| 

6  7t 

4995-1 

34-69 

17  3| 

5  6 

3421-2 

23-76 

20  11  J 

6  8 

5026-5 

34-91 

17  4J 

5  64 

3447-2 

23-94 

21  OJ 

6  8J 

5058-0 

35-12 

17  4| 

5  6£ 

3473-2 

24-12 

21  0| 

6  81 

5089-5 

35-34 

17  6$ 

5  6f 

3499-4 

24-30 

21  if 

6  8| 

5121-2 

35-56 

17  6i 

5  7 

3525-1 

24-48 

21  2| 

6  9 

5153-0 

35-78 

17  7i 

5  7£ 

8552-0 

24-67 

21  3J 

6  9J 

5184-8 

36-01 

17  8 

5  7i 

3578-5 

24-85 

21  4 

6  9| 

5216-8 

36-23 

17  8f 

5  7f 

3605-0 

25-03 

21  4| 

6  9| 

5248-8 

36-45 

17  9| 

5  8 

3631-7 

25-22 

21  6| 

6  10 

5281-0 

36-67 

17  10| 

5  8J 

3658-4 

25-40 

21  6| 

6  10  J 

5313-2 

86-89 

17  Hi 

5  8i 

3685-3 

25-59 

21  7i 

6  10i 

5345-6 

37-12 

17  11* 

5  8| 

3712-2 

25-78 

21  7* 

6  10| 

5378-0 

37-35 

18  Of 

5  9 

3739-3 

25-96 

21  8| 

6  H 

5410-6 

37-57 

18  H 

5  9i 

3766-4 

26-15 

21  9* 

6  11J 

5443-2 

37-80 

18  2i 

5  9i 

3793-7 

26-34 

21  10| 

6  III 

5476-0 

38-03 

18  3i 

5  9f 

3821-0 

26-53 

21  ll| 

6  llf 

5508-8 

38-26 

18  8J 

5  10 

3848-5 

26-72 

21  11| 

7  0 

5541-7 

38-48 

18  4| 

5  10J 

3876-0 

26-92 

22  0$ 

7  0^ 

5574-8 

38-71 

18  5i 

5  10| 

3903-6 

27-11 

22  If 

7  O.V 

5607-9 

38-94 

18  6i 

5  lOf 

3931-4 

27-30 

22  2i 

7  9| 

5641-1 

39-17 

18  7 

5  11 

3959-2 

27-49 

22  3 

7  1 

5674-5 

39-41 

18  7f 

5  1H 

3987-1 

27-69 

22  3t 

7  H 

5707-9 

39-64 

18  8| 

5  Hi 

4015-2 

27-88 

22  4^ 

l  H 

5741-4 

39-87 

18  9| 

5  llf 

4043-3 

28-08 

22  5| 

7  If 

5775-0 

40-10 

APPENDIX.  815 

TABLES  OF  THE  CIECUMFERENCES  OF  CIKCLES,   ETC.— (Continued.) 


Circumfer- 

Diameter 

Area 

Area 

Circumfer- 

Diameter 

Area 

Area 

ence  in  feet 
and  inches. 

in  feet  and 
inches. 

in  square 
inches. 

in  square 
feet. 

ence  in  feet 
and  inches. 

in  feet  and 
inches. 

in  square 
inches. 

in  square 
ieet. 

22  6J 

7  2 

5808-8 

40-34 

26  2£ 

8  4 

7853-9 

54-54 

22  6£ 

7  2} 

5842-6 

40-57 

26  5^ 

8  5 

8011-9 

55-64 

22  7* 

7  2J 

5876-5 

40-80 

26  8| 

8  6 

8171-3 

56-75 

22  8fr 

7  2| 

5910-5 

41-04 

26  11£ 

8  7 

8332-3 

57-86 

22  9± 

7  3 

5944-6 

41-28 

27  2| 

8  8 

8494-9 

58-99 

22  10* 

7  3* 

5978-9 

41-52 

27  5* 

8  9 

8659-0 

60-13 

22  10| 

7  3J 

6013-2 

41-76 

27  9 

8  10 

8824-7 

61-28 

22  11| 

7  3| 

6047-6 

42-00 

28  0£ 

8  11 

8892-0 

62-44 

23  Of 

7  4 

6082-1 

42-24 

28  3J 

9 

9160-9 

63-62 

23  li 

7  4£ 

6116-7 

42-48 

28  6| 

9  1 

9331-3 

64-80 

23  2 

7  4i 

6151-4 

42-72 

28  9^ 

9  2 

9503-3 

66-00 

23  2i 

7  4| 

6186-2 

42-96 

29  0| 

9  3 

9676-9 

67-20 

23  3f 

7  5 

6221-1 

43-20 

29  3f 

9  4 

9852-1 

68-42 

23  4£ 

7  5i 

6256-1 

43-44 

29  7 

9  5 

10028-8 

69-64 

23  5J 

7  5£ 

6291-2 

43-68 

29  10£ 

9  6 

10207-1 

70-88 

23  6 

7  51 

6326-4 

43-93 

30  1± 

9  7 

10386-9 

72-13 

23  6| 

7  6 

6361-7 

44-18 

30  4f 

9  8 

10568-3 

73-39 

23  1\ 

7  6J- 

6397-1 

44-43 

30  7| 

9  9 

10751-3 

74-66 

23  8± 

7  6£ 

6432-6 

44-67 

30  10f 

9  10 

10935-9 

75-94 

23  9£ 

7  6| 

6468-2 

44-92 

31  If 

9  11 

11122-0 

77-24 

23  9J 

7  7 

6503-8 

45-17 

23  10J 

7  7i 

6539-6 

45-41 

31  5 

10 

11309-8 

78-54 

23  llf 

•7  V* 

6575-5 

45-66 

31  8J 

10  1 

11499-0 

79-85 

24  0^ 

7  7f 

66115 

45-91 

31  ll| 

10  2 

11689-9 

81-18 

32  2| 

10  3 

11882-3 

82-52 

24  1 

7  8 

6647-6 

46-16 

32  5| 

10  4 

12076-3 

83-86 

24  H 

7  8J- 

6683-8 

46-42 

32  8% 

10  5 

12271-9 

85-22 

24  2J 

7  8i 

6720-0 

46-67 

32  llf 

10  6 

12469-0 

86-59 

24  3J 

7  8J 

6756-4 

46-92 

33  2£ 

10  7 

12667-7 

87-97 

24  4i 

7  9 

6792-9 

47-17 

33  6i 

10  8 

12868-0 

89-36 

24  4£ 

7  9i 

6829-4 

47-43 

33  9| 

10  9 

13069-8 

90-76 

24  61 

7  9£ 

6866-1 

47-68 

34  Of 

10  10 

13273-3 

92-17 

24  6£ 

7  9* 

6902-9 

47-94 

34  3| 

10  11 

13478-2 

93-60 

24  7£ 

7  10 

6939-7 

48-19 

34  6f 

11 

13684-8 

95-03 

24  8 

7  10J 

6976-7 

48-45 

34  9f 

11  1 

13892-9 

96-48 

24  8£ 

7  10£ 

7013-8 

48-71 

35  0| 

11  2 

14142-6 

97-93 

24  9$ 

7  10| 

7050-9 

48-96 

35  4^ 

11  3 

14313-9 

99-40 

24  10| 

7  11 

7088-2 

49-22 

35  7} 

11  4 

14526-8 

100-88 

24  11| 

7  11} 

7125-5 

49-48 

35  lOf 

11  5 

14741-2 

102-37 

25  0 

7  ll| 

7163-0 

49-74 

36  H 

11  6 

14S57-2 

103-87 

25  01 

7  llf 

7200-5 

50-00 

36  4£ 

11  7 

15174-7 

105-38 

36  7f 

11  8 

15393-8 

106-90 

25  1£ 

8  0 

7238-2 

50-26 

36  10| 

11  9 

15614-5 

108-43 

25  2| 

8  OL 

7275-9 

50-53 

37  2 

11  10 

15836-8 

109-98 

25  3£ 

8  0* 

7313-8 

50-79 

37  5J 

11  11 

16060-6 

111-53 

25  3£ 

8  Of 

7351-7 

51-05 

25  4| 

8  1 

7389-8 

51-32 

37  8| 

12 

16286-0 

113-10 

25  5J 

8  1} 

7427-9 

51-58 

37  Hi 

12  1 

16513-0 

114-67 

25  6i 

8  1£ 

7466-2 

51-85 

38  2f 

12  2 

16741-6 

116-26 

25  7 

8  H 

7504-5 

52-11 

38  5f 

12  3 

16971-7 

117-86 

38  8| 

12  4 

17203-4 

119-47 

25  7£ 

8  2 

7542-9 

52-38 

39  0 

12  5 

17436-7 

121-09 

25  8$ 

8  21- 

7o81'5 

52-65 

39  3J- 

12  6 

17671-5 

122-72 

25  9-$ 

8  2| 

7620-1 

52-92 

39  6| 

12  7 

17907-9 

124-36 

25  10£ 

8  2| 

7658-8 

53-19 

39  9* 

12  8 

18145-9 

126-01 

25  11 

8  3 

7697-7 

53-46 

40  Of 

12  9 

18385-4 

127-68 

25  11| 

8  3| 

7736-6 

53-73 

40  3f 

12  10 

18626-6 

129-35 

26  0£ 

8  3| 

7775-6 

54-00 

40  6| 

12  11 

18869-2 

131-04 

26  H 

8  3f 

7814-7 

54-27 

816 


APPENDIX. 


TABLE  OF  DIAMETERS,   CIRCUMFERENCES,  AND  AREAS  OF  CIRCLES. 


Diam- 
eter. 

Circum- 
ference. 

Circular 
area. 

Diam- 
eter. 

Circum- 
ference. 

Circular 
area. 

Diam- 
eter. 

Circum- 
ference. 

Circular 
area. 

1 

3-1416 

0-7854 

51 

160-22 

2042-82 

101 

317-30 

8011-85 

2 

6-28 

3-14 

52 

163-36 

2123-72 

102 

320-41 

.8171-28 

3 

9-42 

7-07 

53 

166-50 

2206-18 

103 

323-58 

8332-29 

4 

12-57 

12-57 

54 

169-65 

2290-22 

104 

326-73 

8494-87 

5 

15-71 

19-63 

55 

172-79 

2375-83 

105 

329-87 

8659-01 

6 

18-85 

28-27 

56 

175-93 

2463-01 

106 

333-01 

8824-73 

7 

21-99 

38-48 

57 

179-07 

2551-76 

107 

336-15 

8992-02 

8 

25-13 

50-27 

58 

182-21 

2642-08 

108 

339-29 

9160-88 

9 

28-27 

63-62 

59 

185-35 

2733-97 

109 

342-43 

9331-32 

10 

31-42 

78-54 

60 

188-50 

2827-43 

110 

345-57 

9503-32 

11 

34-56 

95-03 

61 

191-64 

2922-47 

111 

348-72 

9676-89 

12 

37-70 

113-10 

62 

194-78 

3019-07 

112 

351-86 

9852-03 

13 

40-84 

132-73 

63 

197-92 

3117-25 

113 

355-00 

10028-75 

14 

43-98 

153-94 

64 

201-06 

3216-99 

114 

358-14 

10207-03 

15 

47-12 

176-71 

65 

204-20 

3318-31 

115 

361-28 

10386-89 

16 

50-26 

201-06 

66 

207-34 

3421-19 

116 

364-42 

10568-32 

17 

53-41 

226-98 

67 

210-49 

3525-65 

117 

367-57 

10751-32 

18 

56-55 

254-47 

68 

213-63 

3631-68 

118 

370-71 

10935-88 

19 

59-69 

283-53 

69 

216-77 

3739-28 

119 

373-85 

11122-02 

20 

62-83 

314-16 

70 

219-91 

3848-45 

120 

376-99 

11309-73 

21 

65-97 

346-36 

71 

223-05 

3959-19 

121 

380-13 

11499-01 

22 

69-11 

380-13 

72 

226-19 

4071-50 

122 

383-27 

11689-87 

23 

72-26 

415-48 

73 

229-34 

4185-39 

123 

386-42 

11882-29 

24 

75-40 

452-39 

74 

232-48 

4300-84 

124 

389-56 

12076-28 

25 

78-54 

490-87 

75 

235-62 

4417-86 

125 

392-70 

12271-85 

26 

81-68 

530-93 

76 

238-76 

4536-46 

126 

395-84 

12468-98 

27 

84-82 

572-56 

77 

241-90 

4656-63 

127 

398-98 

12667-69 

28 

87-96 

615-75 

78 

245-04 

4778-36 

128 

402-12 

12867-96 

29 

91-11 

660-52 

79 

248-19 

4901-67 

129 

405-26 

13069-81 

30 

94-25 

706-86 

80 

251-33 

5026-55 

130 

408-41 

13273-23 

31 

97-39 

754-77 

81 

254-47 

5153-00 

131 

411-55 

13478-22 

32 

100-53 

804-25 

82 

257-61 

5281-02 

132 

414-69 

13684-78 

33 

103-67 

855-30 

83 

260-75 

5410-61 

133 

417-83 

13892-91 

34 

106  -Bl 

907-92 

84 

263-89 

5541-77 

134 

420-97 

14102-61 

35 

109-96 

962-11 

85 

267-03 

5674-50 

135 

424-11 

14313-88 

36 

113-10 

1017-88 

86 

270-18 

5808-80 

136 

427-26 

14526-72 

37 

116-24 

1075-21 

87 

273-32 

5944-68 

137 

430-40 

14741-14 

38 

119-38 

1134-11 

88 

276-46 

6082-12 

,   138 

433-54 

14957-12 

39 

122-52 

1194-59 

89 

279-60 

6221-14 

139 

436-68 

15174-68 

40 

125-66 

1256-64 

90 

282-74 

6361-73 

140 

439-82 

15393-80 

41 

128-80 

1320-25 

91 

285-88 

6503-88 

141 

442-96 

15614-50 

42 

131-95 

1385-44 

92 

289-03 

6647-61 

142 

446-11 

15836-77 

43 

135-09 

1452-20 

93 

292-17 

6792-91 

143 

449-25 

16060-61 

44 

138-23 

1520-53 

94 

295-31 

6939-78 

144 

452-39 

16286-02 

45 

141-37 

1590-43 

95 

298-45 

7088-22 

145 

455-53 

16513-00 

46 

144-51 

1661-90 

96 

301-59 

7238-23 

146 

458-67 

16741-55 

47 

147-65 

1734-94 

97 

304-73 

7389-81 

147 

461-81 

16971-67 

48 

150-80 

1809-56 

98 

307-88 

7542-96 

148 

464-96 

17203-36 

49 

153-94 

1885-74 

99 

311-02 

7697-69 

149 

468-10 

17436-62 

50 

157-08 

19B3-50 

100 

314-16 

7853-98 

150 

471-24 

17671-46 

APPENDIX.  817 

TABLE  OF  DIAMETERS,  CIRCUMFERENCES,  AND  AREAS  OF  CIRCLES. 


Diam- 
eter. 

Circum- 
ference. 

Circular 
area. 

Diam- 
eter. 

Circum- 
ference. 

Circular 
area. 

Diam- 
eter. 

Circum- 
ference. 

Circular 
area. 

151 

474-38 

17907-86 

201 

631-46 

31730-87 

251 

788-54 

49480-87 

152 

477-52 

18145-84 

202 

634-60 

32047-39 

252 

791-68 

49875-92 

153 

480-66 

18385-39 

203 

637-74 

32365-47 

253 

794-82 

50272-55 

154 

483-80 

18626-50 

204 

640-88 

32685-13 

254 

797-96 

50670-75 

155 

486-95 

18869-19 

205 

644-03 

33006-36 

255 

801-11 

51070-52 

156 

490-09 

19113-45 

206 

647-17 

33329-16 

256 

804-25 

51471-86 

157 

493-23 

19359-28 

207 

650-31 

33653-53 

257 

807-39 

51874-76 

158 

496-37 

19606-68 

208 

653-45 

33979-47 

258 

810-53 

52279-24 

159 

499-51 

19855-65 

209 

656-59 

34306-98 

259 

813-67 

52685-29 

160 

502-65 

20106-19 

210 

659-73 

34636-06 

260 

816-81 

53092-96 

161 

505-80 

20358-34 

211 

662-88 

34966-71 

261 

819-96 

53502-11 

162 

508-94 

20611-99 

212 

666-02 

35298-94 

262 

823-10 

53912-87 

163 

512-08 

20867-24 

213 

669-16 

35632-73 

263 

826-24 

54325-21 

164 

515-22 

21124-07 

214 

672-30 

35968-09 

264 

829-38 

54739-11 

165 

518-36 

21382-46 

215 

675-44 

36305-03 

265 

832-52 

55154-59 

166 

521-50 

21642-43 

216 

678-58 

36643-61 

266 

835-66 

55571-63 

167 

524-65 

21903-97 

217 

681-73 

36983-61 

267 

838-80 

55990-25 

168 

527-79 

22167-08 

218 

684-87 

37325-26 

268 

841-95 

56410-44 

169 

530-93 

22431-76 

219 

688-01 

37668-48 

269 

845-09 

56832-20 

170 

534-07 

22698-01 

220 

691-15 

38013-27 

270 

848-23 

57255-53 

171 

537-21 

22965-83 

221 

694-29 

38359-63 

271 

851-37 

57680-43 

172 

540-35 

23235-22 

222 

697-43 

38707-56 

272 

854-51 

58106-90 

173 

543-50 

23506-18 

223 

700-57 

39057-07 

273 

857-65 

58534-94 

174 

546-64 

23778-71 

224 

703-72 

39408-14 

274 

860-80 

58964-55 

175 

549-78 

24052-82 

225 

706-86 

39760-78 

275 

863-94 

59395-74 

176 

552-92 

24328-49 

226 

710-00 

40115-00 

276 

867-08 

59828-49 

177 

556-06 

24605-79 

227 

713-14 

40470-78 

277 

870-22 

60262-82 

178 

559-20 

24884-56 

228 

716-28 

40828-14 

278 

873-36 

60698-72 

179 

562-34 

25164-94 

229 

719-42 

41187-07 

279 

876-50 

61136-18 

180 

565-49 

25446-90 

230 

722-57 

41547-56 

280 

879-65 

61575-22 

181 

568-63 

25730-43 

231 

725-71 

41909-63 

281 

882-79 

62015-82 

182 

571-77 

26015-53 

232 

728-85 

42273-27 

282 

885-93 

62458-00 

183 

574-91 

26302-20 

233 

731-99 

42638-48 

283 

889-07 

62901-75 

184 

578-05 

26590-44 

234 

735-13 

43005-26 

284 

892-21 

63347-07 

185 

581-19 

26880-25 

235 

738-27 

43373-61 

285 

895-35 

63793-97 

186 

584-34 

27171-63 

236 

741-42 

43743-54 

286 

898-49 

64242-43 

187 

587-48 

27464-59 

237 

744-56 

44115-03 

287 

901-64 

64692-46 

188 

590-62 

27759-11 

238 

747-70 

44488-09 

288 

904-78 

65144-07 

189 

593-76 

28055-21 

239 

750-84 

44862-73 

289 

907-92 

65597-24 

190 

596-90 

28352-87 

240 

753-98 

45238-93 

290 

911-06 

66051-99 

191 

600-04 

28652-11 

241 

757-12 

45616-71 

291 

914-20 

66508-30 

192 

603-19 

28952-92 

242 

760-26 

45996-06 

292 

917-34 

66966-19 

193 

606-33 

29255-30 

243 

763-41 

46376-98 

293 

920-49 

67425-65 

194 

609-47 

29559-26 

244 

766-55 

46759-47 

294 

923-63 

67886-68 

195 

612-61 

29864-77 

245 

769-69 

47143-52 

295 

926-77 

68349-28 

196 

615-75 

30171-86 

246" 

772-83 

47529-16 

296 

929-91 

68813-45 

197 

618-89 

30480-52 

247 

775-97 

47916-36 

297 

933-05 

69279-19 

198 

622-03 

30790-75 

248 

779-11 

48305-13 

298 

936-19 

69746-50 

199 

625-18 

31102-55 

249 

782-26 

48695-47 

299 

939-34 

70215-38 

200 

628-32 

31415-93 

250 

785-40 

49087-39 

300 

942-48 

70685-83 

53 


818  APPENDIX. 

TABLE  OF  DIAMETERS,  CIRCUMFERENCES,  AND  AREAS  OF  CIRCLES. 


Diam- 
eter. 

Circum- 
ference. 

Circular 
area. 

Diam- 
eter. 

Circum- 
ference. 

Circular 
area. 

Diam- 
eter. 

Circum- 
ference. 

Circular 
area. 

301 

945-62 

71157-86 

351 

1102-70 

96761-84 

401 

1259-78 

126292-81 

302 

948-76 

71631-45 

352 

1105-84 

97314-76 

402 

1262-92 

126923-48 

303 

951-90 

72106-62 

353 

1108-98 

97867-68 

403 

1266-06 

127553-73 

304 

955-04 

72583-36 

354 

1112-12 

98422-96 

404 

1269-20 

128189-55 

305 

958-19 

73061-66 

355 

1115-26 

98979-80 

405 

1272-34 

128824-93 

306 

961-33 

73541-54 

356 

1118-41 

99538-22 

406 

1275-49 

129461-89 

307 

964-47 

74022-99 

357 

1121-55 

100098-21 

407 

1278-63 

130100-42 

308 

967-61 

74506-01 

358 

1124-69 

100659-27 

408 

1281-77 

130740-52 

309 

970-75 

74990-60 

359 

1127-83 

101222-90 

409 

1284-91 

131382-19 

310 

973-89 

75476-76 

360 

1130-97 

101787-60 

410 

1288-05 

132025-43 

311 

977-03 

75964-50 

361 

1134-11 

102353-87 

411 

1291-19 

132670-24 

312 

980-18 

76453-80 

362 

1137-26 

102921-72 

412 

1294-34 

133316-63 

313 

983-32 

76944-67 

363 

1140-40 

103491  •  13 

413 

1297-48 

133964-58 

314 

986-46 

77437-12 

364 

1143-54 

104062-12 

414 

1300-62 

134614-10 

315 

989-60 

77931-13 

365 

1146-68 

104634-67 

415 

1303-76 

135265-20 

316 

992-74 

78426-72 

366 

1149-82 

105208-80 

416 

1306-90 

135917-86 

317 

995-88 

78923-88 

367 

1152-96 

105784-49 

417 

1310-04 

136572-10 

318 

999-03 

79422-60 

368 

1156-11 

106361-76 

418 

1313-19 

137227-91 

319 

1002-17 

79922-90 

369 

1159-25 

106940-60 

419 

1316-33 

137885-29 

320 

1005-31 

80424-77 

370 

1162-39 

107521-01 

420 

1319-47 

138544-24 

321 

1008-45 

80928-21 

371 

1165-53 

108102-99 

421 

1322-61 

139204-70 

322 

1011-59 

81433-22 

372 

1168-67 

108686-54 

422 

1325-75 

139866-85 

323 

1014-73 

81939-80 

373 

1171-81 

109271-66 

423 

1328-89 

140530-51 

324 

1017-88 

82447-96 

374 

1174-96 

109858-35 

424 

1332-03 

141195-74 

325 

1021-02 

82957-68 

375 

1178-10 

110446-62 

425 

1335-18 

141862-54 

326 

1024-16 

83468-98 

376 

1181-24 

111036-45 

426 

1338-32 

142530-92 

327 

1027-30 

83981-84 

377 

1184-38 

111627-86 

427 

1341-46 

143200-86 

328 

1030-44 

84496-28 

378 

1187-52 

112220-83 

428 

1344-60 

143872-38 

329 

1033-58 

85012-28 

379 

1190-66 

112815-38 

429 

1347-74 

144545-46 

330 

1036-73 

85529-86 

380 

1193-80 

113411-49 

430 

1350-88 

145220-12 

331 

1039-87 

86049-01 

381 

1196-95 

114009-18 

431 

1354-03 

145896-35 

332 

1043-01 

86569-73 

382 

1200-09 

114608-44 

432 

1357-17 

146574-15 

333 

1046-15 

87092-02 

383 

1203-23 

115209-27 

433 

1360-31 

147253-52 

334 

1049-29 

87615-88 

384 

1206-37 

115811-67 

434 

1363-45 

147934-46 

335 

1052-43 

88141-31 

385 

1209-51 

116415-64 

435 

1366-59 

148616-97 

336 

1055-57 

88668-31 

386 

1212-65 

117021-18 

436 

1369-73 

149301-05 

337 

1058-72 

89196-88 

387 

1215-80 

117628-30 

437 

1372-88 

149986-70 

338 

1061-86 

89727-03 

388 

1218-94 

118236-98 

438 

1376-02 

150673-93 

339 

1065-00 

90258-74 

389 

1222-08 

118847-24 

439 

1379-16 

151362-72 

340 

1068-14 

90792-03 

390 

1225-22 

119459-06 

440 

1382-30 

152053-08 

341 

1071-28 

91326-88 

391 

1228-36 

120072-46 

441 

1385-44 

152745-02 

342 

1074-42 

91863-31 

392 

1231-50 

120687-42 

442 

1388-58 

153438-53 

343 

1077-57 

92401-31 

393 

1234-65 

121303-96 

443 

1391-73 

154133-60 

344 

1080-71 

92940-88 

394 

1237-79 

121922-07 

444 

1394-87 

154830-25 

345 

1083-85 

93482-02 

395 

1240-93 

122541-75 

445 

1398-01 

155528-47 

346 

1086-99 

94024-73 

396 

1244-07 

123163-00 

446 

1401-15 

156228-26 

347 

1090-13 

94569-01 

397 

1247-21 

123785-82 

447 

1404-29 

156929-62 

348 

1093-27 

95114-86 

398 

1250-35 

124410-21 

448 

1407-43 

157632-55 

349 

1096-42 

95662-28 

399 

1253-49 

125036-17 

449 

1410  57 

158337-06 

350 

1099-56 

96211-28 

400 

1256-64 

125663-71 

450 

1413-72 

159043-13 

APPENDIX. 


TABLE  OP  DIAMETERS,   CIRCUMFERENCES,  AND  AREAS  OF  CIRCLES. 


Diam- 
eter. 

Circum- 
ference. 

Circular 
area. 

Diam- 
eter. 

Circum- 
ference. 

Circular 
area. 

Diam- 
eter. 

Circum- 
ference. 

Circular 
area. 

451 

1416-86 

159750-77 

501 

1573-94 

197135-72 

551 

1731-02 

238447-67 

452 

1420-00 

160459-99 

502 

1577-08 

197923-48 

552 

1734-16 

239313-96 

453 

1423-14 

161170-77 

503 

1580-22 

198712-80 

553 

1737-30 

240181-83 

454 

1426-28 

161883  13 

504 

1583-36 

199503-70 

554 

1740-44 

241051-26 

455 

1429-42 

162597-06 

505 

1586-50 

200296-17 

555 

1743-58 

241922-27 

456 

1432-57 

163312-55 

506 

1589-65 

201090-20 

556 

1746-73 

242794-85 

457 

1435-71 

164029-62 

507 

1592-79 

201885-81 

557 

1749-87 

243668-99 

458 

1438-85 

164748-26 

508 

1595-93 

202682-99 

558 

1753-00 

244544-61 

459 

1441-99 

165468-47 

509 

1599-07 

203481-74 

559 

1756-15 

245422-00 

460 

1445-13 

166190-25 

510 

1602-21 

204282-06 

560 

1759-29 

246800-86 

461 

1448-27 

166913-60 

511 

1605-35 

205083-95 

561 

1762-43 

247181-30 

462 

1451-42 

167638-53 

512 

1608-49 

205887-42 

562 

1765-57 

248062-30 

4(33 

1454-56 

168365-02 

513 

1611-64 

206692-45 

563 

1768-72 

248946-87 

464 

1457-70 

169093-08 

514 

1614-78 

207499-05 

564 

1771-86 

249832-01 

465 

1460-84 

169822-72 

515 

1617-92 

208307-23 

565 

1775-00 

250718-73 

466 

.1463-98 

170553-92 

516 

1621-06 

209116-97 

566 

1778-14 

251607-01 

467 

1467-12 

171286-70 

517 

1624-20 

209928-29 

567 

1781-28 

252496-87 

468 

1470-26 

172021-05 

518 

1627-34 

210741-18 

568 

1784-42 

253388-30 

469 

1473-41 

172756-97 

519 

1630-49 

211555-63 

569 

1787-57 

254281-30 

470 

1476-55 

173494-45 

520 

1633-63 

212371-66 

570 

1790-71 

255175-86 

471 

1479-69 

174233-51 

521 

1636-77 

213189-26 

571 

1793-85 

256072-00 

472 

1482-83 

174974-14 

522 

•1639-91 

214008-43 

572 

1796-99 

256969-71 

473 

1485-97 

175716-35 

523 

1643-05 

214829-17 

573 

1800-13 

257868-99 

474 

1489-11 

176460-12 

524 

1646-19 

215651-49 

574 

1803-27 

258769-85 

475 

1492-26 

177205-46 

525 

1649-34 

216475-37 

575 

1806-42 

259672-27 

476 

1495-40 

177952-37 

526 

1652-48 

217300-82 

576 

1809-56 

260576-26 

477 

1498-54 

178700-86 

527 

1655-62 

218127-85 

577 

1812-70 

261481-83 

478 

1501-68 

179450-91 

528 

1658-76 

218956-44 

578 

1815-84 

262388-96 

479 

1504-82 

180202-54 

529 

1661-90 

219786-61 

579 

1818-98 

263297-67 

480 

1507-96 

180955-74 

530 

1665-04 

220618-32 

580 

1822-12 

264207-94 

481 

1511-11 

181710-50 

531 

1668-19 

221451-65 

581 

1825-26 

265119-79 

482 

1514-25 

182466-84 

532 

1671-33 

222286-53 

582 

1828-41 

266033-21 

483 

1517-39 

183224-75 

533 

1674-47 

223122-98 

583 

1831-55 

266948-20 

484 

1520-53 

183984-23 

534 

1677-61 

223961-00 

584 

1834-69 

267864-76 

485 

1523-67 

184745-28 

535 

1680-75 

224800-59 

585 

1837-83 

268782-80 

486 

1526-81 

185507-90 

536 

1683-89 

225641-75 

586 

1840-97 

269702-59 

487 

1529-96 

186272-10 

537 

1687-04 

226484-48 

587 

1844-11 

270623-86 

488 

1533-10 

187037-86 

538 

1690-18 

227328-77 

588 

1847-26 

271546-70 

489 

1536-24 

187805-19 

539 

1693-32 

228174-66 

589 

1850-40 

272471-12 

490 

1539-38 

188574-10 

540 

1696-46 

229022-10 

590 

1853-54 

273397-10 

491 

1542-52 

189344-57 

541 

1699-60 

229871-12 

591 

1856-68 

274324-66 

492 

1545-66 

190116-62 

542 

1702-74 

230721-71 

592 

1859-82 

275253-78 

493 

1548-80 

190890-24 

543 

1705-88 

231573-86 

593 

1862-96 

276184-48 

494 

1551-95 

191665-43 

544 

1709-03 

232427-59 

594 

1866-11 

277116-75 

495 

1555-09 

192442-19 

545 

1712-17 

233282-89 

595 

1869-25 

278050-59 

496 

1558-23 

193220-51 

546 

1715-31 

234139-76 

596 

1872-39 

278985-99 

497 

1561-37 

194000-42 

547 

1718-45 

234998-20 

597 

1875-53 

279922-97 

498 

1564-51 

194781-89 

548 

1721-59 

235858-21 

598 

1878-67 

280861-53 

499 

1567-65 

195564-93 

549 

1724-73 

236719-79 

599 

1881-81 

281801-65 

500 

1570-80 

196349-54 

550 

1727-88 

237582-94 

600 

1884-96 

282743-34 

820 


APPENDIX. 


TABLE  OF  SQUARES,   CUBES,   SQUAEE  AND   CUBE  ROOTS  OF    NUMBERS. 


Squares. 

Cubes. 

No. 

Square 
roots. 

Cube 
roots. 

Squares. 

Cubes. 

No. 

Square 
roots. 

Cube 
roots. 

1        1 

1 

i-ooo 

1-000 

4096 

262144 

64 

8-000 

4-000 

4 

8 

2 

1-414 

1-259 

4225 

274625 

65 

8-062 

4-020 

9 

27 

3 

1-732 

1-442 

4356 

287496 

66 

8-124 

4-041 

16 

64 

4 

2-000 

1-587 

4489 

300763 

67 

8-185 

4-061 

25 

125 

5 

2-236 

1-709 

4624 

314432 

68 

8-246 

4-081 

36 

216 

6 

2-449 

1-817 

4761 

328509 

69 

8-306 

4-101 

49 

343 

7 

2-645 

1-912 

4900 

343000 

70 

8-366 

4-121 

64 

512 

8 

2-828 

2-000 

5041 

357911 

71 

8-426 

4-140 

81 

729 

9 

3-000 

2-080 

5184 

373248 

72 

8-485 

4-160 

100 

1000 

10 

3-162 

2-154 

5329 

389017 

73 

8-544 

4-179 

121 

1331 

11 

3-316 

2-223 

5476 

405224 

74 

8-602 

4-198 

144 

1728 

12 

3-464 

2-289 

5625 

421875 

75 

8-660 

4-217 

169 

2197 

13 

3-605 

2-351 

5776 

438976 

76 

8-717 

4-235 

196 

2744 

14 

3-741 

2-410 

5929 

456533 

77 

8-774 

4-254 

225 

3375 

15 

3-872 

2-466 

6084 

474552 

78 

8-831 

4-272 

256 

4096 

16 

4-000 

2-519 

6241 

493039 

79 

8-888 

4-290 

289 

4913 

17 

4-123 

2-571 

6400 

512000 

80 

8-944 

4-308 

324 

5832 

18 

4-242 

2-620 

6561 

531441 

81 

9-000 

4-326 

361 

6859 

19 

4-358 

2-668 

6724 

551368 

82 

9-055 

4-344 

400 

8000 

20 

4-472 

2-714 

6889 

571787 

83 

9-110 

4-362 

441 

9261 

21 

4-582 

2-758 

7056 

592704 

84 

9-165 

4-379 

484 

10648 

22 

4-690 

2-802 

7225 

614125 

85 

9-219 

4-396 

529 

12167 

23 

4-795 

2-843 

7396 

636056 

86 

9-273 

4-414 

676 

13824 

24 

4-898 

2-884 

7569 

658503 

87 

9-327 

4-431 

625 

15625 

25 

5-000 

2-924 

7744 

681472 

88 

9-380 

4-447 

676 

17576 

26 

5-099 

2-962 

7921 

704969 

89 

9-433 

4-'464 

729 

19683 

27 

5-196 

3-000 

8100 

729000 

90 

9-486 

4-481 

784 

21952 

28 

5-291 

3-036 

8281 

753571 

91 

9-539 

4497 

841 

24389 

29 

5-385 

3-072 

8464 

778688 

92 

9-591 

4-514 

900 

27000 

30 

5-477 

3-107 

8649 

804357 

93 

9-643 

4'530 

961 

29791 

31 

5-567 

3-141 

8836 

830584 

94 

9-695 

4-546 

1024 

32768 

32 

5-656 

3-174 

9025 

857374- 

95 

9-746 

4-562 

1089 

35937 

33 

5-744 

3-207 

9216 

884736 

96 

9-797 

4-578 

1156 

39304 

34 

5-830 

3-239 

9409 

912673 

97 

9-848 

4-594 

1225 

42875 

35 

5-916 

3-271 

9604 

941192 

98 

9-899 

4-610 

1296 

46656 

36 

6-000 

3-301 

9801 

970299 

99 

9-949 

4-626 

1369 

50653 

37 

6-082 

3-332 

10000 

1000000 

100 

10-000 

4-641 

1444 

54872 

38 

6-164 

3-361 

10201 

1030301 

101 

10-049 

4-657 

1521 

59319 

39 

6-244 

3-391 

10404 

1061208 

102 

10-099 

4-672 

1600 

64000 

40 

6-324 

3-419 

10609 

1092727 

103 

10-148 

4-687 

1681 

68921 

41 

6-403 

3-448 

10816 

1124864 

104 

10-198 

4-702 

1764 

74088 

42 

6-480 

3-476 

11025 

1157625 

105 

10-246 

4-717 

1849 

79507 

43 

6-557 

3-503 

11236 

1191016 

106 

10-295 

4-732 

1936 

85184 

44 

6-633 

3-530 

11449 

1225043 

107 

10-344 

4-747 

2025 

91125 

45 

6-708 

3-556 

11664 

1259712 

108 

10-392 

4-762 

2116 

97336 

46 

6-782 

3-583 

11881 

1295029 

109 

10-440 

4-776 

2209 

103823 

47 

6-855 

3-608 

12100 

1331000 

110 

10-488 

4-791 

2304 

110592 

48 

6-928 

3-634 

12321 

1367631 

111 

10-535 

4-805 

2401 

117649 

49 

7-000 

3-659 

12544 

1404928 

112 

10-583 

4-820 

2500 

125000 

50 

7-071 

3-684 

12769 

1442897 

113 

10-630 

4-834 

2601 

132651 

51 

7-141 

3-708 

12996 

1481544 

114 

10-677 

4-848 

2704 

140608 

52 

7-211 

3-732 

13225 

1520875 

115 

10-723 

4-862 

2809 

148877 

53 

7-280 

3-756 

13456 

1560896 

116 

10-770 

4-876 

2916 

157464 

54 

7-348 

3-779 

13689 

1601613 

117 

10-816 

4-890 

3025 

166375 

55 

7-416 

3-802 

13924 

1643032 

118 

10-862 

4-904 

3136 

175616 

56 

7-4S3 

3-825 

14161 

1685159 

119 

10-908 

4-918 

3249 

185193 

57 

7-549 

3-848 

14400 

1728000 

120 

10-954 

4-932 

3364 

195112 

58 

7-615 

3-870 

14641 

1771561 

121 

11-000 

4-946 

3481 

205379 

59 

7-681 

3-892 

14834 

1815848 

122 

11-045 

4-959 

3600 

216000 

60 

7-745 

3-914 

15129 

1860867 

123 

11-090 

4-973 

3721 

226981 

61 

7-810 

3-930 

15376 

1906624 

124 

11-135 

4-986 

3844 

238328 

62 

7-874 

3-957 

15625 

1953125 

125 

11-180 

5-000 

3969 

250047 

63 

7-937 

3-979 

15876 

2000376 

126 

11-224 

5-013 

APPENDIX. 


821 


TABLE  OF  SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS  OF  NUMBERS— ( Continued). 


Squares. 

Cubes. 

No. 

Square 
roots. 

Cube 

roots. 

Squares. 

Cubes. 

No. 

Square 
roots. 

Cube 
roots. 

16129 

2048383 

127 

11-269 

5-026 

36100 

6859000 

190 

13-784 

5-748 

16384 

2097152 

128 

11-313 

5-039 

36481 

6967871 

191 

13-820 

5-758 

16641 

2146689 

129 

11-357 

5-052 

36864 

7077888 

192 

13-856 

5-768 

16900 

2197000 

130 

11-401 

5-065 

37249 

7189517 

193 

13-892 

5-778 

17161 

2248091 

131 

11-445 

5-078 

37636 

7301384 

194 

13-928 

5-788 

17424 

2299968 

132 

11-489 

5-091 

38025 

7414875 

195 

13-964 

6-798 

17689 

2352637 

133 

11-532 

5-104 

38416 

7529536 

196 

14-000 

5<808 

17956 

2406104 

134 

11-575 

5-117 

38809 

7645373 

197 

14-035 

5-818 

18225 

2460375 

135 

11-618 

5-129 

39204 

7762392 

198 

14-071 

6-828 

18496 

2515456 

136 

11-661 

5-142 

39601 

7880599 

199 

14-106 

5-838 

18769 

2571353 

137 

11-704 

5-155 

40000 

8000000 

200 

14-142 

5-848 

19044 

2628072 

138 

11-747 

5-167 

40401 

8120601 

201 

14-177 

5-857 

19321 

2685619 

139 

11-789 

5-180 

40804 

8242408 

202 

14-212 

5-867 

19600 

2744000 

140 

11-832 

5-192 

41209 

8365427 

203 

14-247 

5-877 

19881 

2803221 

141 

11-874 

5-204 

41616 

8489664 

204 

14-282 

5-886 

20164 

2863288 

142 

11-916 

5-217 

42025 

8615125 

205 

14-317 

5-896 

20449 

2924207 

143 

11-958 

5-229 

42436 

8741816 

206 

14-352 

5-905 

20736 

2985984 

144 

12-000 

5-241 

42849 

8869743 

207 

14-387 

5-915 

21025 

3048625 

145 

12-041 

5-253 

43264 

8998912 

208 

14-422 

5-924 

21316 

3112136 

146 

12-083 

5-265 

43681 

9129329 

209 

14-456 

5-934 

21609 

3176523 

147 

12-124 

5-277 

44100 

9261000 

210 

14-491 

5-943 

21904 

3241792 

148 

12-165 

5-289 

44521 

9393931 

211 

14-525 

6-953 

22201 

3307949 

149 

12-206 

5-301 

44944 

9528128 

212 

14-560 

5-962 

22500 

3375000 

150 

12-247 

5-313 

45369 

9663597 

213 

14-594 

5-972 

22801 

3442951 

151 

12-288 

5-325 

45796 

9800344 

214 

14-628 

5-981 

23104 

3511008 

152 

12-328 

5-336 

46225 

9938375 

215 

14-662 

5-990 

23409 

3581577 

153 

12-369 

5-348 

46656 

10077696 

216 

14-696 

6-000 

23716 

3652264 

154 

12-409 

5-360 

47089 

10218312 

217 

14-730 

6-009 

24025 

3723875 

155 

12-449 

5-371 

47524 

10360232 

218 

14-764 

6-018 

24336 

3796416 

156 

12-489 

5-383 

47961 

10503459 

219 

14-798 

6-027 

24649 

3869893 

157 

12-529 

5-394 

48400 

10648000 

220 

14-832 

6-036 

24964 

3944312 

158 

12-569 

5-406 

48841 

10793861 

221 

14-866 

6-045 

25281 

4019679 

159 

12-609 

5-417 

49284 

10941048 

222 

14-899 

6-055 

25600 

4096000 

160   12-649 

5-428 

49729 

11089567 

223 

14-933 

6-064 

25921 

4173281 

161 

12-688 

5-440 

50176 

11239424 

224 

14-966 

6-073 

26244 

4251528 

162 

12-727 

5-451 

50625 

11390625 

225 

15-000 

6-082 

26569 

4330747 

163 

12-767 

5-462 

51076 

11543176 

226 

15-033 

6-099 

26896 

4410944 

164 

12-806 

5-473 

51529 

11697083 

227 

15-066 

6-100 

27225 

4492125 

165 

12-845 

5-484 

51984 

11852352 

228 

15-099 

6-109 

27556 

4574296 

166 

12-884 

5-495 

52441 

12008989 

229 

15-132 

6-118 

27889 

4657463 

167 

12-922 

5-506 

52900 

12167000 

230 

15-165 

6-126 

28224 

4741632 

168 

12-961 

5-517 

53361 

12326391 

231 

15-198 

6-135 

28561 

4826809 

169 

13-000 

5-528 

53824 

12487168 

232 

15-231 

6-144 

28900 

4913000 

170 

13-938 

5-539 

54289 

12649337 

233 

15-264 

6-153 

29241 

5000211 

171 

13-076 

5-550 

54756 

12812904 

234 

15-297 

6-162 

29584 

5088448 

172 

13-114 

5-561 

55225 

12977875 

235 

15-329 

6-171 

29929 

5177717 

173 

13-152 

5-572 

55696 

13144256 

236 

15-362 

6-179 

30276 

5268024 

174 

13-190 

5-582 

56169 

13312053 

237 

15-394 

6-188 

30625 

5359375 

175 

1-8-228 

5-593 

56644 

13481272 

238 

15-427 

6-197 

30976 

5451776 

176 

13-266 

5-604 

57121 

13651919 

239 

15-459 

6-205 

31329 

5545233 

177 

13-304 

5-614 

57600 

13824000 

240 

15-491 

6-214 

31684 

5639752 

178 

13-341 

5-625 

58081 

13997521 

241 

15-524 

6-223 

32041 

5735339 

179 

13-379 

5-635 

58564 

14172488 

242 

15-556 

6-231 

32400 

58S2000 

180 

13-416 

5-646 

59049 

14348907 

243 

15-588 

6-240 

32761 

5929741 

181 

13-453 

5-656 

59536 

14526784 

244 

15-620 

6-248 

33124 

6028568 

182 

13-490 

5-667 

60025 

14706125 

245 

15-652 

6-257 

33489 

6128487 

183 

13-527 

5-677 

60516 

14886936 

246 

15-684 

6-265 

33856 

6229504 

184 

13-664 

5-687 

61009 

15069223 

247 

15-716 

6-274 

34225 

6331625 

185 

13-601 

5-698 

61504 

15252992 

248 

15-748 

6-282 

34596 

6434856 

186 

13-638 

5-708 

62001 

15438249 

249 

15-779 

6-291 

34969 

6539203 

187 

13-674 

5-718 

62500 

15625000 

250 

15-811 

6-299 

35344 

6644672 

188 

13-711 

5-728 

63001 

15813251 

251 

15-842 

6-307 

35721 

6751269 

189 

13-747 

5-738 

63504 

16003008 

252 

15-874 

6-316 

822 


APPENDIX. 


TABLE  OF  SQUARES,  CUBES,  SQUARE  AND   CUBE   ROOTS   OF  NUMBERS— (Continued) 


Squares. 

Cubes. 

No. 

Square 
roots. 

Cube 
roots. 

1 
;  Squares. 

Cubes. 

No. 

Square 
roots. 

Cube 
roots. 

64009 

16194277 

253 

15-905 

6-324 

99856 

31554496 

316 

17-116 

.  6-811 

64516 

16387064 

254 

15-937 

6-333 

100489 

31855013 

317 

11-804 

6-818 

65025 

16581375 

255 

15-968 

6-341 

101124 

32157432 

318 

11-832 

6-825 

65536 

16777216 

256 

16-000 

6-349 

101161 

32461759 

319 

11-860 

6-832 

66049 

16974593 

257 

16-031 

6-351 

102400 

32768000 

320 

11-888 

6-839 

66564 

17173512 

258 

16-062 

6-366 

103041 

33076161 

821 

11-916 

6-841 

67081 

17373979 

259 

16093 

6-314 

103684 

33386248 

322 

17-944 

6-854 

6*7600 

17576000 

260 

16-124 

6-382 

104329 

33698267 

323 

17-972 

6-861 

68121 

17779581 

261 

16-155 

6-390 

104976 

34012224 

324 

18-000 

6-868 

68644 

17984728 

262 

16-186 

6-398 

105625 

34328125 

325 

18-027 

6-815 

69169 

18191447 

263 

16-217 

6-406 

106276 

34645976 

326 

18-055 

6-882 

69696 

18399744 

264 

16-248 

6-415 

106929 

34965783 

327 

18-083 

6-889 

70225 

18609625 

265 

16-278 

6-423 

107584 

35287552 

328 

18-110 

6-896 

70156 

18821096 

266 

16-309 

6-431 

108241 

35611289 

329 

18-138 

6-903 

71289 

19034163 

267 

16-340 

6-439 

108900 

35937000 

330 

18-165 

6-910 

71824 

19248832 

268 

16-370 

6-441 

109561 

36264691 

331 

18-V93 

6-911 

12361 

19465109 

269 

16-401 

6-455 

110224 

36594368 

332 

18-220 

6-924 

72900 

19683000 

270 

16-431 

6-463 

110889 

36926037 

333 

18-248 

6-931 

13441 

19902511 

271 

16-462 

6-411 

111556 

37259104 

334 

18-275 

6-938 

13984 

20123643 

272 

16-492 

6-419 

112225 

31595375 

335 

18-303 

6-945 

14529 

20346417 

273 

16-522 

6-481 

112896 

37933056 

336 

18-330 

6-952 

15076 

20570824 

274 

16-552 

6-495 

113569 

38272753 

337 

18-351 

6'958 

15625 

20796875 

275 

16-583 

6-502 

114244 

38614472 

338 

18-384 

6-965 

76176 

21024576 

276 

16-613 

6-510 

114921 

38958219 

339 

18-411 

6-912 

76729 

21253933 

277 

16-643 

6-518 

115600 

39304000 

340 

18-439 

6-919 

77284 

21484952 

278 

16-678 

6-52$ 

116281 

89651821 

341 

18-466 

6-&S6 

77841 

21717639 

279 

16-703 

6-534 

116964 

40001688 

342 

18-493 

6-993 

78400 

21952000 

280 

16-733 

6-542 

117649 

40353607 

343 

18-520 

l-ooo 

18961 

22188041 

281 

16-163 

6-549 

118336 

40701584 

344 

18-541 

1-006 

19524 

22425768 

282 

16-792 

6-557 

119025 

41063625 

345 

18-574 

1-013 

80039 

22665187 

283 

16-822 

6-565 

119716 

41421736 

346 

18-601 

1-020 

80656 

22906304 

284 

16-852 

6-573 

120409 

41781923 

347 

18-621 

1-021 

81225 

23149125 

285 

16-881 

6-580 

121104 

42144192 

348 

18-654 

1-033 

81196 

23393656 

286 

16-911 

6-588 

121801 

42508549 

349 

18-681 

1-040 

82369 

23639903 

287 

16-941 

6-596 

122500 

42815000 

350 

18-108 

1-041 

82944 

23887872 

288 

16-970 

6-603 

123201 

43243551 

351 

18-134 

1-054 

83521 

24137569 

289 

17-000 

6-611 

123904 

43614208 

352 

18-161 

1-060 

84100 

24389000 

290 

17-029 

6-619 

124609 

43986911 

353 

18-188 

1-067 

84681 

24642171 

291 

17-058 

6-626 

125316 

44361864 

354 

18-814 

7-074 

85264 

24897088 

292 

17-088 

6-634 

126025 

44738875 

355 

18-841 

7-080 

85849 

25153757 

293 

17-117 

6-641 

126736 

45118016 

356 

18-861 

7-081 

86436 

25412184 

294 

17-146 

6-649 

127449 

45499293 

357 

18-894 

1-093 

87025 

25672375 

295 

17-175 

6-656 

128164 

45882712 

358 

18-920 

1-100 

81616 

25934836 

296 

17-204 

6-664 

128881 

46268279 

359 

18-941 

1-101 

88209 

26198073 

297 

11-233 

6-671 

129600 

46656000 

360 

18-913 

1-113 

88804 

26463592 

298 

11-262 

6-679 

130321 

47045831 

361 

19-000 

1-120 

89401 

26730899 

299 

11-291 

6-686 

131044 

47437928 

362 

19-026 

1-126 

90000 

27000000 

300 

11-320 

6-694 

131769 

47832147 

363 

19-052 

1-133 

90601 

27270901 

301 

11-349 

6-701 

132496 

48228544 

864 

19-078 

1-140 

91204 

27543608 

302 

11-318 

6-709 

133225 

48627125 

365 

19-104 

1-146 

91809 

27818127 

303 

11-406 

6-716 

133956 

49027896 

366 

19-131 

1-153 

92416 

28094464 

304 

17-435 

6-723 

134689 

49430863 

367 

19-151 

1-159 

93025 

28372625 

305 

17-464 

6-731 

135424 

49836032 

368 

19-183 

1-166 

93636 

28652616 

306 

17-492 

6-738 

136161 

50243409 

369 

19-209 

1-112 

94249 

28934443 

307 

17-521 

6-745 

136900 

50653000 

370 

19-235 

1-179 

94864 

29218112 

308 

17-549 

6-753 

137641 

51064811 

371 

19-261 

7-185 

95481 

29503609 

309 

11-578 

6-160 

138384 

51478848 

372 

19-281 

7-191 

96100 

29791000 

310 

11-606 

6-161 

139129 

51895117 

373 

19-313 

7-198 

9.8121 

30080231 

311 

11-635 

6-775 

139876 

62313624 

374 

19-339 

7-204 

91344 

30371328 

312 

11-663 

6-782 

140625 

52734375 

375 

19-364 

7-211 

97969 

30664297 

313 

11-691 

6-789 

141376 

53157376 

376 

19-390 

7-217 

98596 

30959144 

314 

11-120 

6-796 

142129 

53582633 

377 

19-416 

7-224 

99225 

31255875 

315 

11-148 

6-804 

:  142884 

54010152 

378 

19-442 

7-230 

APPENDIX. 


823 


TABLE  OF  SQUARES,  CUBES,  SQUAEE  AND  CUBE  ROOTS  OF  NUMBERS— ( Continued). 


Squares. 

Cubes. 

No. 

Square 
roots. 

Cube 
roots. 

Squares. 

Cubes. 

No. 

Square 
roots. 

Cube 
roots. 

143641 

54439939 

379 

19-467 

7-236 

195364 

86350888 

442 

21-023 

7-617 

144400 

54872000 

380 

19-493 

7-243 

196249 

86938307 

443 

21-047 

7-623 

145161 

55306341 

381 

19-519 

7-249 

197136 

87528384 

444 

21-071 

V-628 

145924 

55742968 

382 

19-544 

7-255 

198025 

88121125 

445 

21-095 

7-634 

146689 

56181887 

383 

19-570 

7-262 

198916 

88716536 

446 

21-118 

7-640 

147456 

56623104 

384 

19-595 

7-268 

199809 

89314623 

447 

21-142 

7-646 

148225 

57066625 

385 

19621 

7-274 

200704 

89915392 

448 

21-166 

7-651 

148996 

57512456 

386 

19-646 

7-281 

201601 

90518849 

449 

21-189 

7-657 

149769 

57960603 

387 

19-672 

7-287 

202500 

91125000 

450 

21-213 

7-663 

150544 

58411072 

388 

19-697 

7-293 

203401 

91733851 

451 

21-236 

7-668 

151321 

58863869 

389 

19-723 

7-299 

204304 

92345408 

452 

21-260 

7-674 

152100 

59319000 

390 

19-748 

7-306 

205209 

92959677 

453 

21-283 

7-680 

152881 

59776471 

391 

19-773 

7-312 

206116 

93576664 

454 

21-307 

7-685 

153664 

602S6288 

392 

19-798 

7-318 

207025 

94196375 

455 

21-330 

7-691 

154449 

60698457 

393 

19-824 

7-324 

207936 

94818816 

456 

21-354 

7-697 

155236 

61162984 

394 

19-849 

7-331 

208849 

95443993 

457 

21-377 

7-702 

156025 

61629875 

395 

19-874 

7-337 

209764 

96071912 

458 

21-400 

7-708 

156816 

62099136 

396 

19-899 

7-343 

210681 

96702579 

459 

21-424 

7-713 

157609 

62570773 

397 

19-924 

7-349 

211600 

97336000 

460 

21-447 

7-719 

158404 

63044792 

398 

19-949 

7-355 

212521 

97972181 

461 

21-470 

7-725 

159201 

63521199 

399 

19-974 

7-361 

213444 

98611128 

462 

21-494 

7-730 

160000 

64000000 

400 

20-000 

7-368 

214369 

99252847 

463 

21-517 

7-736 

160801 

64481201 

401 

20-024 

7-374 

215296 

99897344 

464 

21-540 

7-741 

161604 

64964808 

402 

20-049 

7-380 

216225 

100544625 

465 

21-563 

7-747 

162409 

65450827 

403 

20-074 

7-386 

217156 

101194696 

466 

21-587 

7-752 

163216 

65939264 

404 

20-099 

7-392 

218089 

101847563 

467 

21-610 

7-758 

164025 

66430125 

405 

20-124 

7-398 

219024 

102503232 

468 

21-633 

7-763 

164836 

66923416 

406 

20-149 

7-404 

219961 

103161709 

469 

21-656 

7-769 

165649 

67419143 

407 

20-174 

7-410 

220900 

103823000 

470 

21-679 

7-774 

166464 

67917312 

408 

20-199 

7-416 

221841 

104487111 

471 

21-702 

7-780 

167281 

68417929 

409 

20-223 

7-422 

222784 

105154048 

472 

21-725 

7-785 

168100 

68921000 

410 

20-248 

7-428 

223729 

105823817 

473 

21-748 

7-791 

168921 

69426531 

411 

20-273 

7-434 

224676 

106496424 

474 

21-771 

7-796 

169744 

69934528 

412 

20-297 

7-441 

225625 

107171875 

475 

21-794 

7-802 

170569 

70444997 

413 

20-322 

7-447 

226576 

107850176 

476 

21-817 

7-807 

171396 

70957944 

414 

20-346 

7-453 

227529 

108531333 

477 

21-840 

7-813 

172225 

71473375 

415 

20-371 

7-459 

228484 

109215352 

478 

21-863 

7-818 

173056 

71991296 

416 

20-396 

7-465 

229441 

109902239 

479 

21-886 

7-824 

173889 

72511713 

417 

20-420 

7-470 

230400 

110592000 

480 

21-908 

7-829 

174724 

73034632 

418 

20-445 

7-476 

231361 

111284641 

481 

21-931 

7-835 

175561 

73560059 

419 

20-469 

7-482 

232324 

111980168 

482 

21-954 

7-840 

176400 

74088000 

420 

20-493 

7-488 

233289 

112678587 

483 

21-977 

7-846 

177241 

74618461 

421 

20-518 

7-494 

234256 

113379904 

484 

22-000 

7-851 

178084 

75151448 

422 

20-542 

7-500 

235225 

114084125 

485 

22-022 

7-856 

178929 

75686967 

423 

20-566 

7-506 

236196 

114791256 

486 

22-045 

7-862 

179776 

76225024 

424 

20-591 

7-512 

237169 

115501303 

487 

22-068 

7-867 

180625 

76765625 

425 

20-615 

7-518 

238144 

116214272 

488 

22-090 

7-872 

181476 

77308776 

426 

20-639 

7-524 

239121 

116930169 

489 

22-113 

7-878 

182329 

77854483 

427 

20-663 

7-530 

240100 

117649000 

490 

22-135 

7-883 

183184 

78402752 

428 

20-688 

7-536 

241081 

118370771 

491 

22-158 

7-889 

184041 

78953589 

429 

20-712 

7-541 

242064 

119095488 

492 

22-181 

7-894 

184900 

79507000 

430 

20-736 

7-547 

243049 

119823157 

493 

22-203 

7-899 

185761 

80062991 

431 

20-760 

7-553 

244036 

120553784 

494 

22-226 

7-905 

186624 

80621568 

432 

20-784 

7-559 

245025 

121287375 

495 

22-248 

7-910 

187489 

81182737 

433 

20-808 

7-565 

246016 

122023936 

496 

22-271 

7-915 

188356 

81746504 

434 

20-832 

7-571 

247009 

122763473 

497 

22-293 

7-921 

189225 

82312875 

435  » 

20-856 

7-576 

248004 

123505992 

498 

22-315 

7-926 

190096 

82881856 

436 

20-880 

7-582 

249001 

124251499 

499 

22-338 

7-931 

190969 

83453453 

437 

20-904 

7-588 

250000 

125000000 

500 

22-360 

7-937 

191844 

84027672 

438 

20-928 

7-594 

251001 

125751501 

501 

22-383 

7-942 

192721 

84604519 

439 

20-952 

7-600 

252004 

126506008 

502 

22-405 

7-947 

193600 

85184000 

440 

20-976 

7-605 

253009 

127263527 

503 

22-427 

7-952 

194481 

85766121 

441 

21-000 

7-611 

254016 

128024064 

504 

22-449   7-958 

824. 


APPENDIX. 


TABLE  OF  SQUARES,  CUBES,  SQUAEE  AND  CUBE  EOOTS  OF  NUMBEES— (Continued'). 


Squares. 

Cubes. 

No. 

Square 
roots. 

Cube 

roots. 

Squares. 

Cubes. 

No. 

Square 
roots. 

Cube 
roots. 

255025 

128787625 

505 

22-472 

7-963 

322624 

183250432 

568 

23-832 

8-281 

256036 

129554216 

506 

,  22-494 

7-968 

323761 

184220009 

569 

23-853 

8-286 

257049 

130323843 

507 

22-516 

7-973 

324900 

185193000 

570 

23-874 

8-291 

258064 

131096512 

508 

22-538 

7-979 

326041 

186169411 

571 

23-895 

8-296 

259081 

131872229 

509 

22-561 

7-984 

327184 

187149248 

572 

23-916 

8-301 

260100 

132651000 

510 

22-583 

7-989 

328329 

188132517 

573 

23-937 

8-305 

261121 

133432831 

511 

22-605 

7-994 

329476 

189119224 

574 

23-958 

8-310 

262144 

134217728 

512 

22-627 

8-000 

330625 

190109375 

575 

23-979 

8-315 

263169 

135005697 

513 

22-649 

8-005 

331776 

191102976 

576 

24-000 

8-320 

264196 

135796744 

514 

22-671 

8-010 

332929 

192100033 

577 

24-020 

8-325 

265225 

136590875 

515 

22-693 

8-015 

334084 

193100552 

578 

24-041 

8-329 

266256 

137388096 

516 

22-715 

8-020 

335241 

194104539 

579 

24-062 

8-334 

267289 

138188413 

517 

22-737 

8-025 

336400 

195112000 

580 

24-083 

8-339 

268324 

138991832 

618 

22-759 

8-031 

337561 

196122941 

581 

24-103 

8-344 

269361 

139798359 

519 

22-781 

8-036 

338724 

197137368 

582 

24-124 

8-349 

270400 

140608000 

520 

22-803 

8-041 

339889 

198155287 

583 

24-145 

8-353 

271441 

141420761 

521 

22-825 

8-046 

341056 

199176704 

584 

24-166 

8-358 

272484 

142236648 

522 

22-847 

8-051 

342225 

200201625 

585 

24-186 

£-363 

273529 

143055667 

523 

22-869 

8-056 

343396 

201230056 

586 

24-207 

8-368 

274576 

143877824 

524 

22-891 

8-062 

344569 

202262003 

587 

24-228 

8-372 

275625 

144703125 

525 

22-912 

8-067 

345744 

203297472 

588 

24-248 

8-377 

276676 

145531576 

526 

22-934 

8-072 

346921 

204336469 

589 

24-269 

8-382 

277729 

146363183 

527 

22-956 

8-077 

348100 

205379000 

590 

24-289 

8-387 

278784 

147197952 

528 

22-978 

8-082 

349281 

206425071 

591 

24-310 

8-391 

279841 

148035889 

529 

23-000 

8-037 

350464 

207474688 

592 

24-331 

8-396 

280900 

148877000 

530 

23-021 

8-092 

351649 

208527857 

593 

24-351 

8-40*1 

281961 

149721291 

531 

23-043 

8-097 

352836 

209584584 

594 

24-372 

8-406 

283024 

150568768 

532 

23-065 

8-102 

354025 

210644875 

595 

24-392 

8-410 

284089 

151419437 

533 

23-086 

8-107 

355216 

211708736 

596 

24-413 

8-415 

285156 

152273304 

534 

23-108 

8-112 

356409 

212776173 

697 

24-433 

8-420 

286225 

153130375 

535 

23-130 

8-118 

357604 

213847192 

598 

24-454 

8-424 

287296 

153990656 

536 

23-151 

8-123 

358801 

214921799 

599 

24-474 

8-429 

288369 

154854153 

537 

23-173 

8-128 

360000 

216000000 

600 

24-494 

8-434 

289444 

155720872 

538 

23-194 

8-133 

361201 

217081801 

601 

24-515 

8439 

290521 

156590819 

539 

23-216 

8-138 

362404 

218167208 

602 

24-535 

8-443 

291600 

157464000 

540 

23-237 

8-143 

363609 

219256227 

603 

24-556 

8-448 

292681 

158340421 

541 

23-259 

8-148 

364816 

220348864 

604 

24-576 

8-453 

293764 

159220088 

542 

23-280 

8-153 

366025 

221445125 

605 

24-596 

8-457 

294849 

160103007 

543 

23-302 

8-158 

367236 

222545016 

606 

24-617 

8-462 

295936 

160989184 

544 

23-323 

8-163 

368449 

223648543 

607 

24-637 

8-467 

297025 

161878625 

545 

23-345 

8-168 

369664 

224755712 

608 

24-657 

8-471 

298116 

162771336 

546 

23-366 

8-173 

370881 

225866529 

609 

24-677 

8-476 

299209 

163667323 

547 

23-388 

8-178 

372100 

226981000 

610 

24-698 

8-480 

300304 

164566592 

548 

23-409 

8-183 

373321 

228099131 

611 

24-718 

8-485 

301401 

165469149 

549 

23-430 

8-188 

374544 

229220928 

612 

24-738 

8-490 

302500 

166375000 

550 

23-452 

8-193 

375769 

230346397 

613 

24-758 

8-494 

303601 

167284151 

551 

23-473 

8-198 

376996 

231475544 

614 

24-779 

8-499 

304704 

168196608 

552 

23-494 

8-203 

378225 

232608375 

615 

24-799 

8-504 

305809 

169112377 

553 

23-515 

8-208 

379456 

233744896 

616 

24-819 

8-508 

306916 

170031464 

554 

23-537 

8-213 

380689 

234885113 

617 

24-839 

8-513 

308025 

170953875 

556 

23-558 

8-217 

381924 

236029032 

618 

24-859 

8-517 

309136 

171879616 

556 

23-579 

8-222 

383161 

237176659 

619 

24-879 

8-522 

310249 

172808693 

557 

23-600 

8-227 

384400 

238328000 

620 

24-899 

8-527 

311364 

173741112 

558 

23-622 

8-232 

385641 

239483061 

621 

24-919 

8-531 

312481 

174676879 

559 

23-643 

8-237 

386884 

240641848 

622 

24-939 

8-536 

313600 

175616000 

560 

23-664 

8-242 

388129 

241804367 

623 

24-959 

8-540 

314721 

176558481 

561 

23-685 

8-247 

389376 

242970624, 

624 

24-979 

8-545 

315844 

177504328 

562 

23-706 

8-252 

390625 

244140625 

625 

25-000 

8-549 

316969 

178453547 

563 

23-727 

8-257 

391876 

245314376 

626 

25-019 

8-554 

318096 

179406144 

564 

23-748 

8-262 

393129 

246491883 

627 

?,5'039 

8-558 

319225 

180362125 

565 

23-769 

8-267 

394384 

247673152 

628 

25-059 

8-563 

320356 

181321496 

566 

23-790 

8-271 

395641 

248858189 

629 

25-079 

8-568 

321489  (182284263 

567 

23-811 

8'276 

396900 

250047000 

630 

25-099 

8-572 

APPENDIX. 


825 


TABLE  OF  SQUARES,  CUBES,  SQUAEE  AND  CUBE  EOOTS  OF  NUMBERS— (Continued). 


Squares. 

Cubes. 

No. 

Square 
roots. 

Cube 
roots. 

Squares. 

Cubes. 

No. 

Square 
roots. 

Cube 

roots. 

398161 

251239591 

631 

25-119 

8-577 

481636 

334255384 

694 

26-343 

8-853 

399424 

252435968 

632 

25-139 

8-581 

483025 

335702375 

695 

26-362 

8-857 

400689 

253636137 

633 

25-159 

8-586 

484416 

337153536 

696 

26-381 

8-862 

401956 

254840104 

634 

25-179 

8-590 

485809 

338608873 

697 

26-400 

8-866 

403225 

256047875 

635 

25-199 

8-595 

487204 

340068392 

698 

26-419 

8-870 

404496 

257259456 

636 

25-219 

8-599 

488601 

341532099 

699 

26-438 

8-874 

405769 

258474853 

637 

25-238 

8-604 

490000 

343000000 

700 

26-457 

8-879 

407044 

259694072 

638 

25-258 

8-608 

491401 

344472101 

701 

26-476 

8-883 

408321 

260917119 

639 

25-278 

8-613 

492804 

345948408 

702 

26-495 

6-887 

409600 

262144000 

.640 

25-298 

8-617 

494209 

347428927 

703 

26-514 

8-891 

410881 

263374721 

641 

25-317 

8-622 

495616 

348913664 

704 

26-532 

8-895 

412164 

264609288 

642 

25-337 

8-626 

497025 

350402625 

705 

26-551 

8-900 

413449 

265847707 

643 

25-357 

8-631 

498436 

351895816 

706 

26-570 

8-904 

414736 

267089984 

644 

25-377 

3-635 

499849 

353393243 

707 

26-589 

8-908 

416025 

268336125 

645 

25-396 

8-640 

501264 

354894912 

708 

26-608 

8-912 

417316 

269586136 

646 

25-416 

8-644 

502681 

356400829 

709 

26-627 

8-916 

418609 

270840023 

647 

25-436 

8-649 

504100 

357911000 

710 

26-645 

8-921 

419904 

272097792 

648 

25-455 

8-653 

505521 

359425431 

711 

26-664 

8-925 

421201 

273359449 

649 

25-475 

8-657 

506944 

360944128 

712 

26-683 

8-929 

422500 

274625000 

650 

25-495 

8-662 

508369 

362467097 

713 

26-702 

8-933 

423801 

275894451 

651 

25-514 

8-666 

509796 

363994344 

714 

26-720 

8-937 

425104 

277167808 

652 

25-534 

8-671 

511225 

365525875 

715 

26-739 

8-942 

426409 

278445077 

653 

25-553 

8-675 

512656 

367061696 

716 

26-758 

8'946 

427716 

279726264 

654 

25-573 

8-680 

514089 

368601813 

717 

26-776 

8-950 

429025 

281011375 

655 

25-592 

8-684 

515524 

370146232 

718 

26-795 

8-954 

430336 

282300416 

656 

25-612 

8-688 

516961 

371694959 

719 

26-814 

8-958 

431649 

283593393 

657 

25-632 

8-693 

518400 

373248000 

720 

26-832 

8-962 

432964 

284890312 

658 

25-651 

8-697 

519841 

374805361 

721 

26-851 

8-966 

4S4281 

286191179 

659 

25-670 

8-702 

521284 

376367048 

722 

26-870 

8-971 

435600 

287496000 

660 

25-690 

8-706 

522729 

377933067 

723 

26-888 

8-975 

436921 

288804781 

661 

25-709 

8-710 

524176 

379503424 

724 

26-907 

8-979 

438244 

290117528 

662 

25-729 

8-715 

525625 

381078125 

725 

26-925 

8-983 

439569 

291434247 

663 

25-748 

8-719 

527076 

382657176 

726 

26-944 

8-987 

440896 

292754944 

664 

25-768 

8-724 

528529 

384240583 

727 

26-962 

8991 

442225 

294079625 

665 

25-787 

8-728 

529984 

385828352 

728 

26-981 

8-995 

443556 

295408296 

666 

25-806 

8-732 

531441 

387420489 

729 

27-000 

9-000 

444889 

296740963 

667 

25-826 

8-737 

532900 

389017000 

730 

27-018 

9-004 

446224 

298077632 

668 

25-845 

8-741 

534361 

390617891 

731 

27-037 

9-008 

447561 

299418309 

669 

25-865 

8-745 

535824 

392223168 

732 

27-055 

9-012 

448900 

300763000 

670 

25-884 

8-750 

537289 

393832837 

733 

27-073 

9-016 

450241 

302111711 

671 

25-903 

8-754 

538756 

395446904 

734 

27-092 

9-020 

451584 

303464448 

672 

25-922 

8-759 

540225 

397065375 

735 

27-110 

9-024 

452929 

304821217 

673 

25-942 

8-763 

541696 

398688256 

736 

27-129 

9-028 

454276 

306182024 

674 

25-961 

8-767 

543169 

400315553 

7S7 

27-147 

9-032 

455625 

307546375 

675 

25-980 

8-772 

544644 

401947272 

738 

27-166 

9-036 

456976 

308915776 

676 

26-000 

8-776 

546121 

403583419 

739 

27-184 

9-040 

458329 

310288733 

677 

26-019 

8-780 

547600 

405224000 

740 

27-202 

9-045 

459684 

311665752 

678 

26-038 

8-785 

549081 

406869021 

741 

27-221 

9-049 

461041 

313046839 

679 

26-057 

8-789 

550564 

408518488 

742 

27-239 

9-053 

462400 

314432000 

680 

26-076 

8-793 

552049 

410172407 

743 

27-258 

9-057 

463761 

315821241 

681 

26-095 

8-797 

553536 

411830784 

744 

27-276 

9-061 

465124 

317214568 

682 

26-115 

8-802 

555025 

413493625 

745 

27-294 

9-065 

466489 

318611987 

683 

26-134 

8-806 

556516 

415160936 

746 

27-313 

9-069 

467856 

320013504 

684 

26-153 

8-810 

558009 

416832723 

747 

27-331 

9-073 

469225 

321419125 

685 

26-172 

8-815 

559504 

418508992 

748 

27-349 

9-077 

470596 

322828856 

686 

26-191 

8-819 

561001 

420189749 

749 

27-367 

9-081 

471969 

324242703 

687. 

26-210 

8-823 

562500 

421875000 

750 

27-386 

9-085 

473344 

325660672 

688 

26'22y 

8-828 

564001 

423564751 

751 

27-404 

9-089 

474721 

327082769 

689 

26-248 

8-832 

565504 

425259008 

752 

27-422 

9-093 

476100 

328509000 

690 

26-267 

8-836 

567009 

426957777 

753 

27-440 

9-097 

477481 

329939371 

691 

26-286 

8'840 

568516 

428661064 

754 

27-459 

9-101 

478864 

331373888 

692 

26-305 

8-845 

570025 

430368875 

755 

27-477 

9-105 

480249 

332812557 

693 

26-324 

8-849 

571536 

432081216 

756 

27-495 

9-109 

826 


APPENDIX. 


TABLE  OF  SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS  OF  NUMBERS— (Continued). 


Squares. 

Cubes. 

No. 

Square 
roots. 

Cube 
roots. 

Squares. 

Cubes. 

No. 

Square 
roots. 

Cube 
roots. 

573049 

433798093 

757 

27-513 

9-113 

672400 

551368000 

820 

28-635 

9-359 

574564 

435519512 

758 

27-531 

9-117 

674041 

553387661 

821 

28-653 

9-363 

576081 

437245479 

759 

27-549 

9-121 

675684 

555412248 

822 

28-670 

9-367 

677600 

438976000 

760 

27-568 

9-125 

677329 

557441767 

823 

28-687 

9-371 

579121 

440711081 

761 

27-586 

9-129 

678976 

559476224 

824 

28-705 

9-375 

580644 

442450728 

762 

27-604 

9-133 

680625 

561515625 

825 

28-722 

9-378 

582169 

444194947 

763 

27-622 

9-137 

682276 

563559976 

826 

28-740 

9-382 

583696 

445943744 

764 

27-640 

9-141 

683929 

565609283 

827 

28-757 

9-386 

685225 

447697125 

765 

27-658 

9-145 

685584 

567663552 

828 

28-774 

9-390 

586756 

449455096 

766 

27-676 

9-149 

687241 

569722789 

829 

28-792 

9-394 

.688289 

451217663 

767 

27-694 

9-153 

688900 

571787000 

830 

28-809 

9-397 

589824 

452984832 

768 

27-712 

9-157 

690561 

573856191 

831 

28-827 

9-401 

591361 

454756609 

769 

27-730 

9-161 

692224 

575930368 

832 

28-844 

9-405 

592900 

456533000 

770 

27-748 

9-165 

693889 

578009537 

833 

28-861 

9-409 

594441 

458314011 

771 

27-766 

9-169 

695556 

580093704 

834 

28-879 

9-412 

695984 

460099648 

772 

27-784 

9-173 

697225 

582182875 

835 

28-896 

9-416 

597529 

461889917 

773 

27-802 

9-177 

698896 

584277056 

836 

28-913 

9-420 

599076 

463684824 

774 

27-820 

9-181 

700569 

586376253 

837 

28-930 

9-424 

•600625 

465484375 

775 

27-833 

9-185 

702244 

588480472 

838 

28-948 

9-427 

602176 

467288576 

776 

27-856 

9-189 

703921 

590589719 

839 

28-965 

9-431 

•603729 

469097433 

777 

27-874 

9-193 

705600 

592704000 

840 

28-98?, 

9-435 

•605284 

470910952 

778 

27-892 

9-197 

707281 

594823321 

841 

29-000 

9-439 

606841 

472729139 

779 

27-910 

9-201 

708964 

596947688 

842 

29-017 

9-442 

•608400 

474552000 

780 

27-928 

9-205 

710649 

599077107 

843 

29-034 

9-446 

609961 

476379541 

781 

27-946 

9-209 

712336 

601211584 

844 

29-051 

9-450 

611524 

478211768 

782 

27-964 

9-213 

714025 

603351125 

845 

29-068 

9-454 

613089 

480048687 

783 

27-982 

9-216 

715716 

605495736 

846 

29-086 

9-457 

-614656 

481890304 

784 

28-000 

9-220 

717409 

607645423 

847 

29-103 

9-461 

616225 

483736625 

785 

28-017 

9-224 

719104 

609800192 

848 

29-120 

9-465 

617796 

485587656 

786 

28-035 

9-228 

720801 

611960049 

849 

29-137 

9-468 

619369 

487443403 

787 

28-053 

9-232 

722500 

614125000 

850 

29-154 

9-472 

620944 

489303872 

788 

28-071 

9-236 

724201 

616295051 

851 

29-171 

9-476 

622521 

491169069 

789 

28-089 

9-240 

725904 

618470208 

852 

29-189 

9-480 

624100 

493039000 

790 

28-106 

9-244 

727609 

620650477 

853 

29-206 

9-483 

625681 

494913671 

791 

28-124 

9-248 

729316 

622835864 

854 

29-223 

9-487 

627264 

496793088 

792 

28-142 

9-252 

731025 

625026375 

855 

29-240 

9-491 

628849 

498677257 

793 

28-160 

9-256 

732736 

627222016 

856 

29-257 

9494 

630436 

500566184 

794 

28-178 

9-259 

734449 

629422793 

857 

29-274 

9-498 

632025 

502459875 

795 

28-195 

9-263 

736164 

631628712 

858 

29-291 

9-502 

•633616 

504358336 

796 

28-213 

9-267 

737881 

633839779 

859 

29-308 

9-505 

635209 

506261573 

797 

28-231 

9-271 

739600 

636056000 

860 

29-325 

9-509 

63680* 

508169592 

798 

28-248 

9-275 

741321 

638277381 

861 

29-342 

9-513 

•638401 

510082399 

799 

28-266 

9-279 

743044 

640503928 

862 

29-359 

9-517 

640000 

512000000 

800 

28-284 

9-283 

744769 

642735647 

863 

29-376 

9-520 

641601 

513922401 

801 

28-301 

9-287 

746496 

644972544 

864 

29-393 

9-524 

643204 

515849608 

802 

28-319 

9-290 

748225 

647214625 

865 

29-410 

9-528 

644809 

517781627 

803 

28-337 

9-294 

749956 

649461896 

866 

29-427 

9-531 

646416 

519718464 

804 

28-354 

.9-298 

751689 

651714363 

867 

29-444 

9-535 

648025 

521660125 

805 

28-372 

9-302 

753424 

653972032 

868 

29-461 

9-539 

649636 

523606616 

806 

28-390 

9-306 

755161 

656234909 

869 

29-478 

9-542 

651249 

525557943 

807 

28-407 

9-310 

756900 

658503000 

870 

29-495 

9-546 

652864 

527514112 

808 

28-425 

9-314 

758641 

660776311 

871 

29-512 

9-550 

654481 

529475129 

809 

28-442 

9-317 

760384 

663054848 

872 

29-529 

9-553 

656100 

531441000 

810 

28-460 

9-321 

762129 

665338617 

873 

29-546 

9-557 

657721 

533411731 

811 

28-478 

9-325 

763876 

667627624 

874 

29-563 

9-561 

659344 

535387328 

812 

28-495 

9-329 

765625 

669921875 

875 

29-580 

9-564 

660969 

537367797 

813 

28-513 

9-333 

767376 

672221376 

876 

29-597 

9-568 

662596 

539353144 

814 

28-530 

9-337 

769129 

674526133 

877 

29-614 

9-571 

664225 

541343375 

815 

28-548 

9-340 

770884 

676836152 

878 

29-631 

9-575 

665856 

543338496 

816 

28-565 

9-344 

772641 

679151439 

879 

29-647 

9-579 

667489 

545338513 

817 

28-583 

9-348 

774400 

681472000 

880 

29-664 

9-582 

669124 

647343432 

818 

28-600 

9-352 

776161 

683797841 

881 

29-681 

9-586 

£70761 

549353259 

819 

28-618 

9-356 

777924 

686128968 

882 

29-698 

9-590 

APPENDIX. 


82T 


TABLE  OF  SQUAEES,  CUBES,  SQUAEE  AND  CUBE  KOOTS  OF  NUMBERS— ( Continued). 


Squares. 

Cubes. 

No. 

Square 
roots. 

Cube 
roots. 

Squares. 

Cubes. 

No. 

Square 
roots. 

Cube 
roots. 

779689 

688465387 

883 

29-715 

9-593 

894916 

846590536 

946 

30-757 

9-816 

781456 

690807104 

884 

29-732 

9-597 

896808 

849278123 

947 

30-773 

9-820 

783225 

693154125 

885 

29-748 

9-600 

898704 

851971392 

948 

30-789 

9-823 

784996 

695506456 

886 

29-765 

9-604 

900601 

854670349 

949 

30-805 

9-827 

786769 

697864103 

887 

29-782 

9-608 

902500 

857375000 

950 

30-822 

9-830 

788544 

700227072 

888 

29-799 

9-611 

904401 

860085351 

951 

30-838 

9-833 

790321 

702595369 

889 

29-816 

9-615 

906304 

862801408 

952 

30-854 

9-837 

792100 

704969000 

890 

29-832 

9-619 

908209 

865523177 

953 

30-870 

9-840 

793881 

707347971 

891 

29-849 

9-622 

910116 

868250664 

954 

80-886 

9-844 

795664 

709732288 

892 

29-866 

9-626 

912025 

870983875 

955 

30-903 

9-847 

797449 

712121957 

893 

29-883 

9-629 

913936 

873722816 

956 

30-919 

9-851 

799236 

714516984 

894 

29-899 

9-633 

915849 

876467493 

957 

80-935 

9-854 

801025 

716917375 

895 

29-916 

9-636 

917764 

879217912 

958 

30-951 

9-857 

802816 

719323136 

896 

29-933 

9-640 

919681 

881974079 

959 

30-967 

9-861 

804609 

721734273 

897 

29-949 

9-644 

921600 

884736000 

960 

30-983 

9-864 

806404 

724150792 

898 

29-966 

9-647 

923521 

887503681 

961 

31-000 

9-868 

808201 

726572699 

899 

29-983 

9-651 

925444 

890277128 

962 

31-016 

9-871 

810000 

729000000 

900 

30-000 

9-654 

927369 

893056347 

963 

31-032 

9-875 

811801 

731432701 

901 

30-016 

9-658 

929296 

895841344 

964 

31-048 

9-878 

813604 

733870808 

902 

30-033 

9-662 

931225 

898632125 

965 

31-064 

9-881 

815409 

736314327 

903 

30-049 

9-665 

933156 

901428696 

966 

31-080 

9-885 

817216 

788763264 

904 

30-066 

9-669 

935089 

904231063 

967 

31-096 

9-888 

819025 

741217625 

905 

30-083 

9-672 

937024 

907039232 

968 

31-112 

9-892 

820836 

743677416 

906 

30-099 

9-676 

938961 

909853209 

969 

31-128 

9-895 

822649 

746142643 

907 

30-116 

9-679 

940900 

912673000 

970 

31-144 

9-898 

824464 

748613312 

908 

30-133 

9-683 

942841 

915498611 

971 

3T160 

9-902 

826281 

751089429 

909 

30-149 

9-686 

944784 

918330048 

972 

31-176 

9-905 

828100 

753571000 

910 

30-166 

9-690 

946729 

921167317 

973 

3T192 

9-909 

829921 

756058031 

911 

30-182 

9-694 

948676 

924010424 

974 

31-208 

9-912 

831744 

758550528 

912 

30-199 

9-697 

950625 

926859375 

975 

31-224 

9-915 

833569 

761048497 

913 

30-215 

9-701 

952576 

929714176 

976 

31-240 

9-919 

835396 

763551944 

914 

30-232 

9-704 

954529 

932574833 

977 

31-256 

9-922 

837225 

766060875 

915 

30-248 

9-708 

956484 

935441352 

978 

31-272 

9-926 

839056 

768575296 

916 

30-265 

9-711 

958441 

938313739 

979 

31-288 

9-929 

840889 

771095213 

917 

30-282 

9-715 

960400 

941192000 

980 

31-304 

9-932 

842724 

773620632 

918 

30-298 

9-718 

962361 

944076141 

981 

31-320 

9-936 

844561 

776151559 

919 

30-315 

9-722 

964324 

946966168 

982 

31-386 

9939 

846400 

778688000 

920 

30-331 

9-725 

966289 

949862087 

983 

31-852 

9-943 

848241 

781229961 

921 

30-347 

9729 

968256 

952763904 

984 

81-368 

9-946 

850084 

783777448 

922 

30-364 

9-732 

970225 

955671625 

985 

31-384 

9-949 

851929 

786330467 

923 

30-380 

9;736 

972196 

958585256 

986 

31-400 

9-953 

853776 

788889024 

924 

30-397 

9-739 

974169 

961504803 

987 

31-416 

9-956 

855625 

791453125 

925 

30-413 

9-743 

976144 

964430272 

988 

31-432 

9-959 

857476 

794022776 

926 

30-430 

9-746 

978121 

967361669 

989 

31-448 

9-963 

859329 

796597983 

927" 

30-446 

9-750 

980100 

970299000 

990 

31-464 

9-966 

861184 

799178752 

928 

30-463 

9-753 

982081 

973242271 

991 

31-480 

9-969 

863041 

801765089 

929 

30-479 

9-757 

984064 

976191488 

992 

31-496 

9-973 

864900 

804357000 

930 

30-495 

9-761 

986049 

979146657 

993 

31-511 

9-976 

866761 

806954491 

931 

30-512 

9-764 

988036 

982107784 

994 

31-527 

9-979 

868624 

809557568 

932 

30-528 

9-767 

990025 

985074875 

995 

31-543 

9-983 

870489 

812166237 

933 

30-545 

9-771 

992016 

988047936 

996 

31-559 

9-986 

872356 

814780504 

934 

30-561 

9-774 

994009 

991026973 

997 

31-575 

9-989 

874225 

817400375 

935 

30-577 

9-778 

996004 

994011992 

998 

31-591 

9-993 

876096 

820025856 

936 

30-594 

9-782 

998001 

997002999 

999 

31-606 

9-996 

877969 

822656953 

937 

30-610 

9-785 

1000000 

1000000000 

1000 

31-622 

10-000 

879844 

825293672 

938 

30-626 

9-788 

1000201 

1003003001 

1001 

31-638 

10-003 

881721 

827936019 

939 

30-643 

9-792 

1004004 

1006012008 

1002 

31-654 

10-006 

883600 

830584000 

940 

30-659 

9-795 

1006009 

1009027027 

1003 

31-670 

10-009 

885481 

833237621 

941 

30-676 

9-799 

1008016 

1012048064 

1004 

31-685 

10-013 

887364 

835896888 

942 

30-692 

9-802 

1010025 

1015075125 

1005 

31-701 

10-016 

889249 

838561807 

943 

30-708 

9-806 

1012036 

1018108216 

1006 

31-717 

10-019 

891136 

841232384 

944 

30-724 

9-809 

1014049 

1021147343 

1007 

31-733 

10-023 

893025 

843908625 

945 

30-740    9-813 

1016064 

1024192512  1008 

31-749 

10-026 

828 


APPENDIX. 
TABLE   OP   RECIPROCALS. 


0 

0 

•1 

2 

3 

•4 

5 

•6 

•7 

•8 

•9 

0 

oo 

10-000 

5-0000 

3-3333 

2-5000 

2-0000 

1-6667 

1-4286 

1-2500 

1-1111 

1 

1-00000 

•90909 

•83333 

•76923 

•71428 

•66667 

•62500 

•58823 

•55555 

•52631 

2 

•50000 

•47619 

•45454 

•43478 

•41667 

•40000 

•38461 

•37037 

•35714 

•34483 

3 

•33333 

•32258 

•31250 

•30303 

•29412 

•28571 

•27778 

•27027 

•26316 

•25641 

4 

•25000 

•24390 

•23810 

•23256 

•22727 

•22222 

•21739 

21277 

•2083.3 

•20408 

5 

•20000 

•19608 

•19231 

•18868 

•18519 

•18182 

•17857 

•17544 

•17241 

•16949 

6 

•16667 

•16393 

•16129 

•15873 

•15625 

•  15385 

•15152 

•14925 

•  14706 

•14493 

7 

•  14286 

•  14085 

•13889 

•  13699 

•13514 

•  13333 

•13158 

•12987 

•12821 

•12658 

8 

•12500 

•12346 

•12195 

•  12048 

•11905 

•11765 

•11628 

•11494 

•11364 

•11236 

9 

•11111 

•10989 

•10870 

•10753 

•10638 

•  10526 

•10417 

•10309 

•  10204 

•10101 

10 

•10000 

•09901 

•09804 

•09709 

•09615 

•09524 

•09434 

•09346 

•09259 

•09174 

11 

•09091 

•09009 

•08929 

•08850 

•08772 

•08696 

•08621 

•08547 

•08475 

•08403 

12 

•08333 

•08264 

•08197 

•08130 

•08065 

•08000 

•07937 

•07874 

•07813 

•07752 

13 

•07692 

•07634 

•07576 

•07519 

•07463 

•07407 

•07353 

•07299 

•07246 

•07194 

14 

•07143 

•07092 

•07042 

•06993 

•06944 

•06897 

•06849 

•06803 

•06757 

•06711 

15 

•06667 

•06623 

•06579 

•06536 

•06494 

•06452 

•06410 

•06369 

•06329 

•06289 

16 

•06250 

•06211 

•06173 

•06135 

•06098 

•06061 

•06024 

•05988 

•05952 

•05917 

17 

•05882 

•05848 

•05814 

•05780 

•05747 

•05714 

•05682 

•05650 

•05618 

•05587 

18 

•05556 

•05525 

•05495 

•05464 

•05435 

•05405 

•05376 

•05348 

•05319 

•05291 

19 

•05263 

•05236 

•05208 

•05181 

•05155 

•05128 

•05102 

•05076 

•05051 

•05025 

20 

•05000 

•04975 

•04950 

•04926 

•04902 

•04878 

•04854 

•04831 

•04808 

•04785 

21 

•04762 

•04739 

•04717 

•04695 

•04673 

•04651 

•04630 

•04608 

•04587 

•04566 

22 

•04545 

•04525 

•04505 

•04484 

•04464 

•04444 

•04425 

•04405 

•04386 

•04367 

23 

•04348 

•04329 

•04310 

•04292 

•04274 

•04255 

•04237 

•04219 

•04202 

•04184 

24 

•04167 

•04149 

•04132 

•04115 

•04098 

•04082 

•04065 

•04049 

•04032 

•04016 

25 

•04000 

•03984 

•03968 

•03953 

•03937 

•03922 

•03906 

•03891 

•03876 

•03861 

26 

•03846 

•03831 

•03817 

•03802 

•03788 

•03774 

•03759 

•03745 

•03731 

•03717 

27 

•03704 

•03690 

•03676 

•03663 

•03650 

•03636 

•03623 

•03610 

•03597 

•03584 

28 

•03571 

•03559 

•03546 

•03534 

•03521 

•03509 

•03497 

•03484 

•03472 

•03460 

29 

•03448 

•03436 

•03425 

•03413 

•03401 

•03390 

•03378 

•03367 

•03356 

•03344 

30 

•03333 

•03322 

•03311 

•03300 

•03289 

•03279 

•03268 

•03257 

•03247 

•03236 

31 

•03226 

•03215 

•03205 

•03195 

•03185 

•03175 

•03165 

•03155 

•03145 

•03135 

32 

•03125 

•03115 

•03106 

•03096 

•03086 

•03077 

•03067 

•03058 

•03049 

•03040 

33 

•03030 

•03021 

•03012 

•03003 

•02994 

•02985 

•02976 

•02967 

•02959 

•02950 

34 

•02941 

•02933 

•02924 

•02915 

•02907 

•02899 

•02890 

•02882 

•02874 

•02865 

35 

•02857 

•02849 

•02841 

•02833 

•02825 

•02817 

•02809 

•02801 

•02793 

•02786 

36 

•02778 

•02770 

•02762 

•02755 

•02747 

•02740 

•02732 

•02725 

•02717 

•02710 

37 

•02703 

•02695 

•02688 

•02681 

•02674 

•02667 

•02660 

•02653 

•02646 

•02639 

38 

•02632 

•02625 

•02618 

•02611 

•02604 

•02597 

•02591 

•02584 

•02577 

•02571 

39 

•02564 

•02558 

•02551 

•02545 

•02538 

•02532 

•02525 

•02519 

•02513 

•02506 

40 

•02500 

•02494 

•02488 

•02481 

•02475 

•02469 

•02463 

•02457 

•02451 

•02445 

41 

•02439 

•02433 

•02427 

•02421 

•02415 

•02410 

•02404 

•02398 

•02392 

•02387 

42 

•02381 

•02375 

•02370 

•02364 

•02358 

•02353 

•02347 

•02342 

•02336 

•02331 

43 

•02326 

•02320 

•02315 

•02309 

•02304 

•02299 

•02294 

-02288 

•02283 

•02278 

44 

•02273 

•02268 

•02262 

•02257 

•02252 

•02247 

02242 

•02237 

•02232 

•08227 

45 

•02222 

•02217 

•02212 

•02208 

•02203 

•02198 

•02193 

•02188 

•02183 

•02179 

46 

•02174 

•02169 

•02165 

•02160 

•02155 

•02151 

•02146 

•02141 

•02137 

•02132 

47 

•02128 

•02123 

•02119 

•02114 

•02110 

•02105 

•02101 

•02096 

•02092 

•02088 

48 

•02083 

•02079 

•02075 

•02070 

•02066 

•02062 

•02058 

•02053 

•02049 

•02045 

49 

•02041 

•02037 

•02033 

•02028 

•02024 

•02020 

•02016 

•02012 

•02008 

•02004 

•o 

•1 

•2 

•3 

4 

•5 

•6 

•7 

•8 

•9 

APPENDIX. 
TABLE  OF  RECIPROCALS—  Continued. 


829 


•0 

•1 

•2 

•3 

•4 

•5 

•6 

•7 

•8 

•9 

50- 

•02000 

•01996 

•01992 

•01988 

•01984 

•01980 

•01976 

•01972 

•01969 

•01965 

51 

•01961 

•01957 

•01953 

•01949 

•01946 

•01942 

•01938 

•01934 

•01931 

•01927 

52 

•01923 

•01919 

•01916 

•01912 

•01908 

•01905 

•01901 

•01898 

•01894 

•01890 

53 

•01887 

•01883 

•01880 

•01876 

•01873 

•01869 

•01866 

•01862 

•01859 

.  -01855 

54 

•01852 

•01848 

•01845 

•01842 

•01838 

•01835 

•01832 

•01828 

•01825 

•01821 

55 

•01818 

•01815 

•01812 

•01808 

•01805 

•01802 

•01799 

•01795 

•01792 

•01789 

56 

•01786 

•01783 

•01779 

•01776 

•01773 

•01770 

•01767 

•01764 

•01761 

•01757 

57 

•01754 

•01751 

•01748 

•01745 

•01742 

•01739 

•01736 

•01733 

•01730 

•01727 

58 

•01724 

•01721 

•01718 

•01715 

•01712 

•01709 

•01706 

•01704 

•01701 

•01698 

59 

•01695 

•01692 

•01689 

•01686 

•01684 

•01681 

•01678 

•01675 

•01672 

•01669 

60 

•01667 

•01664 

•01661 

•01658 

•01656 

•01653 

•01650 

•01647 

•01645 

•01642 

61 

•01639 

•01637 

•01634 

•01631 

•01629 

•01626 

•01623 

•01621 

•01618 

•01616 

62 

•01613 

•01610 

•01608 

•01605 

•01603 

•01600 

•01597 

•01595 

•01592 

•01590 

63 

•01587 

•01585 

•01582 

•01580 

•01577 

•01575 

•01572 

•01570 

•01567 

•01565 

64 

•01563 

•01560 

•01558 

•01555 

•01553 

•01550 

•01548 

•01546 

•01543 

•01541 

65 

•01538 

•01536 

•01534 

•01531 

•01529 

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66 

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67 

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68 

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69 

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70 

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71 

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72 

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73 

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74 

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75 

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76 

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77 

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78 

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79 

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80 

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81 

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82 

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87 

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APPENDIX. 


LATITUDES   AND   DEPARTURES. 


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APPENDIX. 


831 


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1-601 

3-383 

2-134 

4-229 

57f 

32* 

0-843 

0-537 

1-687 

1-075 

2-530 

1-612 

3-374 

2-149 

4-217 

57* 

32| 

0-841 

0-541 

1-682 

1-082 

2-523 

1-623 

3-364 

2-164 

4-205 

671 

33° 

0-839 

0-545 

1-677 

1-089 

2-516 

1-634 

3-355 

2-179 

4-193 

57° 

33± 

0-836 

0-548 

1-673 

1-097 

2-509 

1-645 

3-345 

2-193 

4-181 

56f 

33* 

0-834 

0-552 

1-668 

1-104 

2-502 

1-656 

3-336 

2-208 

4-169 

56* 

33f 

0-831 

0-556 

1-663 

1-111 

2-494 

1-667 

3-326 

2-222 

4-157 

56± 

34° 

0-829 

0-559 

1-658 

1-118 

2-487 

1-678 

3-316 

2-237 

4-145 

56° 

34J 

0-827 

0-563 

1-653 

1-126 

2-480 

1-688 

3-306 

2-251 

4-133 

56f 

34* 

0-824 

0-566 

1-648 

1-133 

2-472 

1-699 

3-297 

2-266 

4-121 

55* 

34| 

0-822 

0-570 

1-643 

1-140 

2-465 

1-710 

3-287 

2-280 

4-108 

65i 

35° 

0-819 

0-574 

1-638 

1-147 

2-457 

1721 

3-277 

2-294 

4-096 

55° 

85J 

0-817 

0-577 

1-633 

1-154 

2-450 

1-731 

3-267 

2-309 

4-083 

54J 

35* 

0-814 

0-581 

1-628 

1-161 

2-442 

1-742 

3-257 

2-323 

4-071 

54* 

35f 

0-812 

0-584 

1-623 

1-168 

2-435 

1-753 

3-246 

2-337 

4-058 

54± 

36° 

0-809 

0-588 

1-618 

1-176 

2-427 

1-763 

3-236 

2-351 

4-045 

54° 

36J 

0-806 

0-591 

1-613 

1-183 

2-419 

1-774 

3-226 

2-365 

4-032 

53f 

3<H 

0-804 

0-595 

1-608 

1-190 

2-412 

1-784 

3-215 

2-379 

4-019 

•53* 

36| 

0-801 

0-598 

1-603 

1-197 

2-404 

1-795 

3-205 

2-393 

4-006 

53J 

31° 

0-799 

0-602 

1-597 

1-204 

2-396 

1-805 

3-195 

2-407 

3-993 

53° 

37J 

0-796 

0-605 

1-592 

1-211 

2-388 

1-816 

3-184 

2-421 

3-980 

52f 

37* 

0-793 

0-609 

1-587 

1-218 

2-380 

1-826 

3-173 

2-435 

3-967 

52* 

37| 

0-791 

0-612 

1-581 

1-224 

2-372 

1-837 

3-163 

2-449 

3-953 

52i 

38° 

0-788 

0-616 

1-576 

1-231 

2-364 

1-847 

3-152 

2-463 

3-940 

52° 

88J 

0-785 

0-619 

1-571 

1-238 

2-356 

1-857 

3-141 

2-476 

3-927 

5  If 

38* 

0-783 

0-623 

1-565 

1-245 

2-348 

1-868 

3-130 

2-490 

3-913 

51* 

38f 

0-780 

0-626 

1-560 

1-252 

2-340 

1-878 

3-120 

2-504 

3-899 

511 

39° 

0-777 

0-629 

1-554 

1-259 

2-331 

1-888 

3-109 

2-517 

3-886 

51° 

39± 

0-774 

0-633 

1-549 

1-265 

2-323 

1-898 

3-098 

2-,  31 

3-872 

50f 

39* 

0-772 

0-636 

1-543 

1-272 

2-315 

1-908 

3-086 

2-544 

3-858 

50* 

39f 

0-769 

0-639 

1-538 

1-279 

2-307 

1-918 

3-075 

2-558 

3-844 

50J 

40° 

0-766 

0-643 

1-532 

1-286 

2-298 

1-928 

3-064 

2-571 

3-830 

50° 

40J 

0-763 

0-646 

1-526 

1-292 

2-290 

1-938 

3-053 

2-584 

3-816 

49f 

40* 

0-760 

0-649 

1-521 

1-299 

2-281 

1-948 

3042 

2-598 

3-802 

49* 

40f 

0-758 

0-653 

1-515 

1-306 

2-273 

1-958 

3-030 

2-611 

3-788 

491 

41° 

0-755 

0-656 

1-509 

1-312 

2-264 

1-968 

3019 

2-624 

3-774 

49° 

41J 

0-752 

0-659 

1-504 

1-319 

2-256 

1978 

3-007 

2-637 

3-759 

48f 

41* 

0-749 

0-663 

1-498 

1-325 

2-247 

1-988 

2-996 

2-650 

3-745 

48* 

41f 

0-746 

0-666 

1-492 

1-332 

2-238 

1-998 

2-984 

2-664 

3-730 

48i 

42° 

0-743 

0-669 

1-486 

1-338 

2-229 

2-007 

2-973 

2-677 

3-716 

48° 

42* 

0-740 

0-672 

1-480 

1-345 

2-221 

2-017 

2-961 

2-689 

3-701 

47f 

42* 

0-737 

0-676 

1-475 

1-351 

2-212 

2-027 

2-949 

2-702 

3-686 

47* 

42f 

0-734 

0-679 

1-469 

1-358 

2-203 

2-036 

2-937 

2-715 

3-672 

47i 

43° 

0-731 

0-682 

1-463 

1-364 

2-194 

2-046 

2-925 

2-728 

3-657 

41° 

43J 

0-728 

0-685 

1-457 

1-370 

2-185 

2-056 

2-913 

2-741 

3-642 

46f 

43* 

0-725 

0-688 

1-451 

1-377 

2-176 

2-065 

2-901 

2-753 

3-627 

46* 

43| 

0-722 

0-692 

1-445 

1-383 

2-167 

2-075 

2-889 

2-766 

3-612 

46i 

44° 

0-719 

0-695 

1-439 

1-389 

2-158- 

2-084 

2-877 

2-779 

3-597 

46° 

44i 

0-716 

0-698 

1-433 

1-396 

2-149 

2-093 

2-865 

2-791 

3-582 

45f 

44* 

0-713 

0-701 

1-427 

1-402 

2-140 

2-103 

2-853 

2-804 

3-566 

45* 

44f 

0-710 

0-704 

1-420 

1-408 

2-131 

2-112 

2-841 

.2-816 

3-551 

45J 

45° 

0-707 

1707 

1-414 

1-414 

2-121 

2-121 

2828 

2-828 

3-536 

45° 

f' 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

•1° 

] 

I 

i               * 

t 

J 

1 

4 

L 

& 

1 

APPENDIX. 


835 


LATITUDES   AND   DEPARTURES. 


t 

s 

6 

7 

S 

0 

* 

SO 

Dep. 

Lat.          Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

30° 

2-500 

5-196        3-000 

6-062 

3-500 

!    6-928 

4-000 

7-794 

4-500 

60° 

80$ 

2-519 

5-183 

3-023 

6-047 

3-526 

6-911 

4-030 

7-775 

4534 

69J 

301 

2-538 

5-170 

3-045 

6-031 

3-553 

6-893 

4-060 

7-755 

4-568 

591 

30f 

2-556 

5-156 

3-068 

6-016 

3-579 

6-875 

4-090 

7735 

4-602 

59} 

31° 

2-575 

5-143 

3-090 

6-000 

3-605 

6-857 

4-120 

7-715 

4-635 

591 

81* 

2-594 

5-129 

3113 

5-984 

3-631 

6-839 

4-150 

7-694 

4-669 

58f 

81* 

2-612 

5-116 

3-135 

5-968 

3-657 

6-821 

4-180 

7-674 

4-702 

581 

31f 

2-631    j 

5-102 

3-157 

5-952 

3-683 

6-803        4-210 

7-653 

4-736 

58} 

32° 

2-650 

5-088 

3-180 

5-936 

3-709 

6-784        4-239 

7-632 

4-769 

58° 

32}  ||    2-668 

5-074 

3-202 

5-920 

3-735 

6-766        4-269 

7-612 

4-802 

57f 

321        2-686 

5-060 

3-224 

5-904 

3-761 

6-747    :    4-298 

7-591 

4-836 

571 

32f 

2-705 

5-046 

3-246 

5-887 

8-787 

6-728    !    4328 

7-569 

4-869 

57} 

33° 

2-723 

5-032 

3-268 

5-871 

8-812 

6-709        4-357 

7-548 

4-902 

5T° 

33} 

2-741 

5-018 

3-290 

5-854 

8-838 

6-690    :    4-386 

7-627 

4-935 

56f 

331 

2-760 

5-003 

3-312 

5-837 

8-864 

6-671         4-416 

7-505 

4-967 

561 

33f 

2-778 

4'989 

3333 

5-820 

8-889 

6-652        4-445 

7-483 

5-000 

56} 

34° 

2-796 

4-974 

3-355 

5-803 

8-914 

6-632        4-474 

7-461 

5-033 

56° 

34} 

2-814 

4-960 

3-377 

5-786 

8-940 

6-613        4-502 

7-439 

5-065 

55f 

341 

2-832 

4-945 

3-398 

5-769 

8-965 

6-593 

4-531 

7-417 

5-098 

651 

34f 

2-850 

4-930 

3-420 

5-752 

8-990 

6-573 

4-560 

7-395 

5-130 

66} 

35° 

2-868 

4-915 

3-441 

5-734 

4-015 

6-553 

4-589 

7-372 

5-162 

"slF 

35} 

2-886 

4-900 

3-463 

5-716 

4-040 

6-533 

4-617 

7-350 

5-194 

54f 

351 

2-904 

4-885 

3-484 

5-699 

4-065 

6-513 

4-646 

7-827 

5-226 

541 

35| 

2-921 

4-869 

3-505 

5-681 

4-090 

6-493 

4-674 

7-304 

5-258 

64} 

36° 

2-939 

4-854 

3-527 

6-663 

4'115 

6-472 

4-702 

7-281 

5-290 

54° 

36} 

2-957 

4-839 

3-548 

5-645 

4-139 

6-452 

4-730 

7'2£8 

5-322 

53f 

361 

2974 

4-823 

3-569 

6-627 

4-164 

6-431 

4-759 

7-235 

5-353 

581 

36f 

2-992 

4-808 

3-590 

6-609 

4-188 

6-410 

4-787 

7-211 

5-385 

63} 

3T° 

3-009 

4-792 

3-611 

5-590 

4-213 

6-389 

4-816 

7-188 

5-416 

53° 

37} 

3-026 

4-776 

3-632 

5-572 

4-237 

6-368 

4-842 

7-164 

5-448 

52f 

371 

3-044 

4-760 

3-653 

5-554 

4-261 

6-347 

4-870 

7-140 

5-479 

621 

37f 

3-061 

4-744 

3-673 

5-535 

4-286 

6-326 

4-898 

7-116 

5-510 

52} 

38° 

3-078 

4-728 

3-694 

5-516 

4-310 

6-304 

4-925 

7-092 

5-541 

52° 

38} 

3-095 

4-712 

3-715 

5-497 

4-334 

6-283 

4-953 

7-068 

5-672 

61f 

381 

3-113 

4-696 

3-735 

5-478 

4-358 

6-261 

4-980 

7-043 

5-603 

511 

38| 

3-130 

4-679 

3-756 

5-459 

4-381 

6-239 

6-007 

7-019 

5-633 

51} 

39° 

3-147 

4-663 

3-776 

5-440 

4-405 

6-217 

6-035 

6994 

5-664 

51° 

39}  1 

3-164 

4-646 

3-796 

5-421 

4-429 

6-195 

6-062 

6-970 

6-694 

50f 

391 

3-180 

4-630 

3-816 

5-401 

4-453 

6-173 

6-089 

6-945 

5-725 

501 

39f 

3-197 

4-613 

3-837 

6-382 

4-476 

6-151 

5-116 

6-920 

5-765 

50} 

40° 

3-214 

4-596 

3-857 

6-362 

4-500 

6-128 

5-142 

6-894 

5-785 

50° 

40} 

3-231 

4-579 

3-877 

5'343 

4-523 

6-106 

5-169 

6-869 

5-815 

49f 

401 

3-247 

4-562 

3-897 

6-323 

4-546 

6-083 

5-196 

6-844 

5-845 

491 

40f 

3-264 

4-545 

3-917 

5-303 

4-569 

6-061 

6-222 

6-818 

5-875 

49} 

41° 

3-280    I 

4-528 

3-936 

5-283 

4-592 

6-038 

5-248 

6-792 

5-905 

49° 

41* 

3-297 

4-511 

3-956 

6-263 

4-615 

6-015 

6-275 

6-767 

5-934* 

48f 

411 

3-313 

4-494 

3-976 

6-243 

4-638 

5-992 

5-301 

6-741 

6-964 

481 

41* 

3-329 

4-476 

3-995 

5-222 

4-661 

6-968 

5-827 

6-715 

5-993 

fi 

42° 

3-346 

4-459 

4-015 

5-202 

4-684 

5-945 

5-353 

6-688 

6-022 

48° 

42} 

3-362 

4-441 

4-034 

5-182 

4-707 

5-922 

5-379 

6-662 

6-051 

47i 

421 

3-378 

4-424 

4-054 

5-161 

4-729 

5-898 

5-405 

6-635 

6'080 

471 

42| 

3-394 

4-406 

4-073 

6-140 

4-752 

5-875 

6-430 

6-609 

6-109 

4lt 

43° 

3-410 

4-388 

4-092 

5-119 

4-774 

5-851 

5-456 

6-582 

6-138 

4T° 

43} 

3-426 

4-370 

4-111 

5-099 

4-796 

5-827 

5-481 

6-556 

6-167 

46f 

484 

3-442 

4-352 

4-130 

5-078 

4-818 

5-803 

6-507 

6-528 

6-196 

461 

43| 

3-458    ! 

4-334 

4-149 

5-057 

4-841 

5-779 

5-532 

6-501 

6-224 

46} 

44° 

3-473 

4-316 

4-168 

5-035 

4-863 

5-755 

5-657 

6-474 

6-262 

46° 

44} 

3-489 

4-298 

4-187 

5-014 

4-885 

5-730 

5-582 

6-447 

6-280 

45| 

441 

3-505 

4-280 

4-206 

4-993 

4-906 

5-706 

5-607 

6-419 

6-308 

451 

44| 

3-520 

4-261 

4-224 

4-971 

4-928 

5-681 

6-632 

6-392 

6-336 

45} 

45° 

3-536 

4-243 

4-243 

4.950 

4-950 

5-657 

5-667 

6-364 

6-364 

45° 

be 

Lat. 

Dep. 

Lat. 

Dep.         Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

t"i 
(C3 

J 

5 

6 

7 

8 

9 

1 

836 


APPENDIX. 


NATURAL,     SINES     AND    COSINES. 


O° 

1° 

2" 

3° 

4=° 

/ 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

f 

0 

00000 

Unit. 

01745 

99985 

03490 

99939 

05234 

99863 

06976 

99756 

60 

1 

00029 

Unit. 

01774 

99984 

03519 

99938 

05263 

99861 

07005 

99754' 

59 

2 

00058 

Unit. 

01803 

99984 

03548 

99937 

05292 

99860 

07034 

99752 

58 

3 

00087 

Unit. 

01832 

99983 

03577 

99936 

05321 

99858 

07063 

99750 

57 

4 

00116 

Unit. 

01862 

99983 

03606 

99935 

05350 

99857 

07092 

99748 

56 

5 

00145 

Unit. 

01891 

99982 

03635 

99934 

05379 

99855 

07121 

99746 

55 

6 

00175 

Unit. 

01920 

99982 

03664 

99933 

05408 

99854 

07150 

99744 

54 

7 

00204 

Unit. 

01949 

99981 

03693 

99932 

05437 

99852 

07179 

99742 

53 

8 

00233 

Unit. 

01978 

99980 

03723 

99931 

05466 

99851 

07208 

99740 

52 

9 

00262 

Unit. 

02007 

99980 

03752 

99930 

05495 

99849 

07237 

99738 

51 

10 

00291 

Unit. 

02036 

99979 

03781 

99929 

05524 

99847 

07266 

99736 

50 

11 

00320 

99999 

02065 

99979 

03810 

99927 

05553 

99846 

07295 

99734 

49 

12 

00349 

99999 

02094 

99978 

03839 

99926 

05582 

99844 

07324 

99731 

48 

13 

00378 

99999 

02123 

99977 

03868 

99925 

05611 

99842 

07353 

99729 

47 

14 

00407 

99999 

02152 

99977 

03897 

99924 

05640 

99841 

07382 

99727 

46 

15 

00436 

99999 

02181 

99976 

03926 

99923 

05669 

99839 

07411 

99725 

45 

16 

00465 

99999 

02211 

99976 

03955 

99922 

05698 

99838 

07440 

99723 

44 

17 

00495 

99999 

02240 

99975 

03984 

99921 

05727 

99836 

07469 

99721 

43 

18 

00524 

99999 

02269 

99974 

04013 

99919 

05756 

99834 

07498 

99719 

42 

19 

00553 

99998 

02298 

99974 

04042 

99918 

05785 

99833 

07527 

99716 

41 

20 

00582 

99998 

02327 

99973 

04071 

99917 

05814 

99831 

07556 

99714 

40 

21 

00611 

99998 

02356 

99972 

04100 

99916 

05844 

99829 

07585 

99712 

39 

22 

00640 

99998 

02385 

99972 

04129 

99915 

05873 

99827 

07614 

99710 

38 

23 

00669 

99998 

02414 

99971 

04159 

99913 

05902 

99826 

07643 

99708 

37 

24 

00698 

99998 

02443 

99970 

04188 

99912 

05931 

99824 

07672 

99705 

36 

25 

00727 

99997 

02472 

99969 

04217 

99911 

05960 

99822 

07701 

99703 

35 

26 

00756 

99997 

02501 

99969 

04246 

99910 

05989 

99821 

07730 

99701 

34 

27 

00785 

99997 

02530 

99968 

04275 

99909 

06018 

99819 

07759 

99699 

33 

28 

00814 

99997 

02560 

99967 

04304 

99907 

06047 

99817 

07788 

99696 

32 

29 

00844 

99996 

02589 

99966 

04333 

99906 

06076 

99815 

07817 

99694 

31 

30 

00873 

99996 

02618 

99966 

04362 

99905 

06105 

99813 

07846 

99692 

30 

31 

00902 

99996 

02647 

99P65 

04391 

99904 

06134 

99812 

07875 

99689 

29 

32 

00931 

99996 

02676 

99964 

04420 

99902 

06163 

99810 

07904 

99687 

28 

33 

00960 

99995 

02705 

99963 

04449 

99901 

06192 

99808 

07933 

99685 

27 

34 

00989 

99995 

02734 

99963 

04478 

99900 

06221 

99806 

07962 

99683 

26 

35 

01018 

99995 

02763 

99962 

04507 

99898 

06250 

99804 

07991 

99680 

25 

36 

01047 

99995 

02792 

99961 

04536 

99897 

06279 

99803 

08020 

99678 

24 

37 

01076 

99994 

02821 

99960  i 

04565 

99896 

06308 

99801 

08049 

99676 

23 

38 

01105 

99994 

02850 

99959 

04594 

99894 

06337 

99799 

08078 

99673 

22 

39 

01134 

99994 

02879 

99959 

04623 

99893 

06366 

99797 

08107 

99671 

21 

40 

01164 

99993 

02908 

99958 

04653 

99892 

06395 

99795 

08136 

99668 

20 

41 

01193 

99993 

02938 

99957 

04682 

99890 

06424 

99793 

08165 

99666 

19 

42 

01222 

99993 

02967 

99956 

04711 

99889 

06453 

99792 

08194 

99664 

18 

43 

01251 

99992 

02996 

99955 

04740 

99888 

06482 

99790 

08223 

99661 

17 

44 

01280 

99992 

03025 

99954 

04769 

99886 

06511 

99788 

08252 

99659 

16 

45 

01309 

99991 

03054 

99953 

04798 

99885 

06540 

99786 

08281 

99657 

15 

46 

01338 

99991 

03083 

99952 

04827 

99883 

06569 

99784 

08310 

99654 

14 

47 

01367 

99991 

03112 

99952 

04856 

99882 

06598 

99782 

08339 

99652 

13 

48 

01396 

99990 

03141 

99951 

04885 

99881  ! 

06627 

99780 

08368 

99649 

12 

49 

01425 

99990 

03170 

99950 

04914 

99879 

06656 

99778 

08397 

99647 

11 

50 

01454 

99989 

03199 

99949 

04943 

99878 

06685 

99776 

08426 

99644 

10 

51 

01483 

99989 

03228 

99948 

04972 

99876 

06714 

99774 

08455 

99642 

9 

52 

01513 

99989 

03257 

99947 

05001 

99875 

06743 

99772 

08484 

99639 

8 

53 

01542 

99988 

03286 

99946 

05030 

99873 

06773 

99770 

08513 

99637 

7 

54 

01571 

99988 

03316 

99945 

05059 

99872 

06802 

99768 

08542 

99635 

6 

55 

01600 

99987 

03345 

99944 

05088 

99870 

06831 

99766 

08571 

99632 

5 

56 

01629 

99987 

03374 

99943 

05117 

99869 

06860 

99764 

08600 

99630 

4 

57 

01658 

99986 

03403 

99942 

05146 

99867 

06889 

99762 

08629 

99627 

3 

58 

01687 

99986 

03432 

99941 

05175 

99866 

06918 

99760 

08658 

99625 

2 

59 

01716 

99985 

03461 

99940 

05205 

99864 

06947 

99758 

08687 

99622 

1 

60 

01745 

99985 

03490 

99939 

05234 

99863 

06976 

99756 

08716 

99619 

0 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

t 

8O° 

88°     | 

87" 

8G° 

85° 

/ 

APPENDIX. 


837 


NATURAL.    SINKS     AND    COSINES. 


5° 

G° 

7-0 

8° 

0° 

/ 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

/ 

0 

08716 

99619 

10453 

99452 

12187 

99255 

13917 

99027 

15643 

98769 

60 

1 

08745 

99617 

10482 

99449 

12216 

99251 

13946 

99023 

15672 

98764 

59 

2 

08774 

99614 

10511 

99446 

12245 

99248 

13975 

99019 

15701 

98760 

58 

3 

08803 

99612 

10540 

99443 

12274 

99244 

14004 

99015 

15730 

98755 

57 

4 

08831 

99609 

10569 

99440 

12302 

99240 

14033 

99011 

15758 

98751 

56 

5 

08860 

99607 

10597 

99437 

12331 

99237 

14061 

99006 

15787 

98746 

55 

6 

08889 

99604 

10626 

99434 

12360 

99233 

14090 

99002 

15816 

98741 

54 

7 

08918 

99602 

10655 

99431 

12389 

99230 

14119 

98998 

15845 

98737 

53 

8 

08947 

99599 

10684 

99428 

12418 

99226 

14148 

98994 

15873 

98732 

52 

9 

08976 

99596 

10713 

99424 

12447 

99222 

14177 

98990 

15902 

98728 

51 

10 

09005 

99594 

10742 

99421 

12476 

99219 

14205 

98986 

15931 

98723 

50 

11 

09034 

99591 

10771 

99418 

12504 

99215 

14234 

98982 

15959 

98718 

49 

12 

09063 

99588 

10800 

99415 

12533 

99211 

14263 

98978 

15988 

98714 

48 

13 

09092 

99586 

10829 

99412 

12562 

99208 

14292 

98973 

16017 

98709 

47 

14 

09121 

99583 

10858 

99409 

12591 

99204 

14320 

98969 

16046 

98704 

46 

15 

09150 

99580 

10887 

99406 

12620 

99200 

14349 

98965 

16074 

98700 

45 

16 

09179 

99578 

10916 

99402 

12649 

99197 

14378 

98961 

16103 

98695 

44 

17 

09208 

99575 

10945 

99399 

12678 

99193 

14407 

98957 

16132 

98690 

43 

18 

09237 

99572 

10973 

99396 

12706 

99189 

14436 

98953 

16160 

98686 

42 

19 

09266 

99570 

11002 

99393 

12735 

99186 

14464 

98948 

16189 

98681 

41 

20 

09295 

99567 

11031 

99390 

12764 

99182 

14493 

98944 

16218 

98676 

40 

21 

09324 

99564 

11060 

99386 

12793 

99178 

14522 

98940 

16246 

98671 

39 

22 

09353 

99562 

11089 

99383 

12822 

99175 

14551 

98936 

16275 

98667 

38 

23 

09382 

99559 

11118 

99380 

12851 

99171 

14580 

98931 

16304 

98662 

37 

24 

09411 

99556 

11147 

99377 

12880 

99167 

14608 

98927 

16333 

98657 

36 

25 

09440 

99553 

11176 

99374 

12908 

99163 

14637 

98923 

16361 

98652 

35 

26 

09469 

99551 

11205 

99370 

12937 

99160 

14666 

98919- 

16390 

98648 

34 

27 

09498 

99548 

11234 

99367 

12966 

99156 

14695 

98914 

16419 

98643 

33 

28 

09527 

99545 

11263 

99364 

12995 

99152 

14723 

98910 

16447 

98638 

32 

29 

09556 

99542 

11291 

99360 

13024 

99148 

14752 

98906 

16476 

98633 

31 

30 

09585 

99540 

11320 

99357 

13053 

99144 

14781 

98902 

16505 

98629 

30 

31 

09614 

99537 

11349 

99354 

13081 

99141 

14810 

98897 

16533 

98624 

29 

32 

09642 

99534 

11378 

99351 

13110 

99137 

14838 

98893 

16562 

98619 

28 

33 

09671 

99531 

11407 

99347 

13139 

99133 

14867 

98889 

16591 

98614 

27 

34 

09700 

99528 

11436 

99344 

13168 

99129 

14896 

98884 

16620 

98609 

26 

35 

09729 

99526 

11465 

99341 

13197 

99125 

14925 

98880 

16648 

98604 

25 

36 

09758 

99523 

11494 

99337 

13226 

99122 

14954 

98876 

16677 

98600 

24 

37 

09787 

99520 

11523 

99334 

13254 

99118 

14982 

98871 

16706 

98595 

23 

38 

09816 

99517 

11552 

99331 

13283 

99114 

15011 

98867 

16734 

98590 

22 

39 

09845 

99514 

11580 

99327 

13312 

99110 

15040 

98863 

16763 

98585 

21 

40 

09874 

99511 

11609 

99324 

13341 

99106 

15069 

98858 

16792 

98580 

20 

41 

09903 

99508 

11638 

99320 

13370 

99102 

15097 

98854 

16820 

98575 

19 

42 

09932 

99506 

11667 

99317 

13399 

99098 

15126 

98849 

16849 

98570 

18 

43 

09961 

99503 

11696 

99314 

13427 

99094 

15155 

98845 

16878 

98565 

17 

44 

09990 

99500 

11725 

99310 

13456 

99091 

15184 

98841 

16906 

98561 

16 

45 

10019 

99497 

11754 

99307 

13485 

99087 

15212 

98836 

16935 

98556 

15 

46 

10048 

99494 

11783 

99303 

13514 

99083 

15241 

98832 

16964 

98551 

14 

47 

10077 

99491 

11812 

99300 

13543 

99079 

15270 

98827 

16992 

98546 

13 

48 

10106 

99488 

11840 

99297 

13572 

99075 

15299 

98823 

17021 

98541 

12 

49 

10135 

99485 

11869 

99293 

13600 

99071 

15327 

98818 

17050 

98536 

11 

50 

10164 

99482 

11898 

99290 

13629 

99067 

15356 

98814 

17078 

98531 

10 

51 

10192 

99479 

11927 

99286 

13658 

99063 

15385 

98809 

17107 

98526 

9 

52 

10221 

99476 

11956 

99283 

13687 

99059 

15414 

98805 

17136 

98521 

8 

53 

10250 

99473 

11985 

99279 

13716 

99055 

15442 

98800 

17164 

98516 

7 

54 

10279 

99470 

12014 

99276 

13744 

99051 

15471 

98796 

17193 

98511 

6 

55 

10308 

99467 

12043 

99272 

13773 

99047 

15500 

98791 

17222 

98506 

5 

56 

10337 

99464 

12071 

99269 

13802 

99043 

15529 

98787 

17250 

98501 

4 

57 

10366 

99461 

12100 

99265 

13831 

99039 

15557 

98782 

17279 

98496 

3 

58 

10395 

99458 

12129 

99262 

13860 

99035 

15586 

98778 

17308 

98491 

2 

59 

10424 

99455 

12158 

99258 

13889 

99031 

15615 

98773 

17336 

98486 

1 

60 

10453 

99452 

12187 

99255 

13917 

99027 

15643 

98769 

17365 

98481 

0 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

/ 

84° 

83° 

83° 

81" 

8O° 

/ 

838 


APPENDIX. 


NATURAL,     SINES     AND    COSINES. 


1O« 

11° 

13° 

13° 

14° 

/ 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

f 

0 

17365 

98481 

19081 

98163 

20791 

97815 

22495 

97437 

24192 

97030 

60 

1 

17393 

98476 

19109 

98157 

20820 

97809 

22523 

97430  ! 

24220 

97023 

59 

2 

17422 

98471 

19138 

98152 

20848 

97803 

22552 

97424 

24249 

97015 

58 

3 

17451 

98466 

19167 

98146 

20877 

97797 

22580 

97417 

24277 

97008 

57 

4 

17479 

98461 

19195 

98140 

20905 

97791 

22608 

97411 

24305 

97001 

56 

5 

17508 

98455 

19224 

98135 

20933 

97784 

22637 

97404 

24333 

96994   55 

6 

17537 

98450 

19252 

98129 

20962 

97778 

22665 

:  97398 

24362 

96987   54 

7 

17565 

98445 

19281 

98124 

20990 

97772 

22693 

97391 

24390 

96980 

53 

8 

17594 

98440 

19309 

98118 

21019 

97766 

22722 

97384 

24418 

96973 

52 

9 

17623 

98435 

19338 

98112 

21047 

97760 

22750 

j  97378 

24446 

96966 

51 

10 

17651 

98430 

19366 

98107 

21076 

97754 

22778 

:  97371 

24474 

96959 

50 

11 

17680 

98425 

19395 

98101 

21104 

97748 

22807 

97365 

24503 

96952 

49 

12 

17708 

98420 

19423 

98096 

21132 

97742 

22835 

97358 

24531 

96945 

48 

13 

17737 

98414 

19452 

98090 

21161 

97735 

22863 

97351 

24559 

96937 

;47 

14 

17766 

98409 

19481 

98084 

21189 

97729 

22892 

97345 

24587 

96930 

46: 

15 

17794 

98404 

19509 

98079 

21218 

97723   22920 

97338 

24615 

96923 

45 

16 

17823 

98399 

19538 

98073 

21246 

97717  ''  22948 

97331 

24644 

96916 

44 

17 

17852 

98394  ! 

19566 

98067 

21275 

97711  1  22977 

97325 

24672 

96909 

43 

18 

17880 

98389 

19595 

98061 

21303 

97705  1  23005 

97318 

24700 

96902 

'42 

19 

17909 

98383 

19623 

98056 

21331 

97698  !  23033 

97311  : 

24728 

96894 

41 

20 

17937 

98378 

19652 

98050 

21360 

97692   23062 

97304 

24756 

1  96887 

40 

21 

17966 

98373 

19680 

98044 

21388 

97686  ;  23090 

97298 

24784 

96880 

39 

22 

17995 

98368 

19709 

98039 

21417 

97680  i  23118 

97291 

24813 

96873 

:38 

23 

18023 

98362 

19737 

98033 

21445 

97673  ;  23146 

97284 

24841 

96866 

37 

24 

18052 

98357 

19766 

98027 

21474 

97667 

23175 

97278 

24869 

96858   36 

25 

18081 

98352 

19794 

98021 

21502 

97661 

23203 

97271 

24897 

96851   35 

26 

18109 

98347 

19823 

98016 

21530 

97655 

23231 

97264 

24925 

'96844 

34 

27 

18138 

98341 

19851 

98010 

21559 

97648 

23260 

97257 

24954 

96837 

33 

28 

18166 

98336 

19880 

98004 

21587 

97642 

23288 

97251 

24982 

96829 

32 

29 

18195 

98331 

19908 

97998 

21616 

97636 

23316 

97244 

25010 

96822 

31 

30 

18224 

98325 

19937 

97992 

21644 

97630 

23345 

97237 

25038 

;  96815 

30 

31 

18252 

98320 

19965 

97987 

21672 

97623 

23373 

97230 

25066 

96807 

29 

32 

18281 

98315 

19994 

97981 

21701 

97617 

23401 

97223 

25094 

96800 

28. 

33 

18309 

98310 

20022 

97975 

21729 

97611 

23429 

97217 

25122 

96793 

27 

34 

18338 

98304 

20051 

97969 

21758 

97604 

23458 

97210 

25151 

96786 

26 

35 

18367 

98299 

20079 

97963 

21786 

97&9S 

23486 

'  97203 

25179 

96778 

25 

36 

18395 

98294 

20108 

97958 

21814 

97592 

23514 

:  97196 

25207 

96771 

24 

37 

18424 

98288 

20136 

97952 

21843 

97585 

23542 

97189 

25235 

96764 

23 

38 

18452 

98283 

20165 

97946 

21871 

97579 

23571 

97182 

25263 

96756 

22 

39 

18481 

98277 

20193 

97940 

21899 

97573 

23599 

97176 

25291 

96749 

21 

40 

18509 

98272 

20222 

97934 

21928 

97566 

23627 

97169 

25320 

96742 

20 

41 

18538 

98267 

20250 

97928 

21956 

97560 

23656 

97162 

25348 

96734 

19 

42 

18567 

98261 

20279 

97922 

21985 

97553 

23684 

97155 

25376 

96727 

18 

43 

18595 

98256 

20307 

97916 

22013 

97547 

23712 

97148 

25404 

96719 

17 

44 

18624 

98250 

20336 

97910 

22041 

97541 

23740 

97141 

25432 

96712 

16 

45 

18652 

98245 

20364 

97905 

22070 

97534 

23769 

97134 

25460 

96705 

15 

46 

18681 

98240 

20393 

97899 

22098 

97528 

23797 

97127 

25488 

96697 

14 

47 

18710 

98234 

20421 

97893 

22126 

97521 

23825 

97120 

25516 

96690 

13 

48. 

18738 

98229 

20450 

97887 

22155 

97515 

23853 

97113 

25545 

96682 

12 

49 

18767 

98223 

20478 

97881 

22183 

97508 

23882 

97106 

25573 

96675 

11 

50 

18795 

98218 

20507 

97875 

22212 

97502 

23910 

97100 

25601 

96667 

10 

51 

18824 

98212 

20535 

97869 

22240 

97496 

23938 

97093 

25629 

96660 

9 

52 

18852 

98207 

20563 

97863 

22268 

97489 

23966 

97086 

25657 

96653 

8 

53 

18881 

98201 

20592 

97857 

22297 

97483 

23995 

97079 

25685 

96645 

7 

54 

18910 

98196 

20620 

97851 

22325 

97476 

24023 

97072 

25713 

96638 

6 

55 

18938 

98190 

20649 

97845 

22353 

97470 

24051 

97065 

25741 

96630 

5 

56 

18967 

98185 

20677 

97839 

22382 

97463 

24079 

97058 

25769 

96623 

4 

57 

18995 

98179 

20706 

97833 

22410 

97457 

24108 

97051 

25798 

96615 

3 

58 

19024 

98174 

20734 

97827 

22438 

97450 

24136 

97044 

25826 

96608 

2 

59 

19052 

98168 

20763 

97821 

22467 

97444 

24164 

97037 

25854 

96600 

1 

60 

19081 

98163 

20791 

97815 

22495 

97437 

24192 

97030 

25882 

96593 

0 

Cosine. 

:  Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

/ 

70° 

78° 

77° 

70" 

75° 

f 

APPENDIX. 


NATURAL,     SINES     AND    COSINES. 


15° 

16° 

17° 

18° 

10" 

/ 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

/  • 

0 

25882 

96593 

27564 

96126 

29237 

95630 

30902 

95106 

32557 

94552 

60 

1 

25910 

96585 

27592 

96118 

29265 

95622 

30929 

95097 

32584 

94542 

59 

2 

25938 

96578 

27620 

96110 

29293 

95613 

30957 

95088 

32612 

94533 

58 

3 

25966 

96570 

27648 

96102 

29321 

95605 

30985 

95079 

32639 

94523 

57 

4 

25994 

96562 

27676 

96094 

29348 

:95596 

31012 

95070 

32667 

94514 

56 

5 

26022 

96555 

27704 

96086 

29376 

95588 

31040 

95061 

32694 

94504 

55 

6 

26050 

96547 

27731 

96078 

29404 

95579 

31068 

95052 

32722 

94495 

54 

7 

26079 

96540 

27759 

96070 

29432 

95571 

31095 

95043 

32749 

94485 

53 

8 

26107 

96532 

27787 

96062 

29460 

95562 

31123 

!95033 

32777 

94476 

52 

9 

26135 

96524 

27815 

96054 

29487 

95554 

31151 

J95024 

32804 

:94466 

51 

10 

26163 

96517 

27843 

96046 

29515 

95545 

31178 

J95015 

32832 

94457 

:50 

11 

26191 

96509 

27871 

96037 

29543 

95536 

31206 

95006 

32859 

94447 

49 

12 

26219 

96502 

27899 

96029 

29571 

95528 

31233 

94997 

32887 

94438 

48 

13 

26247 

96494 

27927 

96021 

29599 

95519 

31261 

94988 

32914 

94428 

47 

14 

26275 

96486 

27955 

96013 

29626 

95511 

31289 

94979 

32942 

94418 

46 

15 

26303 

96479 

27983 

96005 

29654 

95502 

31316 

94970 

32969 

94409 

45 

16 

26331 

96471 

28011 

95997 

29682 

95493 

31344 

94961 

32997 

'94399 

44 

17 

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19 

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41 

20 

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40 

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27 

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41 

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19 

42 

27060 

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28736 

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30403 

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18 

43 

27088 

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30431 

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32089 

94712 

33737 

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17 

44 

27116 

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32116 

94702 

33764 

94127 

16 

45 

27144 

96246 

28820 

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30486 

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32144 

94693 

33792 

94118 

15 

46 

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32171 

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14 

47 

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12 

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50 

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10 

51 

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32309 

94637 

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9 

52 

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29015 

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30680 

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32337 

94627 

33983 

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8 

53 

27368 

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29042 

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30708 

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32364 

94618 

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7 

54 

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96174 

29070 

95681 

30736 

95159 

32392 

94609 

34038 

94029 

6 

55 

27424 

96166 

29098 

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30763 

95150 

32419 

94599 

34065 

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5 

56  !  27452 

96158 

29126 

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32447 

94590 

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4 

57 

27480 

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3 

58 

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32502 

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2 

59 

27536 

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95639  !  30874 

95115 

32529 

94561 

34175 

93979 

1 

60 

27564 

96126 

29237 

95630 

30902 

95106 

32557 

94552 

34202 

93969 

i  0 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

/ 

/ 

74°           73° 

73° 

71° 

7O° 

840 


APPENDIX. 


NATURAL.     SINES     AND    COSINES. 


30° 

31° 

22" 

23" 

34=° 

/ 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

/ 

0 

34202 

93969 

35837 

93358 

37461 

92718 

39073 

92050 

40674 

91355 

60 

1 

34229 

93959 

35864 

93348 

37488 

92707 

39100 

92039 

40700 

91343 

59 

2 

34257 

93949 

35891 

93337 

37515 

92697 

39127 

92028 

40727 

91331 

58 

3 

34284 

93939 

35918 

93327 

37542 

92686 

39153 

92016 

40753 

91319 

57 

4 

34311 

93929 

35945 

93316 

37569 

92675 

39180 

92005 

40780 

91307 

56 

5 

34339 

93919 

35973 

93306 

37595 

92664 

39207 

91994 

40806 

91295 

55 

6 

34366 

93909 

36000 

93295 

37622 

92653 

39234 

91982 

40833 

91283 

54 

7 

34393 

93899 

36027 

93285 

37649 

92642 

39260 

91971 

40860 

91272 

53 

8 

34421 

93889 

36054 

93274 

37676 

92631 

39287 

91959 

40886 

91260 

52 

9 

34448 

93879 

36081 

93264 

37703 

92620 

39314 

91948 

40913 

91248 

51 

10 

34475 

93869 

36108 

93253 

37730 

92609 

39341 

91936 

40939 

91236 

50 

11 

34503 

93859 

36135 

93243 

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92598 

39367 

91925 

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91224 

49 

12 

34530 

93849 

36162 

93232 

37784 

92587 

39394 

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40992 

91212 

48 

13 

34557 

93839 

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91902 

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47 

14 

34584 

93829 

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46 

15 

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45 

16 

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44 

17 

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91856 

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91152 

43 

18 

34694 

93789 

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91845 

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42 

19 

34721 

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39581 

91833 

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91128 

41 

20 

34748 

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40 

21 

34775 

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39 

22 

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38 

23 

34830 

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91080 

37 

24 

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93728 

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38107 

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91775 

41310 

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36 

25 

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91056  ' 

35. 

26 

34912 

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34 

27 

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91741 

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91032 

33 

28 

34966 

93688 

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93063 

38215 

92410 

39822 

91729 

41416 

91020 

32 

29 

34993 

93677 

36623 

93052 

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39848 

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41443 

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31 

30 

35021 

93667 

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38268 

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30 

31 

35048 

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29 

32 

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28 

33 

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27 

34 

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41 

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18 

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17 

44 

35402 

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92892 

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92231 

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41840 

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16 

45 

35429 

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15 

46 

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14 

47 

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40328 

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41919 

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13 

48 

35511 

93483 

37137 

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92186 

40355 

91496 

41945 

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12 

49 

35538 

93472 

37164 

92838 

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92175 

40381 

91484 

41972 

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11 

50 

35565 

93462 

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92827 

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92164 

40408 

91472 

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10 

51 

35592 

93452 

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92816 

38832 

92152 

40434 

91461 

42024 

90741 

9 

52 

35619 

93441 

37245 

92805 

38859 

92141 

40461 

91449 

42051 

90729 

8 

53 

35647 

93431 

37272 

92794 

38886 

92130 

40488 

91437 

42077 

90717 

7 

54 

35674 

93420 

37299 

92784 

38912 

92119 

40514 

91425 

42104 

90704 

6 

55 

35701 

93410 

37326 

92773 

38939 

92107 

40541 

91414 

42130 

90692 

5 

56 

35728 

93400 

37353 

92762 

38966 

92096 

40567 

91402 

42156 

90680 

4 

57 

35755 

93389 

37380 

92751 

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92085 

40594 

91390 

42183 

90668 

3 

58 

35782 

93379 

37407 

92740 

39020 

92073 

40621 

91378 

42209 

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2 

59 

35810 

93368 

37434 

92729 

39046 

92062 

40647 

91366 

42235 

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1 

00 

35837 

93358 

37461 

92718 

39073 

92050 

40674 

91355 

42262 

90631 

0 

I 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

eo« 

es° 

G7° 

GO" 

05° 

/ 

APPENDIX. 


841 


NATURAL.     SINES     AND    COSINES. 


35° 

30° 

37° 

3S« 

39° 

Siiie. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine 

Sine. 

Cosine 

Sine. 

Cosine 

/ 

0 

42262 

90631 

43837 

89879 

45399 

89101 

46947 

88295 

48481 

87462 

60 

1 

42288 

90618 

43863 

89867 

45425 

89087 

46973 

88281 

48506 

87448 

59 

2 

42315 

90606 

43889 

89854 

45451 

89074 

46999 

88267 

48532 

87434 

58 

3 

42341 

90594 

43916 

89841 

45477 

89061 

47024 

88254 

48557 

87420 

57 

4 

42367 

90582 

43942 

89828 

45503 

89048 

47050 

88240 

48583 

87406 

56 

5 

42394 

90569 

43968 

89816 

45529 

89035 

47076 

88226 

48608 

87391 

55 

6 

42420 

90557 

43994 

89803 

45554 

89021 

47101 

88213 

48634 

87377 

54 

7 

42446 

90545 

44020 

89790 

45580 

89008 

47127 

88199 

48659 

87363 

53 

8 

42473 

90532 

44046 

89777 

45606 

88995 

47153 

88185 

48684 

87349 

52 

9 

42499 

90520 

44072 

89764 

45632 

88981 

47178 

88172 

48710 

87335 

51 

10 

42525 

90507 

44098 

89752 

45658 

88968 

47204 

88158 

48735 

87321 

50 

11 

42552 

90495 

44124 

89739 

45684 

88955 

47229 

88144 

48761 

87306 

49 

12 

42578 

90483 

44151 

89726 

45710 

88942 

47255 

88130 

48786 

87292 

48 

13 

42604 

90470 

44177 

89713 

45736 

88928 

47281 

88117 

48811 

87278 

47 

14 

42631 

90458 

44203 

89700 

45762 

88915 

47306 

88103 

48837 

87264 

46 

15 

42657 

90446 

44229 

89687 

45787 

88902 

47332 

88089 

48862 

87250 

45 

16 

42683 

90433 

44255 

89674 

45813 

88888 

47358 

88075 

48888 

87235 

44 

17 

42709 

90421 

44281 

89662 

45839 

88875 

47383 

88062 

48913 

87221 

43 

18 

42736 

90408 

44307 

89649 

45865 

88862 

47409 

88048 

48938 

87207 

42 

19 

42762 

90396 

44333 

89636 

45891 

88848 

47434 

88034 

48964 

87193 

41 

20 

42788 

90383 

•44359 

89623 

45917 

88835 

47460 

88020 

48989 

87178 

40 

21 

42815 

90371 

44385 

89610 

45942 

88822 

47486 

88006 

49014 

87164 

39 

22 

42841 

90358 

44411 

89597 

45968 

88808 

47511 

87993 

49040 

87150 

38 

23 

42867 

90346 

44437 

89584 

45994 

88795 

47537 

87979 

49065 

87136 

37 

24 

42894 

90334 

44464 

89571 

46020 

88782 

47562 

87965 

49090 

87121 

36 

25 

42920 

90321 

44490 

89558 

46046 

88768 

47588 

87951 

49116 

87107 

35 

26 

42946 

90309 

44516 

89545 

46072 

88755 

47614 

87937 

49141 

87093 

34 

27 

42972 

90296 

44542 

89532 

46097 

88741 

47639 

87923 

49166 

87079 

33 

28 

42999 

90284 

44568 

89519 

46123 

88728 

47665 

87909 

49192 

87064 

32 

29 

43025 

90271 

44594 

89506 

46149 

88715 

47690 

87896 

49217 

87050 

31 

30 

43051 

90259 

44620 

89493 

46175 

88701 

47716 

87882 

49242 

87036 

30 

31 

43077 

90246 

44646 

89480 

46201 

88688 

47741 

87868 

49268 

87021 

29 

32 

43104 

90233 

44672 

89467 

46226 

88674 

47767 

87854 

49293 

87007 

28 

33 

43130 

90221 

44698 

89454 

46252 

88661 

47793 

87840 

49318 

86993 

27 

34 

43156 

90208 

44724 

89441 

46278 

88647 

47818 

87826 

49344 

86978 

26 

35 

43182 

90196 

44750 

89428 

46304 

88634 

47844 

87812 

49369 

86964 

25 

36 

43209 

90183 

44776 

89415 

46330 

88620 

47869 

87798 

49394 

86949 

24 

37 

43235 

90171 

44802 

89402 

46355 

88607 

47895 

87784 

49419 

86935 

23 

38 

43261 

90158 

44828 

89389 

46381 

88593 

47920 

87770 

49445 

86921 

22 

39 

43287 

90146 

44854 

89376 

46407 

88580 

47946 

87756 

49470 

86906 

21 

40 

43313 

90133 

44880 

89363 

46433 

88566 

47971 

87743 

49495 

86892 

20 

41 

43340 

90120 

44906 

89350 

46458 

88553 

47997 

87729 

49521 

86878 

19 

42 

43366 

90108 

44932 

89337 

46484 

88539 

48022 

87715 

49546 

86863 

18 

43 

43392 

90095 

44958 

89324 

46510 

88526 

48048 

87701 

49571 

86849 

17 

44 

43418 

90082 

44984 

89311 

46536 

88512 

48073 

87687 

49596 

86834 

16 

45 

43445 

90070 

45010 

89298 

46561 

88499 

48099 

87673 

49622 

86820 

15 

46 

43471 

90057 

45036 

89285 

46587 

88485 

48124 

87659 

49647 

86805 

14 

47 

43497 

90045 

45062 

89272 

46613 

88472 

48150 

87645 

49672 

86791 

13 

48 

43523 

90032 

45088 

89259 

46639 

88458 

48175 

87631 

49697 

86777 

12 

49 

43549 

90019 

45114 

89245 

46664 

88445 

48201 

87617 

49723 

86762 

11 

50 

43575 

90007 

45140 

89232 

46690 

88431 

48226 

87603 

49748 

86748 

10 

51 

43602 

89994 

45166 

89219 

46716 

88417 

48252 

87589 

49773 

86733 

9 

52 

43628 

89981 

45192 

89206 

46742 

88404 

48277 

87575 

49798 

86719 

8 

53 

43654 

89968 

45218 

89193 

46767 

88390 

48303 

87561 

49824 

86704 

7 

54 

43680 

89956 

45243 

89180 

46793 

88377 

48328 

87546 

49849 

86690 

6 

55 

43706 

89943 

45269 

89167 

46819 

88363 

48354 

87532 

49874 

86675 

5 

56 

43733 

89930 

45295 

89153 

46844 

88349 

48379 

87518 

49899 

86661 

4 

57 

43759 

89918 

45321 

89140 

46870 

88336 

48405 

87504 

49924 

86646 

3 

58 

43785 

89905 

45347 

89127 

46896 

88322 

48430 

87490 

49950 

86632 

2 

59 

43811 

89892 

45373 

89114 

46921 

88308 

48456 

87476 

49975 

86617 

1 

60 

43837 

89879 

45399 

89101 

46947 

88295 

48481 

87462 

50000 

86603 

0 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

/ 

O4" 

ea° 

63° 

ei« 

eo° 

/ 

842 


APPENDIX. 


NATURAL     SINES     AND    COSINES^ 


3O° 

31° 

•33° 

33° 

34° 

/ 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

f 

0 

50000 

86603 

51504 

85717 

52992 

84805 

54464 

83867 

55919 

82904 

60 

1 

50025 

86588 

51529 

85702 

53017 

84789 

54488 

83851 

55943 

82887 

59 

2 

50050 

86573 

51554 

85687 

53041 

84774 

54513 

83835 

55968 

82871 

58 

3 

50076 

86559 

51579 

85672 

53066 

84759 

54537 

83819 

55992 

82855 

57 

4 

50101 

86544 

51604 

85657 

53091 

84743 

54561 

83804 

56016 

82839 

56 

5 

50126 

86530 

51628 

85642 

53115 

84728 

54586 

83788 

56040 

82822 

55 

6 

50151 

86515 

51653 

85627 

53140 

84712 

54610 

83772 

56064 

82806 

54 

7 

50176 

86501 

51678 

85612 

53164 

84697 

54635 

83756 

56088 

82790 

53 

8 

50201 

86486 

51703 

85597 

53189 

84681 

54659 

83740 

56112 

82773 

52 

9 

50227 

86471 

51728 

85582 

53214 

84666 

54683 

83724 

56136 

82757 

51 

10 

50252 

86457 

51753 

85567 

53238 

84650 

54708 

83708 

56160 

82741 

50 

11 

50277 

86442 

51778 

85551 

53263 

84635 

54732 

83692 

56184 

82724 

49 

12 

50302 

86427 

51803 

85536 

53288 

84619 

54756 

83676 

56208 

82708 

48 

13 

50327 

86413 

51828 

85521 

53312 

84604 

54781 

83660 

56232 

82692 

47 

14 

50352 

86398 

51852 

85506 

53337 

84588 

54805 

83645 

56256 

82675 

46 

15 

50377 

86384 

51877 

85491 

53361 

84573 

54829 

83629 

56280 

82659 

45 

16 

50403 

86369 

51902 

85476 

53386 

84557 

54854 

83613 

56305 

82643 

44 

17 

50428 

86354 

51927 

85461 

53411 

84542 

54878 

83597 

56329 

82626 

43 

18 

50453 

86340 

51952 

85446 

53435 

84526 

54902 

83581 

56353 

82610 

42 

19 

50478 

86325 

51977 

85431 

53460 

84511 

54927 

83565 

56377 

82593 

41 

20 

50503 

86310 

52002 

85416 

53484 

84495 

54951 

83549 

56401 

82577 

40 

21 

50528 

86295 

52026 

85401 

53509 

84480 

54975 

83533 

56425 

82561 

39 

22 

50553 

86281 

52051 

85385 

53534 

84464 

54999 

83517 

56449 

82544 

38 

23 

50578 

86266 

52076 

85370 

53558 

84448 

•.  55024 

83501 

56473 

82528 

37 

24 

50603 

86251 

52101 

85355 

53583 

84433 

55048 

83485 

56497 

82511 

36 

25 

50628 

86237 

52126 

85340 

53607 

84417 

55072 

83469 

56521 

82495 

35 

26 

50654 

86222 

52151 

85325 

53632 

84402 

55097 

83453 

56545 

82478 

34 

27 

50679 

86207 

52175 

85310 

53656 

84386 

55121 

83437 

56569 

82462 

33 

28 

50704 

86192 

52200 

85294 

53681 

84370 

55145 

83421 

56593 

82446 

32 

29 

50729 

86178 

52225 

85279 

53705 

84355 

55169 

83405 

56617 

82429 

31 

30 

50754 

86163 

52250 

85264 

53730 

84339 

55194 

83389 

56641 

82413 

30 

31 

50779 

86148 

52275 

85249 

53754 

84324 

55218 

83373 

56665 

82396 

29 

32 

50804 

86133 

52299 

85234 

53779 

84308 

55242 

83356 

56689 

82380 

28 

33 

50829 

86119 

52324 

85218 

53804 

84292 

55266 

83340 

56713 

82363 

27 

34 

50854 

86104 

52349 

85203 

53828 

84277 

55291 

:  83324 

56736 

82347 

26 

35 

50879 

86089 

52374 

85188 

53853 

84261 

55315 

:  83308 

56760 

82330 

25 

36 

50904 

86074 

52399 

85173 

53877 

84245 

55339 

;  83292 

56784 

82314 

24 

37 

50929 

86059 

52423 

85157 

53902 

84230 

55363 

1  83276 

56808 

82297 

23 

38 

50954 

86045 

52448 

85142 

53926 

84214 

55388 

!  83260 

1  56832 

82281 

22 

39 

50979 

86030 

52473 

85127 

53951 

84198 

55412 

i  83244 

56856 

82264 

21 

40 

51004 

86015 

52498 

85112 

53975 

84182 

55436 

83228 

56880 

82248 

20 

41 

51029 

86000 

52522 

85096 

54000 

84167 

55460 

83212 

56904 

82231 

19 

42 

51054 

85985 

52547 

85081 

54024 

84151 

55484 

83195 

56928 

82214 

18 

43 

51079 

85970 

52572 

85066 

54049 

84135 

55509 

83179 

56952 

82198 

17 

44 

51104 

85956 

52597 

i  85051 

54073 

84120 

55533 

83163 

56976 

82181 

16 

45 

51129 

85941 

52621 

!  85035 

54097 

84104 

55557 

83147 

57000 

82165 

15 

46 

51154 

85926 

52646 

.  85020 

'  54122 

84088 

55581 

!  83131 

57024 

82148 

14 

47 

51179 

85911 

52671 

'  85005 

54146 

84072 

55605 

83115 

57047 

82132 

13 

48 

51204 

85896 

52696 

;  84989 

54171 

84057 

55630 

83098 

57071 

82115 

12 

49 

51229 

85881 

52720 

1  84974 

54195 

84041 

55654 

83082 

57095 

82098 

11 

50 

51254 

85866 

52745 

'••  84959 

54220 

84025 

55678 

83066 

57119 

82082 

10 

51 

51279 

85851 

52770 

84943 

54244 

84009 

55702 

83050 

57143 

82065 

9 

52 

51304 

85836 

52794 

84928 

54269 

83994 

55726 

83034 

57167 

82048 

8 

53 

51329 

85821 

52819 

84913 

54293 

83978 

55750 

83017 

57191 

82032 

7 

54 

51354 

85806 

52844 

84897 

54317 

83962 

55775 

83001 

57215 

82015 

6 

55 

51379 

85792 

52869 

84882 

54342 

83946 

55799 

82985 

57238 

81999 

5 

56 

51404 

85777 

52893 

84866 

54366 

83930 

55823 

82969 

57262 

81982 

4 

57 

51429 

85762 

52918 

84851 

54391 

83915 

55847 

82953 

57286 

81965 

3 

58 

51454 

85747 

52943 

84836 

54415 

83899 

55871 

82936 

57310 

81949 

2 

59 

51479 

85732 

52967 

:  84820 

54440 

83883 

55895 

82920 

57334 

81932 

1 

60 

51504 

85717 

52992 

84805 

54464 

83867 

55919 

82904 

57358 

81915 

0 

Cosine. 

Sine. 

Cosine. 

Sine. 

'Cosine. 

Sine. 

Cosine. 

;  Sine. 

Cosine. 

Sine. 

/ 

5O« 

58° 

S7° 

5O° 

;       55° 

:  / 

APPENDIX. 


843 


NATURAL,     SINES     AND    COSINES. 


35° 

3O° 

371" 

38° 

3O» 

/ 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

,  /" 

0 

57358 

81915 

58779 

80902 

60182 

79864 

61566 

78801 

62932 

77715 

60 

1 

57381 

81899 

58802 

80885 

60205 

'  79846 

61589 

78783 

62955 

77696 

59 

2 

57405 

81882 

58826 

80867 

60228 

79829 

61612 

78765 

62977 

77678 

58 

3 

57429 

81865 

58849 

80850 

60251 

79811 

61635 

78747 

63000 

77660 

57 

4 

57453 

81848 

58873 

;  80833 

60274 

79793 

61658 

78729 

63022 

77641 

56 

5 

57477 

81832 

58896 

80816 

60298 

79776 

61681 

78711 

63045 

77623 

55 

6 

57501 

81815 

58920 

80799 

60321 

79758 

61704 

78694 

63068 

77605 

54 

7 

57524 

81798 

58943 

80782 

60344 

79741 

61726 

78676 

63090 

77586 

53 

8 

57548 

81782 

58967 

80765 

60367 

79723 

61749 

78658 

63113 

77568 

52 

9 

57572 

81765 

58990 

80748 

60390 

79706 

61772 

78640 

63135 

77550 

51 

10 

57596 

81748 

59014 

80730 

60414 

79688 

61795 

78622 

63158 

77531 

50 

11 

57619 

81731 

59037 

80713 

60437 

79671 

61818 

78604 

63180 

77513 

49 

12 

57643 

81714 

59061 

80696 

60460 

79653 

61841 

78586 

63203 

77494 

48 

13 

57667 

81698 

59084 

80679 

60483 

79635 

61864 

78568 

63225 

77476 

47 

14 

57691 

81681 

59108 

80662 

60506 

79618 

61887 

78550 

63248 

77458 

46 

15 

57715 

81664 

59131 

80644 

60529 

79600 

61909 

78532 

63271 

77439 

45 

16 

57738 

81647 

59154 

;  80627 

60553 

:  79583 

61932 

78514 

63293 

77421 

44 

17 

57762 

81631 

I  59178 

80610 

60576 

79565 

61955 

78496 

63316 

77402 

43 

18 

57786 

81614 

59201 

80593 

60599 

79547 

61978 

78478 

63338 

77384 

42 

19 

57810 

81597 

59225 

80576 

60622 

79530 

62001 

78460 

63361 

77366 

41 

20 

57833 

81580 

59248 

80558 

60645 

79512 

62024 

78442 

63383 

77347 

40 

21 

57857 

81563 

59272 

80541 

60668 

:  79494 

62046 

78424 

63406 

77329 

39 

22 

57881 

81546 

59295 

80524 

60691 

79477 

62069 

i  78405 

63428 

77310 

38 

23 

57904 

81530 

59318 

80507 

60714 

i  79459 

62092 

78387 

63451 

77292 

37 

24 

57928 

81513 

59342 

80489 

60738 

79441 

62115 

!  78369 

63473 

77273 

36 

25 

57952 

81496 

59365 

80472 

60761 

79424 

62138 

78351 

63496 

77255 

35 

26 

57976 

81479 

59389 

i  80455 

60784 

79406 

62160 

78333 

63518 

77236 

34 

27 

57999 

81462 

59412 

80438 

60807 

79388 

62183 

78315 

63540 

77218 

33 

28 

58023 

81445 

59436 

80420 

60830 

79371 

62206 

78297 

63563 

77199 

32 

29 

58047 

81428 

59459 

80403 

60853 

79353 

62229 

i  78279 

63585 

77181 

31 

30 

58070 

81412 

59482 

80386 

60876 

79335 

62251 

78261 

63608 

77162 

30 

31 

58094 

81395 

59506 

80368 

60899 

79318 

62274 

78243 

63630 

77144 

29 

32 

58118 

81378  |  59529 

:  80351 

60922 

.  79300 

62297 

78225 

63653 

77125 

28 

33 

58141 

81361 

59552 

80334 

60945 

79282 

62320 

78206 

63675 

77107 

27 

34 

58165 

81344 

59576 

!  80316 

60968 

;  79264 

62342 

78188 

63698 

77088 

26 

35 

58189 

81327   59599 

80299 

;  60991 

!  79247 

62365 

78170 

63720 

77070 

25 

36 

58212 

81310   59622 

80282 

.  61015 

:  79229 

!  62388 

;  78152 

63742 

77051 

24 

37 

58236 

81293 

59646 

80264 

61038 

79211 

62411 

78134 

63765 

77033 

23 

38 

58260 

81276 

59669 

80247 

61061 

79193 

62433 

78116 

63787 

77014 

22 

39 

58283 

81259   59693 

80230 

.  61084 

79176  '  62456 

78098 

63810 

76996 

21 

40 

58307 

81242   59716 

80212 

61107 

79158 

62479 

78079 

63832 

76977 

20 

41 

58330 

81225   59739 

80195 

61130 

79140 

62502 

78061 

63854 

76959 

19 

42 

58354 

81208   59763 

80178 

61153 

:  79122 

62524 

:  78043 

63877 

76940 

18 

43 

58378 

81191 

59786 

80160 

61176 

79105 

62547 

78025 

63899 

76921 

17 

4*4 

58401 

81174 

59809 

80143 

61199 

79087 

'62570 

78007 

63922 

76903 

16 

45 

58425 

81157 

59832 

80125 

•  61222 

79069 

62592 

77988 

63944 

76884 

15 

46 

58449 

81140 

59856 

80108 

61245 

79051 

:  62615 

77970 

63966 

76866 

14 

47 

58472 

81123 

59879 

80091 

61268 

79033 

•  62638 

77952 

63989 

76847 

13 

48 

58496 

81106 

59902 

80073 

61291 

79016 

62660 

77934 

64011 

;  76828 

12 

49 

58519 

81089 

59926 

80056 

61314 

78998  !  62683 

77916 

64033 

76810 

11 

50 

58543 

81072 

59949 

'  80038 

61337 

78980 

62706 

i  77897 

64056 

76791 

10 

51 

58567 

81055 

59972 

80021 

61360 

78962 

62728 

:  77879 

64078 

76772 

9 

52 

58590 

81038 

59995 

80003 

61383 

78944 

62751 

i  77861 

64100 

76754 

8 

53 

58614 

81021 

60019 

79986 

61406 

78926 

62774 

•  77843 

64123 

76735 

7 

54 

58637 

81004 

60042 

79968 

61429 

78908 

62796 

j  77824 

64145 

76717 

6 

55 

58661 

80987 

60065 

79951 

61451 

78891 

62819 

77806 

64167 

76698 

5 

56 

58684 

80970 

60089 

79934 

61474 

78873 

62842 

77788 

64190 

76679 

4 

57 

58708 

80953 

60112 

79916 

61497 

78855 

62864 

77769 

64212 

76661 

3 

58 

58731 

80936 

60135 

79899 

61520 

78837 

62887 

77751 

64234 

76642 

2 

59 

58755 

80919 

60158 

79881 

61543 

78819 

62909 

77733 

64256 

76623 

1 

60 

58779 

80902 

60182 

79864 

61566 

78801 

62932 

77715 

64279 

76604 

0 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

/  ' 

54,0 

53° 

£53° 

51" 

SO° 

/ 

844 


APPENDIX. 


NATURAL.     SINKS     AND    COSINES. 


4O° 

<tl° 

43° 

4,3° 

4=4=° 

/ 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

/ 

0 

64279 

76604 

65606 

75471 

66913 

74314 

68200 

73135 

69466 

71934 

60 

1 

64301 

76586 

65628 

75452 

66935 

74295 

68221 

73116 

69487 

71914 

59 

2 

64323 

76567 

65650 

75433 

66956 

74276 

68242 

73096 

69508 

71894 

58 

3 

64346 

76548 

65672 

75414 

66978 

74256 

68264 

73076 

69529 

71873 

57 

4 

64368 

76530 

65694 

75395 

66999 

74237 

68285 

73056 

69549 

71853 

56 

5 

64390 

76511 

65716 

75375 

67021 

74217 

68306 

73036 

69570 

71833 

55 

6 

64412 

76492 

65738 

75356 

67043 

74198 

68327 

73016 

69591 

71813 

54 

7 

64435 

76473 

65759 

75337 

67064 

74178 

68349 

72996 

69612 

71792 

53 

8 

64457 

76455 

65781 

75318 

67086 

74159 

68370 

72976 

69633 

71772 

52 

9 

64479 

76436 

65803 

75299 

67107 

74139 

68391 

72957 

69654 

71752 

51 

10 

64501 

76417 

65825 

75280 

67129 

74120 

68412 

72937 

69675 

71732 

50 

11 

64524 

76398 

65847 

75261 

67151 

74100 

68434 

72917 

69696 

71711 

49 

12 

64546 

76380 

65869 

75241 

67172 

74080 

68455 

72897 

69717 

71691 

48 

13 

64568 

76361 

65891 

75222 

67194 

74061 

68476 

72877 

69737 

71671 

47 

14 

64590 

76342 

65913 

75203 

67215 

74041 

68497 

72857 

69758 

71650 

46 

15 

64612 

76323 

65935 

75184 

67237 

74022 

68518 

72837 

69779 

71630 

45 

16 

64635 

76304 

65956 

75165 

67258 

74002 

68539 

72817 

69800 

71610 

44 

17 

64657 

76286 

65978 

75146 

67280 

73983 

68561 

72797 

69821 

71590 

43 

18 

64679 

76267 

66000 

75126 

67301 

73963 

68582 

72777 

69842 

71569 

42 

1? 

64701 

76248 

66022 

75107 

67323 

73944 

68603 

72757 

69862 

71549 

41 

20 

64723 

76229 

66044 

75088 

67344 

73924 

68624 

72737 

69883 

71529 

40 

21 

64746 

76210 

66066 

75069 

67366 

73904 

68645 

72717 

69904 

71508 

39 

22 

64768 

76192 

66088 

75050 

67387 

73885 

68666 

72697 

69925 

71488 

38 

23 

64790 

76173 

66109 

75030 

67409 

73865 

68688 

72677 

69946 

71468 

37 

24 

64812 

76154 

66131 

75011 

67430 

73846 

68709 

72657 

69966 

71447 

36 

25 

64834 

76135 

66153 

74992 

67452 

73826 

68730 

72637 

69987 

71427 

3.5 

26 

64856 

76116 

66175 

74973 

67473 

73806 

68751 

72617 

70008 

71407 

34 

27 

64878 

76097 

66197 

74953 

67495 

73787 

68772 

72597 

70029 

71386 

33 

28 

64901 

76078 

66218 

74934 

67516 

73767 

68793 

72577 

70049 

71366 

32 

29 

64923 

76059 

66240 

74915 

67538 

73747 

68814 

72557 

70070 

71345 

31 

30 

64945 

76041 

66262 

74896 

67559 

73728 

68835 

72537 

70091 

71325 

30 

31 

64967 

76022 

66284 

74876 

67580 

73708 

68857 

72517 

70112 

71305 

29 

32 

64989 

76003 

66306 

74857 

67602 

73688 

68878 

72497 

70132 

71284 

28 

33 

65011 

75984 

66327 

74838 

67623 

73669 

68899 

72477 

70153 

71264 

27 

34 

65033 

75965 

66349 

74818 

67645 

73649 

68920 

72457 

70174 

71243 

26 

35 

65055 

75946 

66371 

74799 

67666 

73629 

68941 

72437 

70195 

71223 

25 

36 

65077 

75927 

66393 

74780 

67688 

73610 

68962 

72417 

70215 

71203 

24 

37 

65100 

75908 

66414 

74760 

67709 

73590 

68983 

72397 

70236 

71182 

23 

38 

65122 

75889 

66436 

74741 

67730 

73570 

69004 

72377 

70257 

71162 

22 

39 

65144 

75870 

66458 

74722 

67752 

73551 

69025 

72357 

70277 

71141 

21 

40 

65166 

75851 

66480 

74703 

67773 

73531 

69046 

72337 

70298 

71121 

20 

41 

65188 

75832 

66501 

74683 

67795 

73511 

69067 

72317 

70319 

71100 

19 

42 

65210 

75813 

66523 

74664 

67816 

73491 

69088 

72297 

70339 

71080 

18 

43 

65232 

75794 

66545 

74644 

67837 

73472 

69109 

72277 

70360 

71059 

17 

44 

65254 

75775 

66566 

74625 

67859 

73452 

69130 

72257 

70381 

71039 

18 

45 

65276 

75756 

66588 

74606 

67880 

73432 

69151 

72236 

70401 

71019 

15 

46 

65298 

75738 

66610 

74586 

67901 

73413 

69172 

72216 

70422 

70998 

14 

47 

65320 

75719 

66632 

74567 

67923 

73393 

69193 

72196 

70443 

70978 

13 

48 

65342 

75700 

66653 

74548 

67944 

73373 

69214 

72176 

70463 

70957 

12 

49 

65364 

75680 

66675 

74528 

67965 

73353 

69235 

72156 

70484 

70937 

11 

50 

65386 

75661 

66697 

74509 

67987 

73333 

69256 

72136 

70505 

70916 

10 

51 

65408 

75642 

66718 

74489 

68008 

73314 

69277 

72116 

70525 

70896 

9 

52 

65430 

75623 

66740 

74470 

68029 

73294 

69298 

72095 

70546 

70875 

8 

53 

65452 

75604 

66762 

74451 

68051 

73274 

69319 

72075 

70567 

70855 

7 

54 

65474 

75585 

66783 

74431 

68072 

73254 

69340 

72055 

70587 

70834 

6 

55 

65496 

75566 

66805 

74412 

68093 

73234 

69361 

72035 

70608 

70813 

5 

56 

65518 

75547 

66827 

74392 

68115 

73215 

69382 

72015 

70628 

70793 

4 

57 

65540 

75528 

66848 

74373 

68136 

73195 

69403 

71995 

70649 

70772 

3 

58 

65562 

75509 

66870 

74353 

68157 

73175 

69424 

71974 

70670 

70752 

2 

59 

65584 

75490 

66891 

74334 

68179 

73155 

69445 

71954 

70690 

70731 

1 

60 

65606 

75471 

66913 

74314 

68200 

73135 

69466 

71934 

70711 

70711 

0 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

Cosine. 

Sine. 

4O« 

48° 

4:7° 

46° 

4»«> 

/ 

APPENDIX. 


845 


LOGARITHMS    OP     NUMBERS. 


N. 

O 

1 

3 

3 

4L 

5 

6 

7 

S 

O 

I>. 

100 

00  0000 

0434 

0868 

1301 

1734 

2166 

2598 

3029 

3461 

3891 

432 

101 

4321 

4751 

5181 

5609 

6038 

6466 

6894 

7321 

7748 

8174 

428 

102 

*  8600 

9026 

9451 

9876 

+300 

0724 

1147 

1570 

1993 

2415 

424 

103 

01  2837 

3259 

3680 

4100 

4521 

4940 

5360 

5779 

6197 

6616 

419 

104 

*  7033 

7451 

7868 

8284 

8700 

9116 

9532 

9947 

+361 

0775 

416 

105 

02  1189 

1603 

2016 

2428 

2841 

3252 

3664 

4075 

4486 

4896 

412 

106 

5306 

5715 

6125 

6533 

6942 

7350 

7757 

8164 

8571 

8978 

408 

107 

*  9384 

9789 

+195 

0600 

1004 

1408 

1812 

2216 

2619 

3021 

404 

108 

03  3424 

3826 

4227 

4628 

5029 

5430 

5830 

6230 

6629 

7028 

400 

109 

*  7426 

7825 

8223 

8620 

9017 

9414 

9811 

+207 

0602 

0998 

396 

110 

04  1393 

1787 

2182 

2576 

2969 

3362 

3755 

4148 

4540 

4932 

393 

111 

5323 

5714 

6105 

6495 

6885 

7275 

7664 

8053 

8442 

8830 

389 

112 

*  9218 

9606 

9993 

+380 

0766 

1153 

1538 

1924 

2309 

2694 

386 

113 

05  3078 

3463 

3846 

4230 

4613 

4996 

5378 

5760 

6142 

6524 

382 

114 

*6905 

7286 

7666 

8046 

8426 

8805 

9185 

9563 

9942 

+320 

379 

115 

06  0698 

1075 

1452 

1829 

2206 

2582 

2958 

3333 

3709 

4083 

376 

116 

4458 

4832 

5206 

5580 

5953 

6326 

6699 

7071 

7443 

7815 

372 

117 

*  8186 

8557 

8928 

9298 

9668 

+038 

0407 

0776 

1145 

1514 

369 

118 

07  1882 

2250 

2617 

2985 

3352 

3718 

4085 

4451 

4816 

5182 

366 

119 

5547 

5912 

6276 

6640 

7004 

7368 

7731 

8094 

8457 

8819 

363 

120 

*9181 

9543 

9904 

+266 

0626 

0987 

1347 

1707 

2067 

2426 

360 

121 

08  2785 

3144 

3503 

3861 

4219 

4576 

4934 

5291 

5647 

6004 

357 

122 

6360 

6716 

7071 

7426 

7781 

8136 

8490 

8845 

9198 

9552 

355 

123 

*  9905 

+258 

0611 

0963 

1315 

1667 

2018 

2370 

2721 

3071 

351 

124 

09  3422 

3772 

4122 

4471 

4820 

5169 

5518 

5866 

6215 

6562 

349 

125 

*  6910 

7257 

7604 

7951 

8298 

8644 

8990 

9335 

9681 

+026 

346 

126 

10  0371 

0715 

1059 

1403 

1747 

2091 

2434 

2777 

3119 

3462 

343 

127 

3804 

4146 

4487 

4828 

5169 

5510 

5851 

6191 

6531 

6871 

340 

128 

*  7210 

7549 

7888 

8227 

8565 

8903 

9241 

9579 

9916 

+253 

338 

129 

11  0590 

0926 

1263 

1599 

1934 

2270 

2605 

2940 

3275 

3609 

335 

130 

3943 

4277 

4611 

4944 

5278 

5611 

5943 

6276 

6608 

6940 

333 

131 

*7271 

7603 

7934 

8265 

8595 

8926 

9256 

9586 

9915 

+245 

330 

132 

12  0574 

0903 

1231 

1560 

1888 

2216 

2544 

2871 

3198 

3525 

328 

133 

3852 

4178 

4504 

4830 

5156 

5481 

5806 

6131 

6456 

6781 

325 

134 

*7105 

7429 

7753 

8076 

8399 

8722 

9045 

9368 

9690 

+012 

323 

135 

13  0334 

0655 

0977 

1298 

1619 

1939 

2260 

2580 

2900 

3219 

321 

136 

3539 

3858 

4177 

4496 

4814 

5133 

5451 

5769 

6086 

6403 

318 

137 

6721 

7037 

7354 

7671 

7987 

8303 

8618 

8934 

9249 

9564 

315 

138 

*9879 

+194 

0508 

0822 

1136 

1450 

1763 

2076 

2389 

2702 

314 

139 

14  3015 

3327 

3639 

3951 

4263 

4574 

4885 

5196 

5507 

5818 

311 

140 

6128 

6438 

6748 

7058 

7367 

7676 

7985 

8294 

8603 

8911 

309 

141 

*  9219 

9527 

9835 

+142 

0449 

0756 

1063 

1370 

1676 

1982 

307 

142 

15  2288 

2594 

2900 

3205 

3510 

3815 

4120 

4424 

4728 

5032 

305 

143 

5336 

5640 

5943 

6246 

6549 

6852 

7154 

7457 

7759 

8061 

303 

144 

*  8362 

8664 

8965 

9266 

9567 

9868 

+168 

0469 

0769 

1068 

301 

145 

16  1368 

1667 

196*7 

2266 

2564 

2863 

3161 

3460 

3758 

4055 

299 

146 

4353 

4650 

4947 

5244 

5541 

5838 

6134 

6430 

6726 

7022 

297 

147 

7317 

7613 

7908 

8203 

8497 

8792 

9086 

9380 

9674 

9968 

295 

148 

17  0262 

0555 

0848 

1141 

1434 

1726 

2019 

2311 

2603 

2895 

293 

149 

3186 

3478 

3769 

4060 

,  4351 

4641 

4932 

5222 

5512 

5802 

291 

150 

6091 

6381 

6670 

6959 

7248 

7536 

7825 

8113 

8401 

8689 

289 

151 

*8977 

9264 

9552 

9839 

»126 

0413 

0699 

0985 

1272 

1558 

287 

152 

18  1844 

2129 

2415 

2700 

2985 

3270 

3555 

3839 

4123 

4407 

285 

153 

4691 

4975 

5259 

5542 

5825 

6108 

6391 

6674 

6956 

7239 

283 

154 

*7521 

7803 

8084 

8366 

8647 

8928 

9209 

9490 

9771 

+051 

281 

155 

19  0332 

0612 

0892 

1171 

1451 

1730 

2010 

2289 

2567 

2846 

279 

156 

3125 

3403 

3681 

3959 

4237 

4514 

4792 

5069 

5346 

5623 

278 

157 

5900 

6176 

6453 

6729 

7005 

7281 

7556 

7832 

8107 

8382 

276 

158 

*  8657 

8932 

9206 

9481 

9755 

+029 

0303 

0577 

0850 

1124 

274 

159 

20  1397 

1670 

1943 

2216 

2488 

2761 

3033 

3305 

3577 

3848 

272 

N. 

O 

1 

3 

3 

4 

5 

e 

7 

8 

O 

r>. 

•846 


APPENDIX. 


LOGARITHMS    OF     NUMBERS. 


IV. 

O 

1 

9 

3 

4  '• 

5  i 

0  ; 

7  ' 

8 

O 

r>. 

160 

20  4120  i 

4391 

4663 

4934 

5204 

5475 

5746 

6016 

6286 

6556 

271 

161 

6826  ' 

7096 

7365 

7634 

7904 

8173 

8441 

8710 

8979 

9247 

269 

162 

*  9515 

9783 

*051 

0319 

0586 

0853 

1121 

1388 

1654 

1921 

267 

163 

21  2188 

2454 

2720 

2986 

3252 

3518 

3783 

4049 

4314 

4579 

266 

164 

4844 

5109 

5373 

5638 

5902 

6166 

6430 

6694 

6957 

7221 

264 

165 

7484 

7747 

8010 

8273 

8536 

8798 

9060 

9323 

9585 

9846 

262 

166 

22  0108 

0370 

0631 

0892 

1153 

1414 

1675 

1936 

2196 

2456 

261 

167 

2716 

2976 

3236 

3496 

3755 

4015 

4274 

4533 

4792 

5051 

259 

168 

5309 

5568 

5826 

6084 

6342 

6600; 

6858  , 

7115 

7372 

7630 

258 

169 

*7887 

8144 

8400 

8657 

8913 

9170: 

9426' 

9682 

9938 

*193 

256 

170 

23  0449 

0704 

0960 

1215 

1470 

1724 

1979 

2234 

2488 

2742 

254 

171 

2996 

3250 

3504 

3757 

4011 

4264 

4517 

4770 

5023 

5276 

253 

172 

5528 

5781 

6033 

6285 

6537 

6789 

7041 

7292 

7544 

7795 

252 

173 

*8046 

8297 

8548 

8799 

9049 

9299 

9550 

9800 

»050 

0300 

250 

174 

24  0549 

0799 

1048 

1297 

1546 

1795 

2044 

2293 

2541 

2790 

249 

175 

3038 

3286 

3534 

3782 

4030 

4277 

4525 

4772 

5019 

5266 

248 

176 

5513 

5759 

6006 

6252 

6499 

6745 

6991 

7237  . 

7482 

7728 

246 

177 

*7973 

8219 

8464 

8709 

8954 

9198 

9443 

9687 

9932 

*176 

245 

178 

25  0420 

0664 

0908 

1151 

1395 

1638 

1881 

2125 

2368 

2610 

243 

179 

2853 

3096 

3338 

3580 

3822 

4064 

4306 

4548 

4790 

5031 

242 

180 

5273 

5514 

5755 

5996 

6237 

6477 

6718 

6958 

7198 

7439 

241 

181 

7679 

7918 

8158 

8398 

8637 

8877 

9116 

9355 

9594 

9833 

239 

182 

26  0071 

0310 

0548 

0787 

1025 

1263 

1501 

1739 

1976 

2214 

238 

183 

2451 

2688 

2925 

3162 

3399 

3636 

3873 

4109 

4346 

4582 

237 

184 

4818 

5054 

5290 

5525 

5761 

5996 

6232 

6467 

6702 

6937 

235 

185 

7172 

7406 

7641 

7875 

8110 

8344 

8578 

8812 

9046 

9279 

2%34 

186 

*  9513 

9746 

9980 

»213 

0446 

0679 

0912 

1144 

1377 

1609 

233 

187 

27  1842 

2074 

2306 

2538 

2770 

3001 

3233 

3464 

3696 

3927 

232 

188 

4158 

4389 

4620 

4850 

5081 

5311 

5542 

5772 

6002 

6232 

230 

189 

6462 

6692 

6921 

7151 

7380 

7609 

7838 

8067 

8296 

8525 

229 

190 

*8754 

8982 

9211 

9439 

9667 

9895 

»123 

0351 

0578 

0806 

228 

191 

28  1033 

1261 

1488 

1715 

1942 

2169 

2396 

2622 

2849 

3075 

227 

192 

3301 

3527 

3753 

3979 

4205 

4431 

4656 

4882 

5107 

5332 

226 

193 

5557 

5782 

6007 

6232 

6456 

6681 

6905 

7130 

7354 

7578 

225 

194 

7802 

8026   8249 

8473 

8696 

8920 

9143 

9366 

9589 

9812 

223 

195 

29  0035 

0257 

0480 

0702 

0925 

1147 

1369 

1591 

1813 

2034 

222 

196 

2256 

2478 

2699 

2920 

3141 

3363 

3584 

3804 

4025 

4246 

221 

197 

4466 

4687 

4907 

5127 

5347 

5567 

5787 

6007 

6226 

6446 

220 

198 

6665 

6884 

7104 

7323 

7542 

7761 

7979 

8198 

8416 

8635 

219 

199 

*  8853 

9071 

9289 

9507 

9725 

9943 

*161 

0378 

0595 

0813 

218 

200 

30  1030 

1247 

1464 

1681 

1898 

2114 

2331 

2547 

2764 

2980 

217 

201 

3196 

3412 

3628 

3844 

4059 

4275 

4491 

4706 

4921 

5136 

216 

20'2 

5351 

5566 

5781 

5996 

6211 

6425 

6639 

6854 

7068 

7282 

215 

203 

7496 

7710 

7924 

8137 

8351 

8564 

8778 

8991 

9204 

9417 

213 

204 

*  9630 

9843 

«056 

0268 

0481 

0693 

0906 

1118 

1330 

1542 

212 

205 

31  1754 

1966 

2177 

2389 

2600 

2812 

3023 

3234 

3445 

3656 

211 

206 

3867 

4078 

4289 

4499 

4710 

4920 

5130 

5340 

5551 

5760 

210 

207 

5970 

6180 

6390 

6599 

6809 

7018 

7227 

7436 

7646 

7854 

209 

208 

8063 

8272 

8481 

8689 

8898 

9106 

9314 

9522 

9730 

9938 

208 

209 

32  0146 

0354 

0562 

0769 

0977 

1184 

1391 

1598 

1805 

2012 

207 

210 

2219 

2426 

2633 

2839 

3046 

3252 

3458 

3665 

3871 

4077 

206 

211 

4282 

4488 

4694 

4899 

5105 

5310 

•5516 

5721 

5926 

6131 

205 

212 

6336 

6541 

6745 

6950 

7155 

7359 

7563 

7767 

7972 

8176 

204 

213 

*8380 

8583 

8787 

8991 

9194 

9398 

9601 

9805 

*008 

0211 

203 

214 

33  0414 

0617 

0819 

1022 

1225 

1427 

1630 

1832 

2034 

2236 

202 

215 

2438 

2640 

2842 

3044 

3246 

3447 

3649 

3850 

4051 

4253 

202 

216 

4454 

4655 

4856 

5057 

5257 

5458 

5658 

5859 

6059 

6260 

201 

217 

6460 

6660 

6860 

7060 

7260 

7459 

7659 

7858 

8058 

8257 

200 

218 

*  8456 

8656 

8855 

9054 

9253 

9451 

9650 

9849 

»047 

0246 

199 

219 

34  0444 

0642 

0841 

1039 

1237 

1435 

1632 

1830 

2028 

2225 

198 

N. 

0      1 

2 

3 

4     5      O      7 

8 

O 

J>. 

APPENDIX. 


847 


LOGARITHMS    OP     NUMBERS. 


IV. 

o 

1     3 

.  » 

4, 

5 

—  ;  —  r- 
G      7  ' 

8 

e 

r>. 

220 

34  2423 

2620 

2817 

3014 

3212 

3409 

3606 

3802 

3999 

4196 

197 

221 

4392 

4589 

4785 

4981 

5178 

5374 

5570' 

5766 

5962 

6157 

196 

222 

6353 

6549 

6744 

6939 

7135 

7330 

7525 

7720 

7915 

8110 

195 

223 

*  8305 

8500   8694 

8889 

9083 

9278 

9472 

9666 

9860 

4054 

194 

224 

35  0248 

0442  |  0636 

0829 

1023 

1216 

1410 

1603 

1796 

1989 

193 

225 

2183 

2375 

2568 

2761 

2954 

3147 

3339 

3532 

3724 

3916 

193 

226 

4108 

4301 

4493 

4685 

4876 

5068 

5260 

5452 

5643 

5834 

192 

227 

6026   6217 

6408 

6599 

6790 

6981 

7172 

7363 

7554 

7744 

191 

228 

7935 

8125 

8316 

8506 

8696 

8886 

9076 

9266 

9456 

9646 

190 

229 

*  9835 

*025 

0215 

0404 

0593 

0783 

0972 

1161 

1350 

1539 

189 

230 

36  1728 

1917 

2105 

2294 

2482 

2671 

2859 

3048 

3236 

3424 

188 

231 

3612 

3800 

3988 

4176 

4363 

4551 

4739 

4926 

5113 

5301 

188 

232 

5488 

5675 

5862 

6049 

6236 

6423 

6610 

6796 

6983 

7169 

187 

233 

7356 

7542 

7729 

7915 

8101 

8287 

8473 

8659 

8845 

9030 

186 

234 

*  9216 

9401 

9587 

9772 

9958 

»143 

0328 

0513 

0698 

0883 

185 

235 

37  1068 

1253 

1437 

1622 

1806 

1991 

2175 

"2360 

2544 

2728 

184 

236 

2912 

3096 

3280 

3464 

3647 

3831 

4015 

4198 

4382 

4565 

184 

237 

4748 

4932 

5115 

5298 

5481 

5664 

5846 

6029 

6212 

6394 

183 

238 

6577 

6759 

6942 

7124 

7306 

7488 

7670 

7852 

8034 

8216 

182 

239 

*  8398 

8580 

8761 

8943 

9124 

9306 

9487 

9668 

9849 

*030 

181 

240 

38  0211 

0392 

0573 

0754 

0934 

1115 

1296 

1476 

1656 

1837 

181 

241 

2017 

2197 

2377 

2557 

2737 

2917 

3097 

3277 

3456 

3636 

180 

242 

3815 

3995 

4174 

4353 

4533 

4712 

4891 

5070 

5249 

5428 

179 

243 

5606 

5785 

5964 

6142 

6321 

6499 

6677 

6856 

7034 

7212 

178 

244 

7390 

7568 

7746 

7923 

8101 

8279 

8456 

8634 

8811 

8989 

178 

245 

*  9166 

9343 

9520 

9698 

9875 

*051 

0228 

0405 

0582 

0759 

177 

246 

39  0935 

1112 

1288 

1464 

1641 

1817 

1993 

2169 

2345 

2521 

176 

247 

2697   2873   3048 

3224 

3400 

3575 

3751 

3926 

4101 

4277 

176 

248 

4452   4627 

4802 

4977 

5152 

5326 

5501 

5676 

5850 

6025 

175 

249 

6199 

6374 

6548 

6722 

6896 

7071 

7245 

7419 

7592 

7766 

174 

250 

7940 

8114 

8287 

8461 

8634 

8808 

8981 

9154 

9328 

9501 

173 

251 

*  9674   9847 

*020 

0192 

0365 

0538 

0711 

0883 

1056 

1228 

173 

252 

40  1401 

1573 

1745 

1917 

2089 

2261 

2433 

2605 

2777 

2949 

172 

253 

3121 

3292 

3464 

3635 

3807 

3978 

4149 

4320 

4492 

4663 

171 

254 

4834 

5005 

5176 

5346 

5517 

5688 

5858 

6029 

6199 

6370 

171 

255 

6540 

6710 

6881 

7051 

7221 

7391 

7561 

7731 

7901 

8070 

170 

256 

8240 

8410 

8579 

8749 

8918 

9087 

9257 

9426 

9595 

9764 

169 

257 

*  9933 

*102 

0271 

0440 

0609 

0777 

0946 

1114 

1283 

1451 

169 

258 

41  1620 

1788 

1956 

2124 

2293 

2461 

2629 

2796 

2964 

3132 

168 

259 

3300 

3467 

3635 

3803 

3970 

4137 

4305 

4472 

4639 

4806 

167 

260 

4973 

5140 

5307 

5474 

5641 

5808 

5974 

6141 

6308 

6474 

167 

261 

6641    6807 

6973 

7139 

7306 

7472 

7638 

7804 

7970 

8135 

166 

262 

8301    8467 

8633 

8798 

8964 

9129 

9295 

9460 

9625 

9791 

165 

263 

*  9956    »121 

0286 

0451 

0616 

0781 

0945 

1110 

1275 

1439 

165 

264 

42  1604 

1768 

1933 

2097 

2261 

2426 

2590 

2754 

2918 

3082 

164 

265 

3246 

3410 

3574 

3737 

3901 

4065 

4228 

4392 

4555 

4718 

164 

266 

4882   5045 

5208 

5371 

5534 

5697 

5860 

6023 

6186 

6349 

163 

267 

6511    6674 

6836 

6999 

7161 

7324 

7486 

7648 

7811 

7973 

162 

268 

8135   8297 

8459 

8621 

8783 

8944 

9106 

9268 

9429 

9591 

162 

269 

*  9752 

9914 

»075 

0236 

0398 

0559 

0720 

0881 

1042 

1203 

161 

270 

43  1364 

1525 

1685 

1846 

2007 

2167 

2328 

2488 

2649 

2809 

161 

271 

2969   3130 

3290 

3450 

3610 

3770 

3930 

4090 

4249 

4409 

160 

272 

4569   4729 

4888 

5048 

5207 

5367 

5526 

5685 

5844 

6004 

159 

273 

6163   6322 

6481 

6640 

6799 

6957 

7116 

7275 

7433 

7592 

159 

274 

7751 

7909 

8067 

8226 

8384 

8542 

8701 

8859 

9017 

9175 

158 

275 

*  9333 

9491 

9648 

9806 

9964 

»122 

0279 

0437 

0594 

0752 

158 

276 

44  0909 

1066 

1224 

1381 

1538 

1695 

1852 

2009 

2166 

2323 

157 

277 

2480 

2637 

2793 

2950 

3106 

3263 

3419 

3576 

3732 

3889 

157 

278 

4045 

4201 

4357 

4513 

4669 

4825 

4981 

5137 

5293 

5449 

156 

279     5604 

5760 

5915 

6071 

6226 

6382 

6537 

6692 

6848 

7003 

155 

IV. 

0      13 

*J 

4, 

5 

G 

7 

H 

0 

r>. 

848 


APPENDIX. 


LOGARITHMS    OF     NUMBERS. 


N. 

0 

1 

3 

3 

4, 

5 

6 

7 

8 

O 

r>. 

280 

44  7158 

7313 

7468 

7623 

7778 

7933 

8088 

8242 

8397 

8552 

155 

281 

*8706 

8861 

9015 

9170 

9324 

9478 

9633 

9787 

9941 

»095 

154 

282 

45  0249 

0403 

0557 

0711 

0865 

1018 

1172 

1326 

1479 

1633 

154 

283 

1786 

1940 

2093 

2247 

2400 

2553 

2706 

2859 

3012 

3165 

153 

284 

3318 

3471 

3624 

3777 

3930 

4082 

4235 

4387 

4540 

4692 

153 

285 

4845 

4997 

5150 

5302 

5454 

5606 

5758 

5910 

6062 

6214 

152 

286 

6366 

6518 

6670 

6821 

6973 

7125 

7276 

7428 

7579 

7731 

152 

287 

7882 

8033 

8184 

8336 

8487 

8638 

8789 

8940 

9091 

9242 

151 

288 

*  9392 

9543 

9694 

9845 

9995 

»146 

0296 

0447 

0597 

0748 

151 

289 

46  0898 

1048 

1198 

1348 

1499 

1649 

1799 

1948 

2098 

2248 

150 

290 

2398 

2548 

2697 

2847 

2997 

3146 

3296 

3445 

3594 

3744 

150 

291 

3893 

4042 

4191 

4340 

4490 

4639 

4788 

4936 

5085 

5234 

149 

292 

5383 

5532 

5680 

5829 

5977 

6126 

6274 

6423 

6571 

6719 

149 

293 

6868 

7016 

7164 

7312 

7460 

7608 

7756 

7904 

8052 

8200 

148 

294 

8347 

8495 

8643 

8790 

8938 

9085 

9233 

9380 

9527 

9675 

148 

295 

*  9822 

9969 

*116 

0263 

0410 

0557 

0704 

0851 

0998 

1145 

147 

296 

47  1292 

1438 

1585 

1732 

1878 

2025 

2171 

2318 

2464 

2610 

146 

297 

2756 

2903 

3049 

3195 

3341 

3487 

3633 

3779 

3925 

4071 

146 

298 

4216 

4362 

4508 

4653 

4799 

4944 

5090 

5235 

5381 

5526 

146 

299 

5671 

5816 

5962 

6107 

6252 

6397 

6542 

6687 

6832 

6976 

145 

300 

7121 

7266 

7411 

7555 

7700 

7844 

7989 

8133 

8278 

8422 

145 

301 

8566 

8711 

8855 

8999 

9143 

9287 

9431 

9575 

9719 

9863 

144 

302 

48  0007 

0151 

0294 

0438 

0582 

0725 

0869 

1012 

1156 

1299 

144 

303 

1443 

1586 

1729 

1872 

2016 

2159 

2302 

2445 

2588 

2731 

143 

304 

2874 

3016 

3159 

3302 

3445 

3587 

3730 

3872 

4015 

4157 

143 

305 

4300 

4442 

4585 

4727 

4869 

5011 

5153 

5295 

5437 

5579 

142 

306 

5721 

5863 

6005 

6147 

6289 

6430 

6572 

6714 

6855 

6997 

142 

307 

7138 

7280 

7421 

7563 

7704 

7845 

7986 

8127 

8269 

8410 

141 

308 

8551 

8692 

8833 

8974 

9114 

9255 

9396 

9537 

9677 

9818 

141 

309 

*  9958 

*099 

0239 

0380 

0520 

0661 

0801 

0941 

1081 

1222 

140 

310 

49  1362 

1502 

1642 

1782 

1922 

2062 

2201 

2341 

2481 

2621 

140 

311 

2760 

2900 

3040 

3179 

3319 

3458 

3597 

3737 

3876 

4015 

139 

312 

4155 

4294 

4433 

4572 

4711 

4850 

4989 

5128 

5267 

5406 

139 

313 

5544 

5683 

5822 

5960 

6099 

6238 

6376 

6515 

6653 

6791 

139 

314 

6930 

7068 

7206 

7344 

7483 

7621 

7759 

7897 

8035 

8173 

138 

315 

8311 

8448 

8586 

8724 

8862 

8999 

9137 

9275 

9412 

9550 

138 

316 

*9687 

9824 

9962 

*099 

0236 

0374 

0511 

0648 

0785 

0922 

137 

317 

50  1059 

1196 

1333 

1470 

1607 

1744 

1880 

2017 

2154 

2291 

137 

318 

2427 

2564 

2700 

2837 

2973 

3109 

3246 

3382 

3518 

3655 

136 

319 

3791 

3927 

4063 

4199 

4335 

4471 

4607 

4743 

4878 

5014 

136 

320 

5150 

5286 

5421 

5557 

5693 

5828 

5964 

6099 

6234 

6370 

136 

321 

6505 

6640 

6776 

6911 

7046 

7181 

7316 

7451 

7586 

7721 

135 

322 

7856 

7991 

8126 

8260 

8395 

8530 

8664 

8799 

8934 

9068 

135 

323 

*  9203 

9337 

9471 

9606 

9740 

9874 

»009 

0143 

0277 

0411 

134 

324 

51  0545 

0679 

0813 

0947 

1081 

1215 

1349 

1482 

1616 

1750 

134 

325 

1883 

2017 

2151 

2284 

2418 

2551 

2684 

2818 

2951 

3084 

133 

326 

3218 

3351 

3484 

3617 

3750 

3883 

4016 

4149 

4282 

4414 

133 

327 

4548 

4681 

4813 

4946 

5079 

5211 

5344 

5476 

5609 

5741 

133 

328 

5874 

6006 

6139 

6271 

6403 

6535 

6668 

6800 

6932 

7064 

132 

329 

7196 

7328 

7460 

7592 

7724 

7855 

7987 

8119 

8251 

8382 

132 

330 

8514 

8646 

8777 

8909 

9040 

9171 

9303 

9434 

9566 

9697 

131 

331 

*9828 

9959 

»090 

0221 

0353 

0484 

0615 

0745 

0876 

1007 

131 

332 

52  1138 

1269 

1400 

1530 

1661 

1792 

1922 

2053 

2183 

2314 

131 

333 

2444 

2575 

2705 

2835 

2966 

3096 

3226 

3356 

3486 

3616 

130 

334 

3746 

3876 

4006 

4136 

4266 

4396 

4526 

4656 

4785 

4915 

130 

335 

5045 

5174 

5304 

5434 

5563 

5693 

5822 

5951 

6081 

6210 

129 

336 

6339 

6469 

6598 

6727 

6856 

6985 

7114 

7243 

7372 

7501 

129 

337 

7630 

7759 

7888 

8016 

8145 

8274 

8402 

8531 

8660 

8788 

129 

338 

*  8917 

9045 

9174 

9302 

9430 

9559 

9687 

9815 

9943 

»072 

128 

339 

53  0200 

0328 

0456 

0584 

0712 

0840 

0968 

1096 

1223 

1351 

128 

N. 

O 

1 

3 

3 

4= 

5 

O 

7 

& 

O 

T>. 

APPENDIX. 


84:9 


LOGARITHMS    OP     NUMBERS. 


IV. 

O 

1 

3 

3 

4, 

5 

G 

7 

a 

O 

r>. 

340 

53  1479 

1607 

1734 

1862 

1990 

2117 

2245 

2372 

2500 

2627 

128 

341 

2754 

2882 

3009 

3136 

3264 

3391 

3518 

3645 

3772 

3899 

127 

342 

4026 

4153 

4280 

4407 

4534 

4661 

4787 

4914 

5041 

5167 

127 

343 

5294 

5421 

5547 

5674 

5800 

5927 

6053 

6180 

6306 

6432 

126 

344 

6558 

6685 

6811 

6937 

7063 

7189 

7315 

7441 

7567 

7693 

126 

345 

7819 

7945 

8071 

8197 

8322 

8448 

8574 

8699 

8825 

8951 

126 

346 

*  9076 

9202 

9327 

9452 

9578 

9703 

9829 

9954 

+079 

0204 

125 

347 

54  0329 

0455 

0580 

0705 

0830 

0955 

1080 

1205 

1330 

1454 

125 

348 

1579 

1704 

1829 

1953 

2078 

2203 

2327 

2452 

2576 

2701 

125 

349 

2825 

2950 

3074 

3199 

3323 

3447 

3571 

3696 

3820 

3944 

124 

350 

4068 

4192 

4316 

4440 

4564 

4688 

4812 

4936 

5060 

5183 

124 

351 

'5307 

5431 

.  5555 

5678 

5802 

5925 

6049 

6172 

6296 

6419 

124 

352 

6543 

6666 

6789 

6913 

7036 

7159 

7282 

7405 

7529 

7652 

123 

353 

7775 

7898 

8021 

8144 

8267 

8389 

8512 

8635 

8758 

8881 

123 

354 

*  9003 

9126 

9249 

9371 

9494 

9616 

9739 

9861 

9984 

+106 

123 

355 

55  0228 

0351 

0473 

0595 

0717 

•0840 

0962 

1084 

1206 

1328 

122 

356 

1450 

1572 

1694 

1816 

1938 

2060 

2181 

2303 

2425 

2547 

122 

357 

2668 

2790 

2911 

3033 

3155 

3276 

3398 

3519 

3640 

3762 

121 

358 

3883 

4004 

4126 

4247 

4368 

4489 

4610 

4731 

4852 

4973 

121 

359 

5094 

5215 

5336 

5457 

5578 

5699 

5820 

5940 

6061 

6182 

121 

360 

6303 

6423 

6544 

6664 

6785 

6905 

7026 

7146 

7267 

7387 

120 

361 

7507 

7627 

7748 

7868 

7988 

8108 

8228 

8349 

8469 

8589 

120 

362 

8709 

8829 

8948 

9068 

9188 

9308 

9428 

9548 

9667 

9787 

120 

363 

*  9907 

+026 

0146 

0265 

0385 

0504 

0624 

0743 

0863 

0982 

119 

364 

56  1101 

1221 

1340 

1459 

1578 

1698 

1817 

1936 

2055 

2174 

119 

365 

2293 

2412 

2531 

2650 

2760 

2887 

3006 

3125 

3244 

3362 

119 

366 

3481 

3600 

3718 

3837 

3955 

4074 

4192 

4311 

4429 

4548 

119 

367 

4666 

4784 

4903 

5021 

5139 

5257 

5376 

5494 

5612 

5730 

118 

368 

5848 

5966 

6084 

6202 

6320 

6437 

6555 

6673 

6791 

6909 

118 

369 

7026 

7144 

7262 

7379 

7497 

7614 

7732 

7849 

7967 

8084 

118 

370 

8202 

8319 

8436 

8554 

8671 

8788 

8905 

9023 

9140 

9257 

117 

371 

*  9374 

9491 

9608 

9725 

9842 

9959 

+076 

0193 

0309 

0426 

117 

372 

57  0543 

0660 

0776 

0893 

1010 

1126 

1243 

1359 

1476 

1592 

117 

373 

1709 

1825 

1942 

2058 

2174 

2291 

2407 

2523 

2639 

2755 

116 

374 

2872 

2988 

3104 

3220 

3336 

3452 

3568 

3684 

3800 

3915 

116 

375 

4031 

4147 

4263 

4379 

4494 

4610 

4726 

4841 

4957 

5072 

116 

376 

5188 

5303 

5419 

5534 

5650 

5765 

5880 

5996 

6111 

6226 

115 

377 

6341 

6457 

6572 

6687 

6802 

6917 

7032 

7147 

7262 

7377 

115 

378 

7492 

7607 

7722 

7836 

7951 

8066 

8181 

8295 

8410 

8525 

115 

379 

8639 

8754 

8868 

8983 

9097 

9212 

9326 

9441 

9555 

9669 

114 

380 

*9784 

9898 

+012 

0126 

0241 

0355 

0469 

0583 

0697 

0811 

114 

381 

58  0925 

1039 

1153 

1267 

1381 

1495 

1608 

1722 

1836 

1950 

114 

382 

2063 

2177 

2291 

2404 

2518 

2631 

2745 

2858 

2972 

3085 

114 

383 

3199 

3312 

3426 

3539 

3652 

3765 

3879 

3992 

4105 

4218 

113 

384 

4331 

4444 

4557 

4670 

4783 

4896 

5009 

5122 

5235 

5348 

113 

385 

5461 

5574 

5686 

5799 

5912 

6024 

6137 

6250 

6362 

6475 

113 

386 

6587 

6700 

6812 

6925 

7037 

7149 

7262 

7374 

7486 

7599 

112 

387 

7711 

7823 

7935 

8047 

8160 

8272 

8384 

8496 

8608 

8720 

112 

388 

8832 

8944 

9056 

9167 

9279 

9391 

9503 

9615 

9726 

9838 

112 

389 

*  9950 

+061 

0173 

0284 

0396 

0507 

0619 

0730 

0842 

0953 

112 

390 

59  1065 

1176 

1287 

1399 

1510 

1621 

1732 

1843 

1955 

2066 

111 

391 

2177 

2288 

2399 

2510 

2621 

2732 

2843 

2954 

3064 

3175 

111 

392 

3286 

3397 

3508 

3618 

3729 

3840 

3950 

4061 

4171 

4282 

111 

393 

4393 

4503 

4614 

4724 

4834 

4945 

5055 

5165 

5276 

5386 

110 

394 

5496 

5606 

5717 

5827 

5937 

6047 

6157 

6267 

6377 

6487 

110 

395 

6597 

6707 

6817 

6927 

7037 

7146 

7256 

7366 

7476 

7586 

110 

396 

7695 

7805 

7914 

8024 

8134 

8243 

8353 

8462 

8572 

8681 

110 

397 

8791 

8900 

9009 

9119 

9228 

9337 

9446 

9556 

9665 

9774 

109 

398 

*  9883 

9992 

+101 

0210 

0319 

0428 

0537 

0646 

0755 

0864 

109 

399 

60  0973 

1082 

1191 

1299 

1408 

1517 

1625  ' 

1734 

1843 

1951 

109 

N. 

O 

1 

2 

3 

4= 

5 

e 

r 

8 

9 

r>. 

55 


850 


APPENDIX. 


LOGARITHMS    OF    NUMBERS. 


TV. 

O 

1 

3      3 

4 

5      0 

7 

8 

9 

r>. 

400 

60  2060 

2169 

2277   2386 

2494 

2603 

2711 

2819 

2928 

3036 

108 

401 

3144 

3253 

3361 

3469 

3577 

3686 

3794 

3902 

4010 

4118 

108 

402 

4226 

4334 

4442 

4550 

4658 

4766 

4874 

4982 

5089 

5197 

108 

403 

5305 

5413 

5521 

5628 

5736 

5844 

5951 

6059 

6166 

6274 

108 

404 

6381 

6489 

6596 

6704 

6811 

6919 

7026 

7133 

7241 

7348 

107 

405 

7455 

7562 

7669 

7777 

7884 

7991 

8098 

8205 

8312 

8419 

107 

406 

8526 

8633 

8740 

8847 

8954 

9061 

9167 

9274 

9381 

9488 

107 

407 

*  9594 

9701 

9808 

9914 

+021 

0128 

0234 

0341 

0447 

0554 

107 

408 

61  0660 

0767 

0873^ 

0979 

1086 

1192 

1298 

1405 

1511 

1617 

106 

409 

1723 

1829 

1936 

2042 

2148 

2254 

2360 

2466 

2572 

2678 

106 

410 

2784 

2890 

2996 

3102 

3207 

3313 

3419 

3525 

3630 

3736 

106 

411 

3842 

3947 

4053 

4159 

4264 

4370 

4475 

4581 

4686 

4792 

106 

412 

4897 

5003 

5108 

5213 

5319 

5424 

5529 

5634 

5740 

5845 

105 

413 

5950 

6055 

6160 

6265 

6370 

6476 

6581 

6686 

6790 

6895 

105 

414 

7000 

7105 

7210 

7315 

7420 

7525 

7629 

7734 

7839 

7943 

105 

415 

8048 

8153 

8257 

8362 

8466 

8571 

8676 

8780 

8884 

8989 

105 

416 

*  9093 

9198 

9302 

9406 

9511 

9615 

9719 

9824 

9928 

+032 

104 

417 

62  0136 

0240 

0344 

0448 

0552 

0656 

0760 

0864 

0968 

1072 

104 

418 

1176 

1280 

1384 

1488 

1592 

1695 

1799 

1903 

2007 

2110 

104 

419 

2214 

2318 

2421 

2525 

2628 

2732 

2835 

2939 

3042 

3146 

104 

420 

3249 

3353 

3456 

3559 

3663 

3766 

3869 

3973 

4076 

4179 

103 

421 

4282 

4385 

4488 

4591 

4695 

4798 

4901 

5004 

5107 

5210 

103 

422 

5312 

5415 

5518 

5621 

5724 

5827 

5929 

6032 

6135 

6238 

103 

423 

6340 

6443 

6546 

6648 

6751 

6853 

6956 

7058 

7161 

7263 

103 

424 

7366 

7468 

7571 

7673 

7775 

7878 

7980 

8082 

8185 

8287 

102 

425 

8389 

8491 

8593 

8695 

8797 

8900 

9002 

9104 

9206 

9308 

102 

426 

*  9410 

9512 

9613 

9715 

9817 

9919 

+021 

0123 

0224 

0326 

102 

427 

63  0428 

0530 

0631 

0733 

0835 

0936 

1038 

1139 

1241 

1342 

102 

428 

1444 

1545 

1647 

1748 

1849 

1951 

2052 

2153 

2255 

2356 

101 

429 

2457 

2559 

2660  ( 

2761 

2862 

2963 

3064 

3165 

3266 

3367 

101 

430 

3468 

3569 

3670 

3771 

3872 

3973 

4074 

4175 

4276 

4376 

100 

431 

4477 

4578 

4679 

4779 

4880 

4981 

5081 

5182 

5283 

5383 

100 

432 

5484 

5584 

5685 

5785 

5886 

5986 

6087 

6187 

6287 

6388 

100 

433 

6488 

6588 

6688 

6789 

6889 

6989 

7089 

7189 

7290 

7390 

100 

434 

7490 

7590 

7690 

7790 

7890 

7990 

8090 

8190 

8290 

8389 

99 

435 

8489 

8589 

8689 

8789 

8888 

8988 

9088 

9188 

9287 

9387 

99 

436 

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9586 

9686 

9785 

9885 

9984 

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0183 

0283 

0382 

99 

437 

64  0481 

0581 

0680 

0779 

0879 

0978 

1077 

1177 

1276 

1375 

99 

438 

1474 

1573 

1672 

1771 

1871 

1970 

2069 

2168 

2267 

2366 

99 

439 

2465 

2563 

2662 

2761 

2860 

2959 

3058 

3156 

3255 

3354 

99 

440 

3453 

3551 

3650 

3749 

3847 

3946 

4044 

4143 

4242 

4340 

98 

441 

4439 

4537 

4636 

4734 

4832 

4931 

5029 

5127 

5226 

5324 

98 

442 

5422 

5521 

5619 

5717 

5815 

5913 

6011 

6110 

6208 

6306 

98 

443 

6404 

6502 

6600 

6698 

6796 

6894 

6992 

7089 

7187 

7285 

98 

444 

7383 

7481 

7579 

7676 

7774 

7872 

7969 

8067 

8165 

8262 

98 

445 

8360 

8458 

8555 

8653 

8750 

8848 

8945 

9043 

9140 

9237 

97 

446 

*  9335 

9132 

9530 

9627 

9724 

9821 

9919 

+016 

0113 

0210 

97 

447 

65  0308 

0405 

0502 

0599 

0696 

0793 

0890 

0987 

1084 

1181 

97 

448 

1278 

1375 

1472 

1569 

1666 

1762 

1859 

1956 

2053 

2150 

97 

449 

2246 

2343 

2440 

2536 

2633 

2730 

2826 

2923 

3019 

3116 

97 

450 

3213 

3309 

3405 

3502 

3598 

3695 

3791 

3888 

3984 

4080 

96 

451 

4177 

4273 

4369 

4465 

4562 

4658 

4754 

4850 

4946 

5042 

96 

452 

5138 

5235 

5331 

5427 

5523 

5619 

5715 

5810 

5906 

6002 

96 

453 

6098 

6194 

6290 

6386 

6482 

6577 

6673 

6769 

6864 

6960 

96 

454 

7056 

7152 

7247 

7343 

7438 

7534 

7629 

7725 

7820 

7916 

96 

455 

8011 

8107 

8202 

8298 

8393 

8488 

8584 

8679 

8774 

8870 

95 

456 

8965 

9060 

9155 

9250 

9346 

9441 

9536 

9631 

9726 

9821 

95 

457 

*  9916 

+011 

0106 

0201 

0296 

0391 

0486 

0581 

0676 

0771 

95 

458 

66  0865 

0960 

1055 

1150 

1245 

1339 

1434 

1529 

1623 

1718 

95 

459 

1813 

1907 

2002 

2096 

2191 

2286 

2380 

2475 

2569 

2663 

95 

N. 

0 

1 

3 

3 

4= 

5 

O 

7 

a 

0 

r>. 

APPENDIX. 


851 


LOGARITHMS    OP    NUMBERS. 


TV. 

O 

1 

«3 

3 

•4      5 

G 

7 

8 

O 

l>. 

460 

66  2758 

2852 

2947 

3041 

3135 

3230 

3324 

3418 

3512 

3607 

94 

461 

3701 

3795 

3889 

3983 

4078 

4172 

4266 

4360 

4454 

4548 

94 

462 

4642 

4736 

4830 

4924 

5018 

5112 

5206 

5299 

5393 

5487 

94 

463 

5581 

5675 

5769 

5862 

5956 

6050 

6143 

6237 

6331 

6424 

94 

464 

6518 

6612 

6705 

6799 

6892 

6986 

7079 

7173 

7266 

7360 

94 

465 

7453 

7546 

7640 

7733 

7826 

7920 

8013 

8106 

8199 

8293 

93 

466 

8386 

8479 

8572 

8665 

8759 

8852 

8945 

9038 

9131 

9224 

93 

467 

*  9317 

9410 

9503 

9596 

9689 

9782 

9875 

9967 

*060 

0153 

93 

468 

67  0246 

0339 

0431 

0524 

0617 

0710 

0802 

0895 

0988 

1080 

93 

469 

1173 

1265 

1358 

1451 

1543 

1636 

1728 

1821 

1913 

2005 

93 

470 

2098 

2190 

2283 

2375 

2467 

2560 

2652 

2744 

2836 

2929 

92 

471 

3021 

3113 

.  3205 

3297 

3390 

3482 

3574 

3666 

3758 

3850 

92 

472 

3942 

4034 

4126 

4218 

4310 

4402 

4494 

4586 

4677 

4769 

92 

473 

4861 

4953 

5045 

5137 

5228 

5320 

5412 

5503 

5595 

5687 

92 

474 

5778 

5870 

5962 

6053 

6145 

6236 

6328 

6419 

6511 

6602 

92 

475 

6694 

6785 

6876 

6968 

7059 

7151 

7242 

7333 

7424 

7516 

91 

476 

7607 

7698 

7789 

7881 

7972 

8063 

8154 

8245 

8336 

8427 

91 

477 

8518 

8609 

8700 

8791 

8882 

8973 

9064 

9155 

9246 

9337 

91 

478 

*9428 

9519 

9610 

9700 

9791 

9882 

9973 

«063 

0154 

0245 

91 

479 

68  0336 

0426 

0517 

0607 

0698 

0789 

0879 

0970 

1060 

1151 

91 

480 

1241 

1332 

1422 

1513 

1603 

1693 

1784 

1874 

1964 

2055 

90 

481 

2145 

2235 

2326 

2416 

2506 

2596 

2686 

2777 

2867 

2957 

90 

482 

3047 

3137 

3227 

3317 

3407 

3497 

3587 

3677 

3767 

3857 

90 

483 

3947 

4037 

4127 

4217 

4307 

4396 

4486 

4576 

4666 

4756 

90 

484 

4845 

4935 

5025 

5114 

5204 

5294 

5383 

5473 

5563 

5652 

90 

485 

5742 

5831 

5921 

6010 

6100 

6189 

6279 

6368 

6458 

6547 

89 

486 

6636 

5726 

6815 

6904 

6994 

7083 

7172 

7261 

7351 

7440 

89 

487 

7529 

7618 

7707 

7796 

7886 

7975 

8064 

8153 

8242 

8331 

89 

488 

8420 

8509 

8598 

8687 

8776 

8865 

8953 

9042 

9131 

9220 

89 

489 

*  9309 

9398 

9486 

9575 

9664 

9753 

9841 

9930 

*019 

0107 

89 

490 

69  0196 

0285 

0373 

0462 

0550 

0639 

0728 

0816 

0905 

0993 

89 

491 

1081 

1170 

1258 

1347 

1435 

1524 

1612 

1700 

1789 

1877 

88 

492 

1965 

2053 

2142 

2230 

2318 

2406 

2494 

2583 

2671 

2759 

88 

493 

2847 

2935 

3023 

3111 

3199 

3287 

3375 

3463 

3551 

3639 

83 

494 

3727 

3815 

3903 

3991 

4078 

4166 

4254 

4342 

4430 

4517 

88 

495 

4605 

4693 

4781 

4868 

4956 

5044 

5131 

5219 

5307 

5394 

88 

496 

5482 

5569 

5657 

5744 

5832 

5919 

6007 

6094 

6182 

6269 

87 

497 

6356 

6444 

6531 

6618 

6706 

6793 

6880 

6968 

7055 

7142 

87 

498 

7229 

7317 

7404 

7491 

7578 

7665 

7752 

7839 

7926 

8014 

87 

499 

8101 

8188 

8275 

8362 

8449 

8535 

8622 

8709 

8796 

8883 

87 

500 

8970 

9057 

9144 

9231 

9317 

9404 

9491 

9578 

9664 

9751 

87 

501 

*  9838 

9924 

*011 

0098 

0184 

0271 

0358 

0444 

0531 

0617 

87 

502 

70  0704 

0790 

0877 

0963 

1050 

1136 

1222 

1309 

1395 

1482 

86 

503 

1568 

1654 

1741 

1827 

1913 

1999 

2086 

2172 

2258 

2344 

86 

504 

2431 

2517 

2603 

2689 

2775 

2861 

2947 

3033 

3119 

3205 

86 

505 

3291 

3377 

3463 

3549 

3635 

3721 

3807 

3895 

3979 

4065 

86 

506 

4151 

4236 

4322 

4408 

4494 

4579 

4665 

4751 

4837 

4922 

86 

507 

5008 

5094 

5179 

5265 

5350 

5436 

5522 

5607 

5693 

5778 

86 

508 

5864 

5949 

6035 

6120 

6206 

6291 

6376 

6462 

6547 

6632 

85 

509 

6718 

6803 

6888 

6974 

7059 

7144 

7229 

7315 

7400 

7485 

85 

510 

7570 

7655 

7740 

7826 

7911 

7996 

8081 

8166 

8251 

8336 

85 

511 

8421 

8506 

8591 

8676 

8761 

8846 

8931 

9015 

9100 

9185 

85 

512 

*  9270 

9355 

9440 

9524 

9609 

9694 

9779 

9863 

9948 

»033 

85 

513 

71  0117 

0202 

0287 

0371 

0456 

0540 

0625 

0710 

0794 

0879 

85 

514 

0963 

1048 

1132 

1217 

1301 

1385 

1470 

1554 

1639 

1723 

84 

515 

1807 

1892 

1976 

2060 

2144 

2229 

2313 

2397 

2481 

2566 

84 

516 

2650 

2734 

2818 

2902 

2986 

3070 

3154 

3238 

3323 

3407 

84 

517 

3491 

3575 

3650 

3742 

3826 

3910 

3994 

4078 

4162 

4246 

84 

518 

4330 

4414 

4497 

4581 

4665 

4749 

4833 

4916 

5000 

5084 

84 

519 

5167 

5251 

5335 

5418 

5502 

5586 

5669 

5753 

5836 

5920 

84 

TV. 

O 

1 

3 

3 

4= 

5 

G 

7 

a 

O 

r>. 

852 


APPENDIX. 


LOGARITHMS    OF     NUMBERS. 


N. 

O 

1 

3 

3 

4, 

5      0 

7 

8 

9 

I>. 

520 

71  6003 

6087 

6170 

6254 

6337 

6421 

6504 

6588 

6671 

6754 

83 

521 

6838 

6921 

7004 

7088 

7171 

7254 

7338 

7421 

7504 

7587 

83 

522 

7671 

7754 

7837 

7920 

8003 

8086 

8169 

8253 

8336 

8419 

83 

523 

8502 

8585 

8668 

8751 

8834 

8917 

9000 

9083 

9165 

9248 

83 

524 

*  9331 

9414 

9497 

9580 

9663 

9745 

9828 

9911 

9994 

*077 

83 

525 

72  0159 

0242 

0325 

0407 

0490 

0573 

0655 

0738 

0821 

0903 

83 

526 

0986 

1068 

1151 

1233 

1316 

1398 

1481 

1563 

1646 

1728 

82 

527 

1811 

1893 

1975 

2058 

2140 

2222 

2305 

2387 

2469 

2552 

82 

528 

2634 

2716 

2798 

2881 

2963 

3045 

3127 

3209 

3291 

3374 

82 

529 

3456 

3538 

3620 

3702 

3784 

3866 

3948 

4030 

4112 

4194 

82 

530 

4276 

4358 

4440 

4522 

4604 

4685 

4767 

4849 

4931 

5013 

82 

531 

5095 

5176 

5258 

5340 

5422 

5503 

,5585 

5667 

5748 

5830 

82 

532 

5912 

5993 

6075 

6156 

6238 

6320 

6401 

6483 

6564 

6646 

82 

533 

6727 

6809 

6890 

6972 

7053 

7134 

7216 

7297 

7379 

7460 

81 

534 

7541 

7623 

7704 

7785 

7866 

7948 

8029 

8110 

8191 

8273 

81 

535 

8354 

8435 

8516 

8597 

8678 

8759 

8841 

8922 

9003 

9084 

81 

536 

9165 

9246 

9327 

9408 

9489 

9570 

9651 

9732 

9813 

9893 

81 

537 

*  9974 

*055 

0136 

0217 

0298 

0378 

0459 

0540 

0621 

0702 

81 

538 

73  0782 

0863 

0944 

1024 

1105 

1186 

1266 

1347 

1428 

1508 

81 

539 

1589 

1669 

1750 

1830 

1911 

1991 

2072 

2152 

2233 

2313 

81 

540 

2394 

2474 

2555 

2635 

2715 

2796 

2876 

2956 

3037 

3117 

80 

541 

3197 

3278 

3358 

3438 

3518 

3598 

3679 

3759 

3839 

3919 

80 

542 

3999 

4079 

4160 

4240 

4320 

4400 

4480 

4560 

4640 

4720 

80 

543 

4800 

4880 

4960 

5040 

5120 

5200 

5279 

5359 

5439 

5519 

80 

544 

5599 

5679 

5759 

5838 

5918 

5998 

6078 

6157 

6237 

6317 

80 

545 

6397 

6476 

6556 

6635 

6715 

6795 

6874 

6954 

7034 

7113 

80 

546 

7193 

7272 

7352 

7431 

7511 

7590 

7670 

7749 

7829 

7908 

79 

547 

7987 

8067 

8146 

8225 

8305 

8384 

8463 

8543 

8622 

8701 

79 

548 

8781 

8860 

8939 

9018 

9097 

9177 

9256 

9335 

9414 

9493 

79 

549 

*  9572 

9651 

9731 

9810 

9889 

9968 

*047 

0126 

0205 

0284 

79 

550 

74  0363 

0442 

0521 

0600 

0678 

0757 

0836 

0915 

0994 

1073 

79 

551 

1152 

1230 

1309 

1388 

1467 

1546 

1624 

1703 

1782 

1860 

79 

552 

1939 

2018 

2096 

2175 

2254 

2332 

2411 

2489 

2568 

2646 

79 

553 

2725 

2804 

2882 

2961 

3039 

3118 

3196 

3275 

3353 

3431 

78 

554 

3510 

3588 

3667 

3745 

3823 

3902 

3980 

4058 

4136 

4215 

78 

555 

4293 

4371 

4449 

4528 

4606 

4684 

4762 

4840 

4919 

4997 

78 

556 

5075 

5153 

5231 

5309 

5387 

5465 

5543 

5621 

5699 

5777 

78 

557 

5855 

5933 

6011 

6089 

6167 

6245 

6323 

6401 

6479 

6556 

78 

558 

6634 

6712 

6790 

6868 

6945 

7023 

7101 

7179 

7256 

7334 

78 

559 

7412 

7489 

7567 

7645 

7722 

7800 

7878 

7955 

8033 

8110 

78 

•560 

8188 

8266 

8343 

8421 

8498 

8576 

8653 

8731 

8808 

8885 

77 

561 

8963 

9040 

9118 

9195 

9272 

9350 

9427 

9504 

9582 

9659 

77 

562 

*9736 

9814 

9891 

9968 

*045 

0123 

0200 

0277 

0354 

0431 

77 

563 

75  0508 

0586 

0663 

0740 

0817 

0894 

0971 

1048 

1125 

1202 

77 

564 

1279 

1356 

1433 

1510 

1587 

1664 

1741 

1818 

1895 

1972 

77 

565 

2048 

2125 

2202 

2279 

2356 

2433 

2509 

2586 

2663 

2740 

77 

566 

2816 

2893 

2970 

3047 

3123 

3200 

3277 

3353 

3430 

3506 

77 

567 

3583 

3660 

3736 

3813 

3889 

3966 

4042 

4119 

4195 

4272 

77 

568 

4348 

4425 

4501 

4578 

4654 

4730 

4807 

4883 

4960 

5036 

76 

569 

5112 

5189 

5265 

5341 

5417 

5494 

5570 

5646 

5722 

5799 

76 

570 

5875 

5951 

6027 

6103 

6180 

6256 

6332 

6408 

6484 

6560 

76 

571 

6636 

6712 

6788 

6864 

6940 

7016 

7092 

7168 

7244 

7320 

76 

572 

7396 

7472 

7548 

7624 

7700 

7775 

7851 

7927 

8003 

8079 

76 

573 

8155 

8230 

8306 

8382 

8458 

8533 

8609 

8685 

8761 

8836 

76 

574 

8912 

8988 

9063 

9139 

9214 

9290 

9366 

9441 

9517 

9592 

76 

575 

*  9668 

9743 

9819 

9894 

9970 

4045 

0121 

0196 

0272 

0347 

75 

576 

76  0422 

0498 

0573 

0649 

0724 

0799 

0875 

0950 

1025 

1101 

75 

577 

1176 

1251 

1326 

1402 

1477 

1552 

1627 

1702 

1778 

1853 

75 

578 

1928 

2003 

2078 

2153 

2228 

2303 

2378 

2453 

2529 

2604 

75 

579 

2679 

2754 

2829 

2904 

2978 

3053 

3128 

3203 

3278 

3353 

75 

3V. 

O 

1 

9 

3 

A 

5 

e 

7 

0 

O 

r>. 

APPENDIX. 


853 


LOGARITHMS    OF    NUMBERS. 


IV  . 

o 

1 

3 

3 

4 

5 

G 

7 

& 

9 

r>. 

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610 

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6254 

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6609 

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71 

612 

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6822 

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6964 

7035 

7106 

7177 

7248 

7319 

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71 

613 

7460 

7531 

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8027 

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71 

614 

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8310 

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624 

5185 

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625 

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6019 

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632 

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1404 

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69 

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2089 

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2568 

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2774 

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3184 

3252 

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3389 

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3457 

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4003 

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68 

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4139 

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854: 


APPENDIX. 


LOGARITHMS    OF     NUMBERS. 


N. 

o 

1 

3 

3 

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5      0 

7 

8 

9 

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6723 

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7061 

7129 

7197 

7264 

7332 

7400 

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68 

642 

7535 

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7941 

8008 

8076 

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68 

643 

8211 

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67 

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9156 

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9425 

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67 

645 

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9627 

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9964 

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0098 

0165 

67 

646 

81  0233 

0300 

0367 

0434 

0501 

0569 

0636 

0703 

0770 

0837 

67 

647 

0904 

0971 

1039 

1106 

1173 

1240 

1307 

1374 

1441 

1508 

67 

648 

1575 

1642 

1709 

1776 

1843 

1910 

1977 

2044 

2111 

2178 

67 

649 

2245 

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2379 

2445 

2512 

2579 

2646 

2713 

2780 

2847 

67 

650 

2913 

2980 

3047 

3114 

3181 

3247 

3314 

3381 

3448 

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67 

651 

3581 

3648 

3714 

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3848 

3914 

3981 

4048 

4114 

4181 

67 

652 

4248 

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4381 

4447 

4514 

4581 

4647 

4714 

4780 

4847 

67 

653 

4913 

4980 

5046 

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5179 

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5312 

5378 

5445 

5511 

66 

654 

5578 

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5711 

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5910 

5976 

6042 

6109 

6175 

66 

655 

6241 

6308 

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6440 

6506 

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6639 

6705 

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6838 

66 

656 

6904 

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7036 

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7235 

7301 

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7433 

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66 

657 

7565 

7631 

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7764 

7830 

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7962 

8028 

8094 

8160 

66 

658 

8226 

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8424 

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8556 

8622 

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66 

662 

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1251 

1317 

1382 

1448 

66 

663 

1514 

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1645 

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2037 

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65 

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2822 

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3083 

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3279 

3344 

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666 

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3605 

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667 

4126 

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4256 

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4386 

4451 

4516 

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668 

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4971 

5036 

5101 

5166 

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5296 

5361 

65 

669 

5426 

5491 

5556 

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5815 

5880 

5945 

6010 

65 

670 

6075 

6140 

6204 

6269 

6334 

6399 

6464 

6528 

6593 

6658 

65 

671 

6723 

6787 

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6981 

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7175 

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65 

672 

7369 

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7628 

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7821 

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65 

673 

8015 

8080 

8144 

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8338 

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8467 

8531 

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64 

674 

8660 

8724 

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8853 

8918 

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9046 

9111 

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677 

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1102 

1166 

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678 

1230 

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1550 

1614 

1678 

1742 

1806 

64 

679 

1870 

1934 

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2062 

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2189 

2253 

2317 

2381 

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64 

680 

2509 

2573 

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2700 

2764 

2828 

2892 

2956 

3020 

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64 

681 

3147 

3211 

3275 

3338 

3402 

3466 

3530 

3593 

3657 

3721 

64 

682 

3784 

3848 

3912 

3975 

4039 

4103 

4166 

4230 

4294 

4357 

64 

683 

4421 

4484 

4548 

4611 

4675 

4739 

4802 

4866 

4929 

4993 

64 

684 

5056 

5120 

5183 

5247 

5310 

5373 

5437 

5500 

5564 

5627 

63 

685 

5691 

5754 

5817 

5881 

5944 

6007 

6071 

6134 

6197 

6261 

63 

686 

6324 

6387 

6451 

6514 

6577 

6641 

6704 

6767 

6830 

6894 

63 

687 

6957 

7020 

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7210 

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7336 

7399 

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7525 

63 

688 

7588 

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7715 

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7904 

7967 

8030 

8093 

8156 

63 

689 

8219 

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8660 

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63 

690 

8849 

8912 

8975 

9038 

9101 

9164 

9227 

9289 

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9415 

63 

691 

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9541 

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9667 

9729 

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9855 

9918 

9981 

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63 

692 

84  0106 

0169 

0232 

0294 

0357 

0420 

0482 

0545 

0608 

0671 

63 

693 

0733 

0796 

0859 

0921 

0984 

1046 

1109 

1172 

1234 

1297 

63 

694 

1359 

1422 

1485 

1547 

1610 

1672 

1735 

1797 

1860 

1922 

63 

695 

1985 

2047 

2110 

2172 

2235 

2297 

2360 

2422 

2484 

2547 

62 

696 

2609 

2672 

2734 

2796 

2859 

2921 

2983 

3046 

3108 

3170 

62 

697 

3233 

3295 

3357 

3420 

3482 

3544 

3606 

3669 

3731 

3793 

62 

698 

3855 

3918 

3980 

4042 

4104 

4166 

4229 

4291 

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4415 

62 

699 

4477 

4539 

4601 

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IV. 

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7 

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I>. 

APPENDIX. 


855 


LOGARITHMS    OF     NUMBERS.! 


IV. 

<> 

1 

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3 

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5 

O 

7 

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9 

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700 

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701 

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5780 

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5904 

5966 

6028 

6090 

6151 

6213 

6275 

62 

702 

6337 

6399 

6461 

6523 

6585 

6646 

6708 

6770 

6832 

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62 

703 

6955 

7017 

7079 

7141 

7202 

7264 

7326 

7388 

7449 

7511 

62 

704 

7573 

7634 

7696 

7758 

7819 

7881 

7943 

8004 

8066 

8128 

62 

705 

8189 

8251 

8312 

8374 

8435 

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8559 

8620 

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8743 

62 

706 

8805 

8866 

8928 

8989 

9051 

9112 

9174 

9235 

9297 

9358 

61 

707 

9419 

9481 

9542 

9604 

9665 

9726 

9788 

9849 

9911 

9972 

61 

708 

85  0033 

0095 

0156 

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0279 

0340 

0401 

0462 

0524 

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61 

709 

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0769 

0830 

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0952 

1014 

1075 

1136 

1197 

61 

710 

1258 

1320 

1381 

1442 

1503 

1564 

1625 

1686 

1747 

1809 

61 

711 

1870 

1931 

1992 

2053 

2114 

2175 

2236 

2297 

2358 

2419 

61 

712 

2480 

2541 

2602 

2663 

2724 

2785 

2846 

2907 

2968 

3029 

61 

713 

3090 

3150 

3211 

3272 

3333 

3394 

3455 

3516 

3577 

3637 

61 

714 

3698 

3759 

3820 

3881 

3941 

4002 

4063 

4124 

4185 

4245 

61 

715 

4306 

4367 

4428 

4488 

4549 

4610 

4670 

4731 

4792 

4852 

61 

716 

4913 

4974 

5034 

5095 

5156 

5216 

5277 

5337 

5398 

5459 

61 

717 

5519 

5580 

5640 

5701 

5761 

5822 

5882 

5943 

6003 

6064 

61 

718 

6124 

6185 

6245 

6306 

6366 

6427 

6487 

6548 

6608 

6668 

60 

719 

6729 

6789 

6850 

6910 

6970 

7031 

7091 

7152 

7212 

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60 

720 

7332 

7393 

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7513 

7574 

7634 

7694 

7755 

7815 

7875 

60 

721 

7935 

7995 

8056 

8116 

8176 

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8357 

8417 

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60 

722 

8537 

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8657 

8718 

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8838 

8898 

8958 

9018 

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60 

723 

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9198 

9258 

9318 

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9439 

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9559 

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60 

724 

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9859 

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60 

725 

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0757 

0817 

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60 

726 

0937 

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1056 

1116 

1176 

1236 

1295 

1355 

1415 

1475 

60 

727 

1534 

1594 

1654 

1714 

1773 

1833 

1893 

1952 

2012 

2072 

60 

728 

2131 

2191 

2251 

2310 

2370 

2430 

2489 

2549 

2608 

2668 

60 

729 

2728 

2787 

2847 

2906 

2966 

3025 

3085 

3144 

3204 

3263 

60 

730 

3323 

3382 

3442 

3501 

3561 

3620 

3680 

3739 

3799 

3858 

59 

731 

3917 

3977 

4036 

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4155 

4214 

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59 

732 

4511 

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5519 

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59 

734 

5696 

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5814 

5874 

5933 

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6051 

6110 

6169 

6228 

59 

735 

6287 

6346 

6405 

6465 

6524 

6583 

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6701 

6760 

6819 

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736 

6878 

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7114 

7173 

7232 

7291 

7350 

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59 

737 

7467 

7526 

7585 

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7703 

7762 

7821 

7880 

7939 

7998 

59 

738 

8056 

8115 

8174 

8233 

8292 

8350 

8409 

8468 

8527 

8586 

59 

739 

8644 

8703 

8762 

8821 

8879 

8938 

8997 

9056 

9114 

9173 

59 

740 

9232 

9290 

9349 

9408 

9466 

9525 

9584 

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9701 

9760 

59 

741 

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9877 

9935 

9994 

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0111 

0170 

0228 

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59 

742 

87  0404 

0462 

0521 

0579 

0638 

0696 

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0813 

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0930 

58 

743 

0989 

1047 

1106 

1164 

1223 

1281 

1339 

1398 

1456 

1515 

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744 

1573 

1631 

1690 

1748 

1806 

1865 

1923 

1981 

2040 

2098 

58 

745 

2156 

2215 

2273 

2331 

2389 

2448 

2506 

2564 

2622 

2681 

58 

746 

2739 

2797 

2855 

2913- 

2972 

3030 

3088 

3146 

3204 

3262 

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747 

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3379 

3437 

3495 

3553 

3611 

3669 

3727 

3785 

3844 

58 

748 

3902 

3960 

4018 

4076 

4134 

4192 

4250 

4308 

4366 

4424 

58 

749 

4482 

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4714 

4772 

4830 

4888 

4945 

5003 

58 

750 

5061 

5119 

5177 

5235 

5293 

5351 

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5466 

5524 

5582 

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751 

5640 

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5756 

5813 

5871 

5929 

5987 

6045 

6102 

6160 

58 

752 

6218 

6276 

6333 

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58 

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7947 

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57 

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APPENDIX. 


LOGARITHMS    OP     NUMBERS. 


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1442 

1499 

1556 

1613 

1670 

1727 

1784 

1841 

1898 

57 

762 

1955 

2012 

2069 

2126 

2183 

2240 

2297 

2354 

2411 

2468 

57 

763 

2525 

2581 

2638 

2695 

2752 

2809 

2866 

2923 

2980 

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57 

764 

3093 

3150 

3207 

3264 

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3377 

3434 

3491 

3548 

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57 

765 

3661 

3718 

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3832 

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4059 

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57 

766 

4229 

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4512 

4569 

4625 

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4739 

57 

767 

4795 

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4965 

5022 

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5248 

5305 

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768 

5361 

5418 

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5587 

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5813 

5870 

57 

769 

5926 

5983 

6039 

6096 

6152 

6209 

6265 

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6378 

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56 

770 

6491 

6547 

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6716 

6773 

6829 

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56 

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7617 

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778 

0980 

1035 

1091 

1147 

1203 

1259 

1314 

1370 

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56 

779 

1537 

1593 

1649 

1705 

1760 

1816 

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1928 

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2039 

56 

780 

2095 

2150 

2206 

2262 

2317 

2373 

2429 

2484 

2540 

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56 

781 

2651 

2707 

2762 

2818 

2873 

2929 

2985 

3040 

3096 

3151 

56 

782 

3207 

3262 

3318 

3373 

3429 

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3706 

56 

783 

3762 

3817 

3873 

3928 

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4039 

4094 

4150 

4205 

4261 

55 

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4316 

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4427 

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5312 

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55 

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5423 

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5864 

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6030 

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6416 

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796 

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0968 

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1077 

1131 

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1240 

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55 

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54 

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2873 

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54 

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53 

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1051 

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53 

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1264 

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1530 

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1637 

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2063 

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53 

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2222 

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2435 

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53 

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2753 

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2859 

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APPENDIX. 


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53 

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4872 

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53 

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5400 

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5716 

5769 

5822 

5875 

53 

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5927 

5980 

6033 

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6138 

6191 

6243 

6296 

6349 

6401 

53 

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6664 

6717 

6770 

6822 

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6927 

53 

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7033 

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7138 

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7295 

7348 

7400 

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53 

827 

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7663 

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7925 

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52 

828 

8030 

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829 

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4796 

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5312 

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51 

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1000 

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1305 

1356 

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51 

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1458 

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1661 

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51 

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51 

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2474 

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2727 

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51 

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50 

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5709 

5759 

5809 

5860 

5910 

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50 

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6061 

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6162 

6212 

6262 

6313 

6363 

6413 

6463 

50 

864 

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6564 

6614 

6665 

6715 

6765 

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6865 

6916 

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50 

865 

7016 

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7869 

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867 

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50 

868 

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869 

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9819 

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0267 

0317 

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50 

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0566 

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0716 

0765 

0815 

0865 

0915 

0964 

50 

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1014 

1064 

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1163 

1213 

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1313 

1362 

1412 

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50 

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1511 

1561 

1611 

1660 

1710 

1760 

1809 

1859 

1909 

1958 

50 

875 

2008 

2058 

2107 

2157 

2207 

2256 

2306 

2355 

2405 

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50 

876 

2504 

2554 

2603 

2653 

2702 

2752 

2801 

2851 

2901 

2950 

50 

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3000 

3049 

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3247 

3297 

3346 

3396 

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3643 

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5469 

5518 

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6108 

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6207 

6256 

6305 

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6747 

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7532 

7581 

7630 

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7826 

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7924 

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8022 

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8119 

8168 

8217 

8266 

8315 

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49 

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8413 

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8657 

8706 

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8853 

49 

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9048 

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9146 

9195 

9244 

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49 

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49 

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0900 

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1046 

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1143 

1192 

1240 

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49 

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1338 

1386 

1435 

1483 

1532 

1580 

1629 

1677 

1726 

1775 

49 

895 

1823 

1872 

1920 

1969 

2017 

2066 

2114 

2163 

2211 

2260 

48 

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2308 

2356 

2405 

2453 

2502 

2550 

2599 

2647 

2696 

2744 

48 

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2792 

2841 

2889 

2938 

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3034 

3083 

3131 

3180 

3228 

48 

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3276 

3325 

3373 

3421 

3470 

3518 

3566 

3615 

3663 

3711 

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3760 

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3856 

3905 

3953 

4001 

4049 

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900 

4243 

4291 

4339 

4387 

4435 

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4532 

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4821 

4869 

4918 

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5014 

5062 

5110 

5158 

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5207 

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5303 

5351 

5399 

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5495 

5543 

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5688 

5736 

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5832 

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904 

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6216 

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8038 

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8134 

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8325 

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9041 

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9137 

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9232 

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1041 

1089 

1136 

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1231 

1279 

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1421 

1469 

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1611 

1658 

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1753 

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1990 

2038 

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2132 

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2227 

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917 

2369 

2417 

2464 

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2606 

2653 

2701 

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918 

2843 

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2937 

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3032 

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3268 

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919 

3316 

3363 

3410 

3457 

3504 

3552 

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920 

3788 

3835 

3882 

3929 

3977 

4024 

4071 

4118 

4165 

4212 

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921 

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4307 

4354 

4401 

4448 

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4637 

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47 

922 

4731 

4778 

4825 

4872 

4919 

4966 

5013 

5061 

5108 

5155 

47 

923 

5202 

5249 

5296 

5343 

5390 

5437 

5484 

5531 

5578 

5625 

47 

924 

5672 

5719 

5766 

5813 

5860 

5907 

5954 

6001 

6048 

6095 

47 

925 

6142 

6189 

6236 

6283 

6329 

6376 

6423 

6470 

6517 

6564 

47 

926 

6611 

6658 

6705 

6752 

6799 

6845 

6892 

6939 

6986 

7033 

47 

927 

7080 

7127 

7173 

7220 

7267 

7314 

7361 

7408 

7454 

7501 

47 

928 

7548 

7595 

7642 

7688' 

7735 

7782 

7829 

7875 

7922 

7969 

47 

929 

8016 

8062 

8109 

8156 

8203 

8249 

8296 

8343 

8390 

8436 

47 

930 

8483 

8530 

8576 

8623 

8670 

8716 

8763 

8810 

8856 

8903 

47 

931 

8950 

8996 

9043 

9090 

9136 

9183 

9229 

9276 

9323 

9369 

47 

932 

9416 

9463 

9509 

9556 

9602 

9649 

9695 

9742 

9789 

9835 

47 

933 

*  9882 

9928 

9975 

»021 

0068 

0114 

0161 

0207 

0254 

0300 

47 

934 

97  0347 

0393 

0440 

0486 

0533 

0579 

0626 

0672 

0719 

0765 

46 

935 

0812 

0858 

0904 

0951 

0997 

1044 

1090 

1137 

1183 

1229 

46 

936 

1276 

1322 

1369 

1415 

1461 

1508 

1554 

1601 

1647 

1693 

46 

937 

1740 

1786 

1832 

1879 

1925 

1971 

2018 

2064 

2110 

2157 

46 

938 

2203 

2249 

2295 

2342 

2388 

2434 

2481 

2527 

2573 

2619 

46 

939 

2666 

2712 

2758 

2804 

2851 

2897 

2943 

2989 

3035 

3082 

46 

IV. 

0 

1 

3 

3 

4, 

5 

0 

7 

S 

Q 

l>. 

APPENDIX. 


859 


LOGARITHMS    OF     NUMBERS. 


N. 

O 

1 

2 

3 

4= 

5 

e 

7 

8 

& 

l>. 

940 

97  3128 

3174 

3220 

3266 

3313 

3359 

3405 

3451 

3497 

3543 

46 

941 

3590 

3636 

3682 

3728 

3774 

3820 

3866 

3913 

3959 

4005 

46 

942 

4051 

4097 

4143 

4189 

4235 

4281 

4327 

4374 

4420 

4466 

46 

943 

4512 

4558 

4604 

4650 

4696 

4742 

4788 

4834 

4880 

4926 

46 

944 

4972 

5018 

5064 

5110 

5156 

5202 

5248 

5294 

5340 

5386 

46 

945 

5432 

5478 

5524 

5570 

5616 

5662 

5707 

5753 

5799 

5845 

46 

946 

5891 

5937 

5983 

6029 

6075 

6121 

6167 

6212 

6258 

6304 

46 

947 

6350 

6396 

6442 

6488 

6533 

6579 

6625 

6671 

6717 

6763 

46 

948 

6808 

6854 

6900 

6946 

6992 

7037 

7083 

7129 

7175 

7220 

46 

949 

7266 

7312 

7358 

7403 

7449 

7495 

7541 

7586 

7632 

7678 

46 

950 

7724 

7769 

7815 

7861 

7906 

7952 

7998 

8043 

8089 

8135 

46 

951 

8181 

8226 

8272 

8317 

8363 

8409 

8454 

8500 

8546 

8591 

46 

952 

8637 

8683 

8728 

8774 

8819 

8865 

8911 

8956 

9002 

9047 

46 

953 

9093 

9138 

9184 

9230 

9275 

9321 

9366 

9412 

9457 

9503 

46 

954 

9548 

9594 

9639 

9685 

9730 

9776 

9821 

9867 

9912 

9958 

46 

955 

98  0003 

0049 

0094 

0140 

0185 

0231 

0276 

0322 

0367 

0412 

45 

956 

0458 

0503 

0549 

0594 

0640 

0685 

0730 

0776 

0821 

0867 

45 

957 

0912 

0957 

1003 

1048 

1093 

1139 

1184 

1229 

1275 

1320 

45 

958 

1366 

1411 

1456 

1501 

1547 

1592 

1637 

1683 

1728 

1773 

45 

959 

1819 

1864 

1909 

1954 

2000 

2045 

2090 

2135 

2181 

2226 

45 

960 

2271 

2316 

2362 

2407 

2452 

2497 

2543 

2588 

2633 

2678 

45 

961 

2723 

2769 

2814 

2859 

2904 

2949 

2994 

3040 

3085 

3130 

45 

962 

3175 

3220 

3265 

3310 

3356 

3401 

3446 

3491 

3536 

3581 

45 

963 

3626 

3671 

3716 

3762 

3807 

3852 

3897 

3942 

3987 

4032 

45 

964 

4077 

4122 

4167 

4212 

4257 

4302 

4347 

4392 

4437 

4482 

45 

965 

4527 

4572 

4617 

4662 

4707 

4752 

4797 

4842 

4887 

4932 

45 

966 

4977 

5022 

5067 

5112 

5157 

5202 

5247 

5292 

5337 

5382 

45 

967 

5426 

5471 

5516 

5561 

5606 

5651 

5696 

5741 

5786 

5830 

45 

968 

5875 

5920 

5965 

6010 

6055 

6100 

6144 

6189 

6234 

6279 

45 

969 

6324 

6369 

6413 

6458 

6503 

6548 

6593 

6637 

6682 

6727 

45 

970 

6772 

6817 

6861 

6906 

6951 

6996 

7040 

7085 

7130 

7175 

45 

971 

7219 

7264 

7309 

7353 

7398 

7443 

7488 

7532 

7577 

7622 

45 

972 

7666 

7711 

7756 

7800 

7845 

7890 

7934 

7979 

8024 

8068 

45 

973 

8113 

8157 

8202 

8247 

8291 

8336 

8381 

8425 

8470 

8514 

45 

974 

8559 

8604 

8648 

8693 

8737 

8782 

8826 

8871 

8916 

8960 

45 

975 

9005 

9049 

9094 

9138 

9183 

9227 

9272 

9316 

9361 

9405 

45 

976 

9450 

9494 

9539 

9583 

9628 

9672 

9717 

9761 

9806 

9850 

44 

977 

*  9895 

9939 

9983 

+028 

0072 

0117 

0161 

0206 

0250 

0294 

44 

978 

99  0339 

0383 

0428 

0472 

0516 

0561 

0605 

0650 

0694 

0738 

44 

979 

0783 

0827 

0871 

0916 

0960 

1004 

1049 

1093 

1137 

1182 

44 

980 

1226 

1270 

1315 

1359 

1403 

1448 

1492 

1536 

1580 

1625 

44 

981 

1669 

1713 

1758 

1802 

1846 

1890 

1935 

1979 

2023 

2067 

44 

982 

2111 

2156 

2200 

2244 

2288 

2333 

2377 

2421 

2465 

2509 

44 

983 

2554 

2598 

2642 

2686 

2730 

2774 

2819 

2863 

2907 

2951 

44 

984 

2995 

3039 

3083 

3127 

3172 

3216 

3260 

3304 

3348 

3392 

44 

985 

3436 

3480 

3524 

3568 

3613 

3657 

3701 

3745 

3789 

3833 

44 

986 

3877 

3921 

3965 

4009 

4053 

4097 

4141 

4185 

4229 

4273 

44 

987 

4317 

4361 

4405 

4449 

4493 

4537 

4581 

4625 

4669 

4713 

44 

988 

4757 

4801 

4845 

4889 

4933 

4977 

5021 

5065 

5108 

5152 

44 

989 

5196 

5240 

5284 

5328 

5372 

5416 

5460 

5504 

5547 

5591 

44 

990 

5635 

5679 

5723 

5767 

5811 

5854 

5898 

5942 

5986 

6030 

44 

991 

6074 

6117 

6161 

6205 

6249 

6293 

6337 

6380 

6424 

6468 

44 

992 

6512 

6555 

6599 

6643 

6687 

.6731 

6774 

6818 

6862 

6906 

44 

993 

6949 

6993 

7037 

7080 

7124 

7168 

7212 

7255 

7299 

7343 

44 

994 

7386 

7430 

7474 

7517 

7561 

7605 

7648 

7692 

7736 

7779 

44 

995 

7823 

7867 

7910 

7954 

7998 

8041 

8085 

8129 

8172 

8216 

44 

996 

8259 

8303 

8347 

8390 

8434 

8477 

8521 

8564 

8608 

8652 

44 

997 

8695 

8739 

8782 

8826 

8869 

8913 

8956 

9000 

9043 

9087 

44 

998 

9131 

9174 

9218 

9261 

9305 

9348 

9392 

9435 

9479 

9522 

44 

999 

9565 

9609 

9652 

9696 

9739 

9783 

9826 

9870 

9913 

9957 

43 

3V. 

O 

1 

3 

3 

4 

5 

e 

7 

8 

O 

D. 

860 


APPENDIX. 


The  Application  of  Logarithms. — The  logarithm  of  a  number  is  set  down  as  a  decimal, 
and  addition  of  ciphers  to  numbers  does  not  change  the  logarithm  ;  it  is  the  same  for  11, 
110  1100,  but  the  value  of  the  number  is  established  by  figures  to  the  left  of  the  decimal 
point ;  thus,  if  the  number  is  among  the  units,  the  characteristic  is  0 ;  if  in  the  tens,  1 ; 
in  the  hundreds,  2 ;  thousands,  3 ;  tens  of  thousands,  4,  and  so  on  ;  if  the  number  is  a 
decimal  fraction  and  the  first  figure  a  tenth,  the  characteristic  is  1,  if  hundredths  2,  thou- 
sandths 3. 

Multiplication  of  two  numbers  is  performed  by  the  addition  of  their  logarithms  and 
characteristics,  and  finding  the  number  corresponding  to  their  sum  ;  thus,  to  multiply  119 

by  2760. 

Characteristic  of  119  2,  logarithm.         2-075547 

"  2760  3,          "  3-440909 

5-516456 
3284  403 

401  I)  =  132)53(401 


328440-1  528 


200 
132 
~68 

As  the  characteristic  is  5,  the  result  is  6  figures  of  whole  numbers. 
Division  is  performed  by  subtracting  the  logarithm  of  the  divisor  from  that  of  the  divi- 
dend, and  finding  the  logarithm  of  the  remainder  for  the  quotient.     But  if  the  divisor  is 
the  larger,  then  the  characteristic  of  the  remainder  is  —  . 
Thus,  to  divide  500  by  63008. 

Logarithm  of  500  2-698970 

Logarithm  of  63000  =  4-799341 

D  =  69          8-^»  =  65-2 

10 

Logarithm  of  63008  4.799396 

Corresponding  number  -007935  =  3-899574 

Numbers  are  raised  to  any  power  by  multiplying  their  logarithm  by  the  exponents,  and 
roots  are  extracted  by  dividing  the  logarithm.  Thus,  to  get  the  square  of  any  number,  its 
logarithm  is  multiplied  by  2,  for  the  cube  by  3,  for  the  4th  power  by  4  ;  in  like  manner,  to 
obtain  the  square  root  of  the  number,  divide  the  logarithm  by  2  ;  by  3  for  \f  ;  by  4 


for 


. 


The  roots  of  numbers  are  better  expressed  by  fractional  exponents,  thus:  Va  by  a~;*» 
|/a  by  a  8. 

The  raising  of  numbers  to  different  powers  is  extremelj'  simple,  by  logarithms,  when 
the  numbers  are  whole  numbers,  but  becomes  somewhat  more  complicated  when  the  num- 
bers are  decimals. 

Thus,  to  find  the  4th  power  of  -07. 

Logarithm  -07  2-845098 

_  _  4 

8     3-380392 


Number  -00002401  5-380392 
To  extract  the  4th  root  of  -07 — 

Logarithm  -07  2-845098 

Add  2  to  the  characteristic  to  make  it 

divisible  by  4,  and  a  positive  2  to  the  2-2-845098 

logarithm  to  balance  it.  4)4'2-845098 

Number  -5143  1-    711274 


APPENDIX.  861 

The  exponent  of  a  root  is  often  a  decimal ;  thus  the  1/'07  may  be  expressed  by  -07-a8. 

Logarithm  -07  2-845098 

-25 

4225490 
1690196 


•5-21127450 
•5-5 

Number  -5143  1-71127450 

NOTE. — In  this  example,  -5  is  added  to  the  resultant  characteristic  to  bring  it  to  an  integer,  and 
an  equal  positive  amount  to  the  logarithm  to  balance  it. 

The  same  logarithm  as  by  dividing  by  4-  and  corresponding  to  the  number  -5143.  The 
rule  is  to  consider  the  logarithm  as  a  plus  quantity,  and  multiply  by  the  exponent  and  the 
characteristic  as  minus,  and.  after  similar  multiplication,  subtract  it  from  the  first  product. 
When  a  characteristic  has  a  minus  sign  (3),  and  it  is  to  be  subtracted,  the  sign  is  changed 
and  added. 

Thus,  to  divide  10-  by  TV 

Logarithm  10-  1-00000 

rV  I 

Logarithm  of  100-  2-000 

To  divide  TV  Logarithm  TOOOOO 

by  T^T  2- 


Logarithm  of  10'  1*0000 

To  divide  y^1^  Logarithm  3-00000 

by  100  2 

Logarithm  of  -00001  5 

TABLE  OF  RECIPROCALS,  PAGES  828  AND  829. 

Use  of  Reciprocals.  — Reciprocals  may  be  conveniently  used  to  facilitate  computations 
in  long  divisions.  Instead  of  dividing  as  usual,  multiply  the  dividend  by  the  reciprocal 
of  the  divisor.  The  method  is  especially  useful  when  many  different  dividends  are  re- 
quired to  be  divided  by  the  same  divisor.  In  this  case  find  the  reciprocal  of  the  divisor, 
make  a  small  table  of  its  multiples  up  to  nine  times,  and  use  this  as  a  multiplication 
table,  instead  of  actually  performing  the  multiplication  in  each  case. 


SCRAPS. 

IT  is  good  practice  to  collect,  from  the  circulars  of  manufacturers,  and  from 
illustrated  newspapers  and  magazines,  varied  illustrations  of  tools  and  machines, 
engineering  structures,  buildings,  etc.,  and  arrange  them  under  their  appropri- 
ate heads  in  scrap-books.  They  will  be  found  very  useful  in  designing,  not 
only  enabling  one  the  more  readily  to  make  drawings,  but  to  convey  to  the 
draughtsman  the  character  and  proportions  of  the  design  which  is  to  be  made. 
And  those  parts  which  are  of  common  use  and  purchasable  in  the  market  can 
be  readily  arranged  in  position  and  executed  more  economically  than  from  a 
new  design.  There  is  a  saving  in  the  matter  of  drawing,  and  also  in  the  cost 
of  construction. 

A  proper  combination  and  arrangement  of  parts  which  have  served  a  pur- 
pose will  afford  material  for  a  more  practical  and  satisfactory  design  than  ean 
usually  be  made  from  attempts  at  originality.  Knowledge  of  what  has  been 
done  is  economy  in  all  labour.  If  the  construction  or  machine  can  not  be  seen, 
its  picture  can  supply  its  place,  and  its  details  can  be  studied  at  leisure  ;  and 
as  the  education  of  the  eye  is  of  essential  importance  to  the  draughtsman,  let 
him  see  as  much  as  he  can  practically,  and  at  the  same  time  acquire  a  good 
collection  of  scraps  from  which  to  design.  There  are  few  constructions  from 
which  something  of  education  can  not  be  drawn,  parts  if  not  a  whole. 

In  this  view  a  small  collection  of  scraps  has  been  made  pertinent  to  the 
book.  Its  page  does  not  admit  of  the  sizes  which  will  be  found  in  the  illus- 
trated papers  and  magazines — the  quarto  will  be  found  much  more  generally 
useful — and  a  library  of  such  scrap-books  will  furnish  material  for  a  draughts- 
man which  can  not  be  found  in  any  encyclopaidia. 

862 


SCRAPS. 


863 


Compound  Steam  Cylinders.     H.  M.  S.  Spartan. 


Wrought-Iron  Plates  and  Covers. 


Compressed- Air  Locomotive,  St.  Gothard  Tunnel. 


864 


SCRAPS. 


Three-Throw  Crank. 


Forged  weight,  2$.  tons  11  cwt. 
Finished    "      15    "     8    " 


Corrugated  Boiler-Flues. 


Weight,  25  tons  10  cwt. 


SCRAPS. 


865 


56 


Screw  Propeller. 
Vessel,  1400  jrross  tons.     Engines,  130  nominal  English  horse-power 


866 


SCRAPS. 


Spherical  Bearing. 


O®  QJ83OOO 


•1 
I  , 

•k? 

l-l 


il  IPi 

^    i^ 
1^   U* 

C)  ?5          ^  ^   ^. 


Conventional  Signs  of  Riveting. 


F  sfi 


L 


In  the  Wilkinson  stoker  the  coal  is  fed  mechanically  through  an  inclined  pipe  on  to 
the  dead  plate  P  and  slides  down  upon  the  bars,  which  are  hollow  and  set  at  an  angle. 
The  top  of  the  bars  is  stepped,  and  tuyere-shaped  openings  about  J  x  3  inches  are  pro- 
vided in  each  riser.  The  bars  are  carried  at  their  ends  on  hollow  boxes,  and  are  4-inch 
centres.  For  the  feeding,  adjacent  bars  move  in  opposite  directions  by  a  system  of  tog- 
gles driven  by  the  stoker  engine. 


SCRAPS. 


867 


The  Coxe  stoker  consists  of  a  travelling  grate  with  fire  on  its  tipper  surface.  The 
coal  is  fed  by  the  motion  of  the  grate  at  the  front.  There  are  four  blast  compartments, 
A,  B,  C,  D,  under  the  fire  connected  by  dampers.  The  sides  of  the  furnace  are  pro- 
tected by  wrought-iron  water  backs,  through  which  the  water  circulates  under  slight 
pressure. 


The  Stirling  Boiler  consists  of  three  upper  steam-drums  and  a  lower  mud-drum.  All 
the  steam-drums  are  connected  at  the  top,  but  the  front  and  middle  drums  only  'are  con- 
nected in  the  water  space.  Tubes,  3V  diameter ;  movement  of  flame  shown  by  arrows 
around  baffle  plates. 


868 


SCRAPS. 


The  Abendroth  and  Boot  Boiler  was  the  earliest  of  its  type  on  the  market,  and  has 
been  modified  in  its  details  since  its  introduction  to  meet  necessities  which  were  devel- 
oped by  use.  The  section  gives  the  latest  form.  The  angles  of  the  tubes,  with  the  hori- 
zontal and  the  baffle  plates  beneath  and  around  the  tubes  making  a  positive  circulation 
of  the  flame,  are  of  the  original  design,  but  longitudinal  drums  extend  lengthwise  over 
the  tubes  with  a  wrater  circulation  in  the  lower  half  toward  the  rear  and  downward 
by  vertical  pipes  to  the  lower  ends  of  the  tubes.  On  these  vertical  pipes  there  are 
two  cross-drums — the  intermediate  one  to  receive  the  feedwater,  the  lower  for  a  mud- 
drum.  The  long  drums  connect  with  the  steam-drum  placed  above  and  crosswise  of 
them. 


SCRAPS. 


869 


8TO 


SCRAPS. 


Andover,  Mass.,  Steam  Pumping  Plant,  ~by  the  Deane  Steam  Pump  Co.,  Holydke,  Mass. 
Diameter  H.  P.  cylinder,  17";  L.  P.,  30".     Pump  plunger,  8|".     Stroke,  30".     Ca- 
pacity at  205'  plunger  speed,  1,205  gals,  per  minute.     Average  observed  steam  pressure, 
90-3;  water,  139-79  ;  in  test  trial,  pump  exceeded  contract  duty  of  125,000,000. 


Reidler  Valve,  from  LeavitVs  Thames- Ditton  Pump.     (See  page  365.) 


SCRAPS. 


871 


F    THR 

UNIVERSITY  D 


872 


SCRAPS. 


SCRAPS. 


873 


•— -2- i  wr»"i~""".4"""".-f.".~""!| jj 


«  £  S 

§      £  i  £ 

*  Sf  9T  $-  tS- 

Class  "R? 


K--6'9'  -->) 


From  the  "Engineering  News." 


Elliptic  Spring  applied  to  Car  Truck. 


Bolster  Spring. 


OF   THK 

UNTVEBSITY  J   . 


SCRAPS. 


Third  Avenue  Elevated  Railroad, 


Cable-car  Grip. 

The  accompanying  figures  rep- 
resent a  side  elevation  and  an  end 
view  respectively  of  a  cable-car 
grip. 

The  gripping  apparatus  is 
shown  in  its  open  position,  and 
the  cable  is  therefore  running  in- 
operatively  through  it.  When  it 
is  required  to  grip  the  cable  it  is 
merely  necessary  to  pull  over  the 
lever  A,  whereupon  the  lever,  its 
quadrant  frame  and  shank  attach- 
ments C,  are  raised  up  bodily 
about  the  fixed  fulcrum  of  the 
link  c,  and  the  pair  of  rollers  E, 
carried  at  the  lower  extremities 
of  C,  forces  the  jaws  G  close  to- 
gether, and  tightly  grasps  the 
cable  between  the  concave  dies  or 
packing  pieces  h. 


SCRAPS. 


875 


o     l>      7     8     3     10    11    12    13    14  15 


Derrick. 


OF  THT? 

UNIVERSITY 


876 


SCRAPS. 


Canvas  Dams.     (From  Trans.  A.  S.  C.  E.) 


Earth  Portion  of  the  New   Croton  Dam,  showing  RuUtle  Masonry  Care. 


SCRAPS. 


877 


Sweetwater  Arched  Masonry  Dam,  Southern   California. 

The  dimensions  of  this  dam  are  :  Thickness  at  base,  46  ft. ;  thickness  at  top,  12  ft. ; 
height,  90  ft. ;  radius  of  arch  at  top,  222  ft.  The  upper  face  batter  is  1  to  6  to  within 
6  ft.  of  the  top,  thence  vertical ;  on  the  lower  face  it  is  1  to  3  for  28  ft. ;  1  to  4  for  32 
ft. ;  thence  1  to  6  to  the  coping.  In  January,  1895,  a  freshet  discharge  flooded  the  waste 
weir  and  rose  22  inches  over  the  parapet  wall.  The  dam  was  subjected  to  this  cataract 
action  for  a  period  of  forty  hours  without  injury. 


Sear  Valley  Arched  Masonry  Dam,    California. 

This  receives  a  sufficient  support  from  the  arch-action,  and  has  stood  since  1884.  Its 
length  at  top  is  270  ft.,  and  its  radius  of  curvature  is  355  ft.  At  the  centre  the  deviation 
of  the  dam  from  a  straight  line  is  about  27  ft. ,  this  being  the  versed  sine  of  the  sub- 
tended angle.  It  is  38  inches  in  thickness  at  top  and  102  inches  at  a  point  48  ft. 
below. 


878 


SCRAPS. 


SCRAPS. 
BUILDERS'   HARDWARE. 


8T9 


Mortise-Lock,  cover  off. 


Front 

Boxed  Strike,  front.  SHding-door 

Lock. 


Thumb-Piece. 


Knob  and  Rose. 


Escutcheons. 


880 


SCRAPS. 


Sash-Lifts. 


Hook  and  Eye 


Skitter- 
Knob. 


SCRAPS. 


881 


Examples  of  Ancient  Hinges  and  Doors. 


w 


s\\\\\y  SSS3ESSSS  253 

^i 

/K 

///xvy/Vy^/A^y/y/y^/vvx/xi 

Se&steeT 

^3v 

>  : 

hi 

Safe  Construction. 

^' 

\;/N/ 

^5 

^  /  / 

Cast- Iron  Tread. 


57 


882 


SCRAPS. 


gaaaagBii.gai.gaaai.«aH 


FEET 


,  Section,  and  Elevation  of  a  Wooden  Mantel  and  Fire-Place. 


SCRAPS. 


883 


Sectional  Plan  of  Grate  and  Flue. 
Details  of  Fireplace. 


884 


SCRAPS. 


Vestibule  Doors. 


SCRAPS. 


885 


Examples  of  Inlaid  Floors  or  Marquetry. 


886 


SCRAPS. 


Railing. 


SCRAPS. 


887 


888 


SCRAPS. 


Enameled  Tile. 


ri 


Terra  Cotta. 


SCRAPS. 


889 


890 


SCRAPS. 


SCRAPS. 


891 


892 


SCRAPS. 


SCRAPS. 


893 


894 


SCRAPS. 


SCRAPS. 


895 


896 


SCRAPS. 


SCRAPS. 


898 


SCRAPS. 


SCRAPS. 


f    i 


900 


SCRAPS. 


SCRAPS. 


901 


902 


SCRAPS. 


SCRAPS. 


903 


904' 


SCRAPS. 


SCRAPS. 


905 


906 


SCRAPS. 


! 


P/cfure       f/grre         or 


L/ne  of  Measures 


I    \ 


i 


\  X 


/       ' 
/         / 

'        / 


t..  v 

*i\l  \ 

! 


;K\ 


\  \ 

\ 


Perspective  Diagram,     (See  page  714.) 


SCRAPS. 


907 


908 


SCRAPS. 


SCRAPS. 


909 


910 


SCRAPS. 


SCRAPS. 


Coneij  Island. 


912 


SCRAPS. 


Coney  Island. 


INDEX. 


Abendroth  &  Root  water  tube  boiler,  868.     . 

Acanthus  leaf  or  scroll,  863. 

Accumulator  for  water  pressure,  412. 

Acoustics,  general  principles  of,  630. 

Adiabatic  curve,  206. 

ACrial  perspective,  751. 

Air-chambers  of  pumps,  365,  411,  412. 

Air  ducts  to  furnaces,  area  of,  640. 

Air,  flow  of,  diagrams,  791. 

Air-lock,  use  of,  431 ;  Barr-Moran,  435. 

Air  taken  into  and  expired  from  the  lungs  of  a 

person,  636. 
Alloys  and  compositions,  table  of,  810. 

brass,  Muntz  metal,  Babbit-metal,  copper  with 
various  metals  and  proportions,  180. 

chart  of  strength,  Prof.  Thurston,  180. 
Aluminum,  properties  of,  180. 
Anchor  bolts,  kinds  and  strength  of,  253. 
Anchors  for  beams  and  walls,  559. 
Angle  blocks  in  truss  bridges,  499. 

irons,  equal  and  unequal  legs,  dimensions  of,  246. 
Angles,  definition  of,  4;  sum  of,  in  figures,  16. 
Angular  perspective,  example  of,  714. 
Anthemion  or  honeysuckle,  architecture,  683. 
Antimony,  properties  and  use  of,  179. 
Apartment  houses,  609,  610. 
Apron,  for  protection  of  dam,  443. 
Apse,  circular  end  of  a  church,  673 ;  of  basilicas, 

624. 
Arch  and  architrave  mouldings,  679. 

bridges,  parts  and  proportions  of,  518. 

Melan  concrete,  Stockbridge,  Mass.,  522. 
Arched  bridge  in  angular  perspective,  716. 
Arches,  complex,  ogee,  Tudor,  trefoil,  triangular, 
roundheaded,  and  pointed,  667. 

of  the  Minneapolis  Viaduct,  520, 

table  of  dimensions  of,  521. 
Artificial  building  material,  174. 
Ashti  reservoir,  for  irrigation,  India,  438. 
Asphalt  lining  for  reservoirs,  pavement  with  con- 
crete foundation,  476. 
Axle  and  rolling  friction,  199. 
Axles,  car,  261. 

Babbit-metal  for  journal-boxes,  180. 
Babcock  and  Wilcox  water  tube  boiler,  796. 
Ball-and-socket  joint  for  flexible  pipe,  405. 

59  913 


Ball  valves,  varieties  of,  374. 

Baltimore  Academy  of  Music,  ventilation  of,  623. 

heater,  641. 

Baluster  and  newel  post,  579. 
Base  and  base  mouldings,  680. 
Batter  and  offsets  to  retaining  walls,  436. 
Beams,  loading  of,  transverse  stress,  235. 
Bear  Valley  arched  masonry  dam,  877. 
Beetaloo  dam,  concrete,  South  Australia,  444. 
Bell-cots,  designs  for,  673. 
Bell-trap  for  sink,  655. 

Belts,  tight  and  loose,  287 ;  transmission  of  power 
by   diagram,  292 ;  speed   of,  292 ;  width   and 
thickness  of,  293 ;  leather,  canvas,  rubber,  293. 
Bevel  gears,  relative  sizes  of,  310;   mortise,  316 ; 
projection  of,  321;  skew,>323. 

wheel,  isometrical  projection  of,  699. 
Bismuth,  properties  of,  in  fusible  alloys,  179. 
Blocks  for  running  rigging,  333 ;  dimensions  of, 

table,  334. 

Blowers  to  improve  chimney  draft,  368. 
Blue  print  paper  for  reproduction,  731. 
Board  and  timber  measure,  768. 
Body  plans  of  vessels,  wave  lines,  546. 
Boiler,  locomotive,  details  of,  394-396. 

setting,  horizontal  and  tubular,  523. 

stays,  forms  of,  391. 

tubes,  775. 

corrugated  flre-boxes,  395-397. 

Shapley  upright,  396. 

Boilers,  horizontal,  tubular,  proportions  of,  number 
of  tubes,  389,  390. 

water   tube,    395 ;    Babcock    and   Wilcox,  796 ; 
Heine,  797;  Clonbrock,   804;    Stirling,    867; 
Abendroth  and  Root,  868. 
Bolts  and  nuts,  forms  of  threads,  250. 
Bolts,  strength  of,  255. 
Boston  "Water  Works  conduit,  458. 
Boulevard,  wide  avenues,  474. 
Boundary  lines  on  topographical  drawings,  119. 
Bowtel  moulding,  simple  fillet  and  rule  joint,  681. 
Box  car,  elevation  and  plan  of,  539. 

end  of  a  locomotive  rod,  351. 

girders,  strength  and  thickness  of  steel,  245,  246. 
Braces  and  counter  braces,  484. 
Bracing  truss  of  wrought  iron  between  wooden, 
beams,  249. 


914 


INDEX. 


Bracket  for  baluster,  583 ;  ornamental,  886. 

Brass,  composition  of,  180. 

Brick  arches,  architectural,  557. 
pavements,  laying  of,  478. 
walls,  bond  of,  557. 
walls  for  foundations,  428. 

Bricks  arid  brickwork,  dimensions  and  varieties 
of,  174. 

Bridges,  general  principles  of  bracing,  483 ;  Howe 
and  Pratt  trusses,  499 ;  Howe  truss  highway 
bridge,  499-501 ;  combination  truss,  Northern 
Pacific  R.  E.,  502,  503 ;  iron  bridge,  N.  Y.  & 
N.  II.  R.  R.,  503-505 ;  Phoenix  Bridge  Company, 
505-507 ;  Pratt  truss  from  the  Lima  and  Oroya 
R.  R.,  509,  510;  highway  bridge,  King  Bridge 
Company,  508-510  ;  ferry  landing  bridge, 
512;  Rivermont  bridge,  Lynchburg,  514;  ele- 
vation of  a  pier  and  bridge  over  the  Rio  Galis- 
teo,  N.  M.  and  S.  P.  R.  R.,  515;  arch  bridges, 
518 ;  viaduct  at  Minneapolis,  520  ;  Cabin  John 
Bridge,  521 ;  dimensions  of  arch  bridges,  521 ; 
Melan  concrete  arch  bridge,  522 ;  suspension 
bridge,  523. 
spaces  between  the  ports  of  steam  cylinders,  217. 

Bridge  trusses,  rules  for,  498. 

Bridging  of  floor  beams,  558. 

Bristol  board,  54. 

Broad  Street  station,  Philadelphia,  Pa.,  899. 

Brooklyn  Water  Works  conduit,  458. 

Brushes  for  tints,  162. 

Builders'  hardware,  879,  880. 

Building  heated  by  steam,  plan  of,  649. 
in  angular  perspective,  713. 
materials,  168. 

Built  columns,  sections  of,  232. 

Bulkhead  wall,  New  York  city,  419. 

Butler's  pantry,  water  connections,  651. 

Butterfly  valves,  375. 

Buttress,  Norman,  English,  flying,  669. 

By-pass  pipe  to  valves,  376. 

Byzantine  and  Saracenic  doorways,  677. 
ornaments,  685. 

Cabin  John  Bridge,  Washington  conduit,  521. 
Cable-car  grip,  874. 

Caisson,  steel,  428  ;  framing  of  wooden,  432. 
Caissons   for  piers,  of  the  Poughkeepsie,  of  the 

Susquchanna  bridge,  429. 
Cam  punch  and  shear,  414. 
Cams,  eccentrics,  wipers,  343-346. 
Canal,  representation  of  earth  bank,  167. 
Canals,  Erie,  Delaware  and  Raritan,  Chesapeake, 

and  Canadian,  452. 

Cantilever  beams  for  foundations,  416. 
Canvas  dams,  876. 
Cape  Cod  Bay,  map  of,  105. 

Capitals,   Byzantine,   Norman,   Gothic,  667 ;  dis- 
tinct parts,  080. 
Car-axles,  M.  C.  B.  A.,  260. 
Caryatides,  Atlantes,  Hermes  pillars,  664. 
Casement  of  French  window,  578. 
Castings,  crystallization  in  cooling,  178. 


Cast-iron  balls,  volume  and  weight  of,  772  ;  beams, 
forms  of,  241 :  shafts,  258 ;  connecting  rods, 
354 ;  girders,  492 ;  pintle  and  joint  details, 
566 ;  pipes,  standard  weights  of,  772 ;  posts 
protected  from  fire,  564  ;  stairs  and  carriages, 
584  ;  treads  and  platforms,  881. 

Cast-  and  wrought- iron  piles,  427. 

Catch  basins  for  sewers,  471-473. 

Cathedral  of  Bourges,  piers  of,  667. 

Cedar-block  pavement,  479. 

Ceilings,  furring  strips  for,  560,  587. 

Cement-faced  walks,  475. 

Cement,  Portland,  natural,  sand,  176. 

Centennial  Exhibition  1876,  buildings  of,  907. 

Central  Park  roads,  New  York  city,  473. 

Centre  plates  of  railway  truck,  539. 

Centrolinead,  9. 

Chains,  cables,  couplings,  336. 

Chains,  power  transmission  by,  299. 

Chain  wheels  with  pockets,  335. 

Chamfer  plane,  moulded,  677. 

Channel  beams,  section  and  dimensions  of,  245. 

Chimneys,  drawing  and  description  of,  wrought- 
iron,  526-530. 

Chimney  tops  or  cowls,  637. 

Chinese  anchors,  429  ;  capstan,  194. 

Chords,  definition  of,  3 ;  scale  of,  25. 

Churches,  900-906. 

Churches,  theatres,  lecture  rooms,  music  and  legis- 
lative halls,  620-631. 

Circles,  2 ;  radius,  diameter,  chord,  segment,  sec- 
tor, quadrant,  3  ;  tangent,  10 ;  circles  inscribed 
in  polygons,  17  ;  circle  in  a  profile  plane,  per- 
spective of,  712. 

Circumference  of  a  circle,  diameter,  arc,  766. 

Circumferences  and  areas  of  circles,  tables  of,  811- 
819. 

Cisterns  and  tanks  of  wood  and  wrought  iron, 
461. 

Clearances  of  steam  cylinder,  209,  369. 

Clevis,  standard,  510. 

Clonbrock  water  tube  boiler,  804. 

Clutch,  cylinder-friction,  280. 

Coal,  fire,  and  steam,  representation  of,  185. 

Coaling  bins  for  locomotives,  497. 

Cofi'er-dam,417. 

Cohoes  dam,  442. 

Coils,  spiral,  flat,  of  wrought-iron  pipe,  403. 

Cold  rolled  wrought-iron  shafts,  178. 

Columns,  cast-iron,  wrought-iron,  Phoenix,  Key- 
stone, strength  of,  230-232. 

Combination  bridge  truss,  503. 

Compacting  sands  for  foundations,  417-419. 

Compasses,  44  ;  portable,  beam,  45  ;  use  of,  88. 

Composite  beams,  wood,  iron-trussed,  249. 

Composition  and  design  of  figures,  Dictionnaire 
Raisonne"  de  P Architecture,  731. 

Compound  steam  engines,  209. 
steam  cylinders,  863. 

Concrete  base  blocks,  Department  of  Docks,  New 
York  city,  421. 

Concrete,   lime,    and    bituminous    cements,    176 ; 


INDEX. 


915 


floors,  566 ;  sewer  in  situ,  468 ;  walls  for 
houses,  558. 

Conduit  for  electric  and  cable  lines,  482. 

Conduits  for  water  supplies,  of  wood,  cast  and 
wrought  iron,  of  masonry  for  Brooklyn,  Bos- 
ton, and  New  York  city,  457-461. 

Cone  pulleys,  286. 

Conic  sections,  orthographic  projection  of,  127. 

Connecting  and  coupling  rods,  347-354. 

Connections  of  angles  for  I-beams  and  Z-bars, 
566-568. 

Contours,  representation  of  topography,  99  ;  head 
of  Franklin,  100. 

Co-ordinates  of  curvature  for  maps,  table  of,  115. 

Copper  and  brass  rods,  table  of  weights,  776. 

Copper  in  alloys,  179. 

Corbels  and  brackets,  681. 

Corliss  steam  engine,  219,  869;  valve  gear,  220. 

Cornice  from  the  temple  of  Jupiter  Stator  at  Kome, 
683. 

Cornices  in  plaster,  587. 

Corrugated  boiler  Hues  and  furnaces,  392,  864. 

Cottage,  rural  style,  606,  902. 

Cottered  joints,  347. 

Cotton  spindles,  friction  in  driving,  199. 

Country  house,  plan  and  elevation  of,  599. 

Coupled  I-bearns,  242. 

Coupling  and  pulley  combined,  283. 

Coupling  rod,  stub  end  of,  354. 

Couplings,  of  shafts,  face,  273 ;  sleeve,  screw,  cone, 
274;  clamp,  box,  horn,  275;  pipe,  Oldham's, 
Hooke's  universal,  277 ;  clutch,  278 ;  friction 
cone,  Weston  double  friction  cone,  279;  elas- 
tic, Weston  disk,  280;  cylinder  friction 
clutches,  281 ;  magnetic  coupling,  spring  hub, 
282. 

Cow  houses,  633. 

Crank,  path  of,  211. 

Cranks  and  crank  axles,  proportions  of,  hand,  340, 
864. 

Crib  dam  in  Colorado,  439. 

Crib  dock,  422. 

Cross-head  and  guides  of  horizontal  engine,  357. 

Crossing  stones  in  streets,  475. 

Cross-section  paper,  104. 

Croton  conduits,  old  and  new,  reservoirs,  458. 459. 

Croton  dam,  earth  portion  of  new,  876. 

Crowfoot  to  rafter,  488. 

Culvert,  isometrical  projection  of,  702. 

Curbstones,  476. 

Curves,  variable,  adjustable,  40 ;  elliptic,  etc.,  41. 

Curvilineal  figures,  area  of,  767. 

Cycloid,  303;  epicycloid,  hypocycloid,  304;  area 
of,  766. 

Cylindrical  surfaces,  representation  of,  58. 

Cylindrical  valves,  372. 

Damper  valve,  380. 

Damp  stretching  of  drawing  papers,  54. 

Dams,  Lake  McMillan  dam  across  the  Pecos  Kiver, 
Colorado,  437;  Ashti  tank,  India,  438;  crib 
dam,  Colorado,  439 ;  Holyoke  crib  across  the 


Connecticut   River,  440;    across    the   Croton 
River,  441 ;  across  the   Merrimac   at  Lowell, 
442 ;    across    the    Mohawk    at    Cohoes,   442 ; 
Beetaloo   dam,  South  Australia,  443;  canvas 
dams,  876;    Sweetwater    dam,    Bear   Valley 
dam,  877 ;  movable  dam,  Great  Kanawha,  878 ; 
section  of  the  new  Croton  dam,  876. 
Dash-pot  of  a  Corliss  engine,  220. 
Dead  points  in  crank  motion,  212. 
Deafening  of  floors,  560. 
Deane  steam  pump  at  Holyoke,  870. 
Deck  beams,  242. 

Density  of  gases  and  vapours,  table  of,  808. 
Derrick,  drawings  and  details  of,  875. 
Designing  of  a  house,  591. 

Designs,  enlarging  and  reduction  of,  cloth  and 
wall  ornamentation,  60;  ornamental,  in  line 
and  tracery,  77-82. 

Diagram  of  comparison  of  United  States  and  met- 
ric units,  71. 

velocity  and  path  of  water  in  a  flume,  72. 
difference  between  the  charge  per  ton  of  transit 

on  canal  and  railroad,  73. 
annual  product  of  pig  iron  in  the  CJ.  S.,  74. 
railway  time-table,  75. 
mortality  record  with  range  of  temperature  and 

humidity,  76. 

velocity  of  falling  bodies,  196. 
expansions  under  pressures,  208. 
link  movement,  223. 
strength  of  wrought -iron  columns,  234. 
strength  of  wrought-iron  beams,  248. 
strength  of  shafts,  260. 
horse  power  transmitted  by  shafts;  262. 
pressures  on  thrust  collars,  areas  to  resist,  273. 
horse  power  transmitted  by  belts,  292. 
horse  power  transmitted  by  ropes,  297. 
distance  between  pulleys  in  rope  driving,  297. 
pitches  and  faces  of  gears  and  stress,  311. 
elbows,  tecs,  crosses,  and  branches  for  wrought- 
iron  pipes,  402. 

flow  of  water  through  pipes,  785-790. 
proportions  of  the  human  figure,  729. 
flow  of  gas  through  pipes,  792,  793. 
wiring  computer,  806. 
Diapering,  architectural,  687. 
Dike  breakwater,  426. 
Dikes  of  earth  across  salt  marshes,  438. 
Dimensions  of  suspension  bridges,  table  of,  523. 

walls,  New  York  city  building  laws,  569. 
Diminishing  glass,  use  of,  751. 
Discharge  of  weirs,  table  of,  782. 
Dining  rooms,  kitchens,   and   parlours,   sizes   of. 

591. 
Disengagement  of  large  pulley  from  main  shaft, 

277. 

Dished  head  for  wrought-iron  cylinders,  412. 
Distribution  of  water  mains,  462. 
Dividers,  hair,  44  ;  three-legged,  proportional,  45. 
Docks,  bulkhead  of  New  York  Dock  Department, 
420  ;  crib  dock  west  bank,  New  York  harbour, 
423 ;  Thames  embankment,  London,  England, 


916 


INDEX. 


424 ;  iron  pier  Coney  Island,  quay  at  Calais, 

427. 

Domes  and  vaults,  667. 
Doors,  dimensions  of,  parts  of,  stiles,  bottom  rail, 

lock,  parting,  top  panels,  muntin,  architrave, 

studs,  jambs;  sliding  and  folding;  side  and 

transom  lights,  571-574. 

Doorways,  circular-headed,  676  ;  pointed,  677. 
Dormer  windows,  578. 

Double-beat  valves  for  steam  and  water,  372. 
Drawing-board,  36. 
Drawing  pen,  exercises  with,  57. 
Drawing-table,  37. 
Drip  or  cap  stones,  681. 

Driver  or  leader,  and  driven  or  follower,  302. 
Drums  or  wooden  pulleys,  284. 
Dry  rot,  169. 
Dynamic  table,  770. 

Earth,  shrinkage  in  refill,  clay,  glacier  till,  hard- 
pan,  quicksand,  167. 

Eccentrics,  342 ;  curve,  drawing  of,  344 ;  strap  with 
metallic  disks,  349. 

Egg  and  dart,  architecture,  683. 

Egg-shaped  sewers,  equivalent  circular  areas,  table 
of,  468. 

Electrical  units,  771. 

Electric  conduit,  481. 

Electric  lighting,  wiring  for,  scries,  multiple,  three- 
wire  systems,  656. 

Electric  switch,  lamp  socket,  806. 

Elevated  Kailroad,  Third  Avenue,  New  York,  874. 

Elizabethan  style,  689. 

Ellipse,  construction  of,  30 ;  circumference  of,  767. 

Elliptic  spring  applied  to  car  truck,  873. 

Enamelled  brick,  175  ;  tile,  888. 

English  basement  house,  599. 

Entasis  on  columns,  658. 

Equilibrium,  stable  and  unstable,  187. 

Erie  Canal,  locks  of,  453. 

Evaporation,  factors  of,  800. 

Expansion  bolts,  254  :  expansion  coupling,  271. 

Expansion,  law  of,  for  gases,  Mariotte,  206. 

Expansive  working  of  steam,  table  of,  800. 

Factor  of  safety,  229. 

Fan  flush  to  water-closet,  654. 

Fang  nut,  254. 

Fan  in  connection  with  radiators,  648. 

Fan-tracery  vaulting,  668. 

Fifth  powers,  table  of,  772. 

Fire  brick,  175. 

Fireplaces  and  mantel,  584. 

Fireproof  buildings,  563. 

Fireproof  of  old  builders,  561. 

Fire-retarding  constructions,  569-571. 

Flange  connections  for  steam  and  water  pipes, 

398. 

Flash  boards  on  dams,  444. 
Flashings  for  roofs,  587. 

Flexible  joints  for  submerged  water  mains,  405. 
Float  trap  for  condensed  water,  645. 


Flooring  frame,  headers,  trimmers,  tail  beams,  558. 

Floor  plan  of  steel  girders  and  beams,  565. 

Floors,  load  on,  559,  560. 

Flows  of  air,  791 ;  of  gas,  diagram,  792,  793. 
of  water  and  air,  comparison  of,  794  ;  of  water  in 
pipes  and  conduits,  784-790. 

Flues,  stacks  for  house,  585 ;  for  every  room,  636. 

Flumes,  discharge  of,  783 ;  penstock  to  water 
wheel,  457. 

Fly-wheels,  408-411. 

Foliage,  sculptured,  688. 

Foot-pan  and  bidet-pan,  652. 

Free-hand  drawing,  illustrations  :  proportions  of 
the  human  frame,  729 ;  half-tone  of  e'corche' 
figures,  730;  pen  drawing  of  ecorche,  732;  of 
Sandow,  733,  734  ;  drawing  of  figures  geomet- 
rically, 735-737 ;  figures  in  skeleton  lines  and 
manikins,  738  ;  pen  drawing  of  Venus  de  Milo, 
739;  pen  drawings  of  male  hands,  739  ;  of  logs 
and  feet,  of  female  hands  and  arms,  740 ;  of 
children's  hands  and  arms,  of  human  head  and 
face,  741;  of  Electioneer,  742  ;  of  cow,  horse, 
donkey,  743 ;  of  hoofs  and  paws  of  animals, 
noses,  744;  pen  drawing  of  Southern  sketch, 
745;  pumping  station,  drawn  with  toothpick 
and  splatter,  746 ;  Salvini,  Venetian  fete  on 
the  Seine  on  stipple  paper,  747, 748 ;  pen  draw- 
ings of  Alexandre  Dumas,  Erik  Werenskiold, 
749;  wash  drawings  of  flowers,  750;  design  m 
pen  and  ink  by  Fortuny,  752 ;  and  woodcuts 
of  various  sketches  and  paintings,  753-764. 

Foot-walks  in  cities.  474. 

Force,  definition  of,  186. 

Formula  for  the  strength  of  wrought-iron  beams, 
247. 

Foundations  for  structures,  415. 

Four-centred  arch,  proportions  of,  architecture,  669. 

Framing  for  stairs,  headway,  581. 
of  a  caisson,  433. 

Freezing  process  for  foundations,  435. 

Freight  shed,  of  wood,  for  railroad,  494. 

Fret,  guilloche,  architectural  ornaments,  683. 

Frictional  gear,  331-333. 

Friction,  coefficient  of,  Morin's  tables,  197 ;  of  rail- 
way trains.  Chanute,  200. 

Friction-wheels  and  friction-rollers,  199. 

Furring  strips,  560,  587. 

Fusible  alloys,  179,  810. 

Gases  and  vapours,  density  of,  808. 

Gas  fittings,  service  mains,  656. 

Gas,  flow  of,  792,  793. 

Gates,  guard  and  canal,  Cohoes,  444 ;  Lowell,  447  i 

Holyoke,    449 ;     Cheney,    tubular   gates    at 

Windsor  Locks,  449;  Sudbury  Kiver  Conduit, 

451 ;  lock  gates,  453. 

Gate  valves,  Peet,  Coffin,  Pratt  and  Cady,  380. 
Gauging  of  streams,  784. 
Gearing,  spur,  bevel,  and  screw,  301. 
Geological  map  of  the  United  States,  108 ;  sections 

of  the  earth's  crust,  109. 
Geometrical  and  flowing  traceries,  675. 


INDEX. 


917 


Girders,  cast-iron,  table  of  strength  of,  242  ;  plate 

and  lattice,  502 ;  beams,  floor  plan,  565. 
Glacier  till,  167. 
Glass,  representation  and  varieties  of,  transparency 

of,  183. 

Globe  valves,  dimensions  of,  377-378. 
Glue,  mouth,  54. 
Gold,  properties  of,  182. 
Gothic  architecture,  characteristics  of,  665 ;  roofs 

of  churches,   technical    names,   627 ;    towers, 

spires,  671. 

Governors,  balls,  shifting  cams,  407. 
Grades  of  roads  and  highways,  474. 

of  steel,  779. 

Granite  block  pavement,  475. 
Gravity,  centre  of,  186  ;  velocity  due  to,  196. 
Green  economizer  in  chimneys,  796. 
Greenhouses,  designs  for,  634. 
Greenwood  Cemetery,  contoured  map  of,  101. 
Grid,  flexible,  for  indicator  cards,  207. 
Groined  arches  in  concrete,  563. 
Grooved  pulley,  shadow  on,  157. 
Groove  packing,  test  of,  365. 
Guides,  cross-head,  357. 
Guide  pulleys  for  belts,  289. 
Gutters  of  buildings,  586. 

Hard-pan,  167. 

Handrails  of  stairs,  582. 

Hangers,  265-268 :  hanger  bolts,  255. 

Hearth  and  supports,  585. 

Heating  by  hot  water,  645 ;  direct  and  indirect 
radiation,  642-645. 

Heat  and  electrical  unit,  771. 

Heavy  bearings,  friction  of,  200. 

Height  of  stories  of  dwelling  houses,  593. 

Heine  water  tube  boiler,  797. 

Helix,  orthographic  projection  of,  139. 

High-stoop  city  house,  599. 

Highway  bridge,  Pratt  truss,  510. 

Hills,  representation  of,  by  verticals,  98 ;  by  con- 
tours, 99. 

Hinges  and  doors,  ancient,  881. 

Hodgkinson,  experiments  of,  on  columns  and 
beams,  98. 

Hoisting  apparatus  for  small  water  gates,  447. 

Hollow  brick,  563. 

Hood  moulding,  architecture,  681. 

Hooks,  proportions  of,  337. 

Hoosac  Tunnel,  construction  and  completion  of, 
537. 

Horizontal  thrust  of  arch,  519. 

Hospitals,  630. 

Hot-air  furnaces,  638. 

House,  designing  of,  591. 

Housing  for  journals,  414. 

Howe  truss,  499  ;  highway  bridge,  500. 

Hydrants,  382. 

Hydraulic  press,  195;  riveting  machine,  412;  tees 
and  crosses,  404. 

Hydrometrical  and  marine  survey,  plots  of,  105. 

Hyperbola,  construction  of,  34. 


I-beams,  241 ;  table  of  dimensions  and  strength  of 

iron  and  steel,  243,  244,  779. 
Idlers,  or  binders  for  belts,  291. 
Inches  and  sixteenths  in  decimals  of  a  foot,  table 

of,  770. 
Inclined  forces,  resultant  of,  192  ;  plane,  principle 

of,  190. 

India  ink,  grinding,  56  ;  slabs  for,  57. 
Indicator  cards  of  a  steam  engine,  206-210. 
Injector  for  boiler  feed,  336. 

Inked  thumb,  for  representing  a  background,  751. 
Inking  in  of  topographical  drawings,  118. 
Instruments,  drawing,  management  of,  55. 
Internal  gearing,  308 ;  wheel  driven  by  a  pinion 

and  driving  a  pinion,  325. 
Involute,  construction  of,   305 ;  teeth,   rack,   and 

pinion,  308. 
Iron  and  plank  pipes  for  the  conveyance  of  water, 

457. 

Iron  roofs,  corrugated  and  framed,  490. 
Iron  shoes  and  plates  for  braces  and  rafters  of 

roofs,  488. 

Iron  tank  with  inverted-dome  bottom,  461. 
Isle  of  Wight,  chart  of,  106. 
Isometrical  drawing,  illustrations :    Principles  of 

cubic  projections,  curved  lines,  698;  practical 

application  to  projection  of  gear  wheels,  699 ; 

pillow-block,  water-closet  cistern,  culvert,  701 ; 

roof  frame,  plan  and  elevation  of  a  school- 
house,  ship  construction,  704 ;  elevation  of  a 

seaside  resort,  705. 
Italian  campaniles,  670;  schools  of  architecture, 

677. 

Jack-rafters,  dimensions  of,  490. 

Jack-screw,  414. 

Janney  car  coupler,  215. 

Joinings  for  beams,  490. 

Joints,  pipe,  under  heavy  pressure,  399  ;   steam 

pipe,  400. 

Journal  bearings  of  box,  M.  C.  B.  A.,  272. 
Joy's  valve  gear,  226. 

Kentucky,  geological  survey  of,  106. 
Keys,  metal  strips  to  secure  hubs  to  shafts,  259. 
Kinzua  Viaduct,  514. 
Kitchen  range,  boiler,  and  sink,  650. 
Knuckle  joint,  347. 

Korting  blower  to  increase  draft  in  flues,  368. 
Kutter's  formula  for  flow  of  water  in  pipes,  graph- 
ically, 784-790. 

Landing  bridge  for  ferry,  513. 
Lap  and  lead,  slide  valve,  217. 
Latitudes  and  departures,  table  of,  830-835. 
Lattice  bars,  spacing  of,  232. 

deck  bridge,  bill  of  material,  505. 
Lead,  properties  of,  181. 

pipe,  weights  of,  780. 
Leather  link  belting,  301. 

packing  for  pumps  and  cylinders  of  hydraulic 
presses,  363. 


918 


INDEX. 


Legislative  halls,  requirements  of,  630. 

Lettering,  varieties  of,  triangles  for,  62. 

Lever,  principle  of,  188 ;  hand  and  foot,  338 ;  under 
inclined  forces,  195. 

Lewis,  for  raising  stones,  254. 

Lineal  measure,  table  of,  768. 

Line,  geometrical,  2  ;  horizontal,  vertical,  parallel, 
5 ;  irregular,  plotted,  91 ;  orthographic  projec- 
tion of,  122. 

Lines  of  shafting,  laying  out  of,  262. 
position  and  division,  guide  lines,  727. 

Link  belting,  300. 
motion,  222. 

Lintels,  557. 

Liverpool  water-works,  Norton  Tower,  461. 

Load,  dead,  live,  229. 

Lock  nut,  251 ;  washers,  256. 

Locks  of  canals,  453. 

Locomotive,  driving-wheel  of,  341 ;  boiler  for,  395 ; 
plan  and  elevation  of  frame  of,  546 ;  No.  999, 
N.  Y.  C.  &  H.  R.  R.  R.,  871 ;  N.  Y.,  O.  &  W., 
872 ;  distribution  of  load,  873. 

Logarithms  of  numbers,  table  of,  845-859  ;  applica- 
tion of,  860. 

Longitude,  table  of  length  of  a  degree  of, 
116. 

Loop  system  of  piping,  802. 

Louis  Quatorze  style,  Louis  Quinze  style,  690. 

Lundell  electric  motor,  807. 

Machine  and  blacksmith  shop,  city,  614. 

foundations,  535. 
Machines,  location  of,  530. 
Malleable  cast-iron,  178. 
Man-hole,  390;  hand-hole  covers,  863. 
Man-holes,  for  sewer,  470. 
Mansard  roof,  585-586. 
Mantel  and  fireplace,  plan,  section,  and  elevation 

of,  882,  883. 

Mantels,  flues,  jambs,  584. 
Map     projections,     orthographic,     stereograph  ic, 

globular,  Mercator's,  conic,  Bonne's,  polyconic, 

110-115. 

Marine  boiler  of  steamer  Minneapolis,  395. 
Mariotte,  law  of,  206. 
Marquetry,  examples,  885. 
Masonry,  conventional  signs  of,  technical  terms 

for,  representations  of,  171. 
Masonry  curbs  sunk  by  water  jets,  427. 

terms  of,  171. 

Materials,  earth  and  wood,  characteristics  and  rep- 
resentation of,  167-171. 
Measures  of  surface,  768  ;  of  capacity,  769 ;  cubic 

or  solid,  770. 
Mechanical  stokers,  Wilkinson,  Coxe,  866. 

work  or  effect,  201. 
Mensuration,  766. 
Mercator's  projection,  112. 
Meridians,  topographical  drawing,  119. 
Metals,  antimony,  bismuth,  copper,  lead,  tin,  and 

zinc,  properties  of,  179 ;  conventional  signs  to 

represent,  177 ;  table  of  properties  of,  809. 


Metres  and  United  States  units,  graphic  compari- 
son of,  71. 

Mill  constructions,  tiro-retarding,  569. 

Miner's  inch,  784.  * 

Morin,  experiments  of,  on  friction,  and  table  of 
sliding  and  rolling,  197. 

Mortality  and  disease  by  graphics,  76, 77. 

Mortars,  lime,  cement,  sand  cement,  175, 176. 

Mortise  wheels,  proportions  of,  316. 

Motion,  211,  228. 

Moulded  timbers,  682. 

Mouldings,  classical,  Romanesque,   Gothic,  Nor- 
man, 679. 

Greek   and  Roman,  588 ;  stuck  in  wood,  589 ; 
perpendicular  style  of,  682. 

Mounting  paper  and  drawings,  varnishing,  55. 

Movable  d>m,  Great  Kanawha  River,  878. 

Muntz  metal,  180. 

Mutules  and  guttse,  683. 

Nails  and  spikes,  weight,  table  of,  777-778. 

Natural  sines  and  cosines,  table  of,  836-844. 

Neutral  surface  under  transverse  stress,  240. 

New  Haven,  map  of  the  harbour  and  city  of,  101. 

New  York  city  schoolhouse,  a,  619. 

New  York  State  canals,  lock  specification,  455. 

Nipple,  close  and  shoulder,  403. 

Northern  Canal  at  Lowell,  Mass.,  section  of,  452. 

Nuts,  various  forms  of,  251. 

Open  fire  in  a  tavern,  638. 
Orders  of  architecture,  Tuscan,  659. 
Doric,  660. 
Ionic,  662. 

Corinthian  and  Composite,  664. 
Organs  of  churches,  627. 

Ornamental  mouldings,  chevron,  billet,  star,  fir 
cone,  cable,  embattled,  nail  head,  dog  tooth, 
ball  flower,  serpentine,  vine  scroll,  686. 
Ornament,  architectural,  682. 
Orthographic  projection,  121 ;  of  a  point,  of  a  line, 
of  a  solid,  of  simple  bodies,  123;  conic  sec- 
'tions,  127 ;    intersection  of  solids,  130 ;    the 
helix,  139. 

Ox  gall  for  drawing  on  the  ordinary  photograph, 
731. 

Packing  for  water-pumps,  362 ;  of  stuffing-boxes, 

£70. 

Paints,  184. 

Palace  of  Diocletian,  665. 
Pan-closet,  653. 
Panels,  ceilings  in  Italy,  562. 
Pantagraph,  51. 

Paper,  drawing,  tracing,  transfer,  parchment,  he- 
liographic,  52. 

pencils,  chalks,  pens,  ink,  727-728. 

profile  and  cross-section,  71. 
Parabola,  construction  of,  33  ;  area  of,  766. 
Parallel  motions,  215. 
Parallelogram,  rhombus,  rhomboid,  16. 

of  forces,  193. 


INDEX. 


919 


Parallels,  22 ;  parallel  ruler,  drawing  of,  39. 

Parapets,  architectural,  687. 

Paris  boulevard,  475. 

Partitions,  framing  of,  556. 

Passenger  car,  elevations  and  sections  of,  539. 

Patent  Office  requirements,  drawings,  registration, 
765. 

Pavements,  granite- block,  with  and  without  con- 
crete foundation,  476  ;  asphalt,  477  ;  Salt  Lake 
City,  478  ;  brick,  cedar  block,  479. 

Pediments,  brackets,  railing,  886. 

Pelton  water-wheel,  204. 

Pen-and-ink  drawings,  to  clean,  751. 

Pencils,  marks  of,  1. 

Pen,  drawing  or  right-line,  42;  railroad,  border, 
curve,  42 ;  dotting,  43. 

Perspective  drawing,  planes  of,  706 ;  points  of,  par- 
allel and  angular,  707 ;  of  squares,  cubes, 
scales  for,  prisms,  pavement,  horizontal  circle, 
in  profile,  cylinder,  octagonal  prism,  building, 
interior  of  room,  arch  bridge,  schoolhouse, 
cottage,  stairs,  reflection  of  objects  in  water^ 
projection  of  shadows ;  capstan  and  winch,  725. 

Pews,  length  of,  627. 

Pier,  iron  curb  of,  with  piles  driven  inside,  431. 

Piers  of  the  Third  Avenue  Bridge,  431. 

Piers,  Poughkeepsie  Bridge,  430  ;  pile,  497  ;  trestle 
bent,  498;  Kinzua  Viaduct,  513;  over  Kio 
Galisteo,  N.  M.  and  S.  P.  R.  R.,  513 ;  Third 
Avenue  Elevated  Suburban,  515,  516 :  stone 
pier  of  railroad  bridge  over  Susquehanna  at 
Havre  de  Grace,  516;  of  bridge  across  the 
Missouri  at  Bismarck,  517. 

Pile-pier,  497. 

Piles  for  foundations,  417 ;  splicing  of,  419. 

Pillow-block,  isometrical  projection  of,  699. 

Pillow  or  plumber-block,  standard  and  hangers, 
263. 

Pin-nut,  standard,  510. 

Pinion  driving  a  rack,  324. 

Pipe  coupling,  lead,  404. 
for  driven  wells,  table  of,  776. 
air-chamber,  650. 

Pistons  of  steam  engines,  and  of  pumps,  360. 

Piston-ring  and  packing,  362. 

Pitch  of  roof,  486. 

Plan  and  elevations  of  a  small  house,  drawings  of, 
548-553. 

Plane  table,  84. 

Plan  of  church,  transept,  nave,  and  chancel,  625. 

Plastering,  176:  furring  of  walls,  587. 

Plate  girder,  bill  of  material  for,  503. 

Plates  and  covers,  wrought-iron,  863. 
and  wire,  weights  of  wrought  iron  and  brass, 
table  of,  774. 

Platforms  for  foundations,  grillages,  415. 

Plots,  transferring  of,  110. 

Plotting,  scales  used  in,  83 ;  traverse  table  used  in, 
87 ;  meridian  assumed  in,  89 ;  irregular  lines, 
91. 

Plough  for  electric  conduit,  482. 

Plugs  and  caps  for  pipes,  403. 


Plumbing,  649. 

Pneumatic  piles,  431. 

Point,  geometrical,  2  ;  pricking,  43 ;  tracing,  44. 

Polygons,  14;  irregular,  17;  inscribed,  18;  con- 
struction of,  19;  similar,  26;  regular,  areas  of, 
766. 

Pondage,  rule  of,  for  permanent  mill  powers,  436. 

Pop  safety  valve,  382. 

Porous  brick  tiles,  564. 

Ports  of  steam  cylinders,  217 ;  exhaust,  217 ;  di- 
mensions of,  371. 

Principles  of  architectural  design,  691. 

Printing  frame  for  heliographic  paper,  53. 

Proportions  of  the  members  of  a  roof,  489. 

Protractor,  21,  25,  50. 

Privies,  water-closets,  and  outhouses,  593. 

Pulley,  principle  of,  190. 

Pulleys,  282 ;  cast-iron,  283 ;  plate,  wrought-iron 
rim,  split,  pulley  and  coupling  combined, 
wooden-plate  pulley,  drums,  cone,  fast  and 
loose,  286 ;  guide,  289 ;  idlers  or  binders,  291. 

Pumping  engine  at  St.  Louis,  345 ;  Leavitt  pump, 
365;  Worthington,  366;  Deane  pump,  Hoi- 
yoke,  870  ;  Reidler  valves,  to  Leavitt's  pump, 
870. 

Quicksand,  167. 

Quoin  and  pintal  for  bedpost  of  lock,  455. 

Rack  gear  and  pinion,  301 ;  involute  teeth  of,  309 ; 

rack  driving  a  pinion,  325;  pinion  driving 

rack,  324. 

Radiating  surface  for  heating,  643. 
Radiators,  wall  coil,  box  coil,  wrought-iron  tube, 

cast-iron  loop,  cast-iron  pin,  647. 
Rail  joints  of  the  West  Shore  Railroad,  480. 
Railroads,  standard  sections  of  permanent  way, 

480. 

Rails,  standard,  drawing  and  dimensions  of,  481. 
Railway  rolling  stock,  539-543. 

surveys,  plots  of,  103. 
Ranges,  United  States  survey,  93. 
Reciprocals,  table  of,  828 ;  use  of,  861. 
Register  valve  for  steam,  381. 
Reidler  water  valve,  870. 
Renaissance  style,  677 ;  ornaments  of.  688 ;  Tri- 

cento  and  the  Quatrecento,  Cinquecento,  689. 
Reservoirs  for  water-works,  459. 
Retaining  walls,  435. 

River  wall,  Thames  embankment,  422-426. 
Riveted  joints,  lap,  single,  double,  treble  riveted, 

butt  and  angular  connections,  383-386. 
Riveting,  conventional  signs  of,  866. 
Rivets  for  plate  girders,  247;  forms  and  dimen- 
sions of,  383 ;  pitch  of,  777. 
Roads  and  highways,  dirt,  gravel,  oyster  shells, 

Macadam,  Telford,  472,  473. 
Rolled  I-beams,  section  of,  242. 
iron,  table  of  weight  of,  773. 
Rolling  friction  on  roads,  200-201. 
Romanesque  and  Byzantine  architecture,  665. 
church  or  basilicon,  624 ;  pillars,  667. 


920 


INDEX. 


Roman  order,  characteristics  of,  665;    vaulting, 

608 ;  school  of  architecture,  678. 
Roofs,  plans  and  sections  of,  585. 
Roof  truss,  isometricul  projection  of,  702. 

parts  of,  485 ;  varieties  of,  490. 
Rooms,  proportions  and  distribution  of,  589,  594. 
Ropes,  transmission  of  power  by,  293,  299. 
Rubber,  properties  and  use  of,  184. 

ring  joint,  405. 

valves,  374. 

Rudder  post  and  screw  frame,  864. 
Rulers  and  triangles,  36-38. 
Russian  towers,  architecture,  674. 

Safety  valve,  381. 

Safe-vault  construction,  881. 

Sag  of  rope  in  driving,  298. 

Salted  paper,  recipe  for,  731. 

Sand  cement,  176. 

Saracenic  diapers,  architecture,  685. 

Saturated  steam,  table'of,  798. 

Scales,  25 ;  application  of,  27 ;  forms  of,  plotting, 
46;  diagonal,  47;  vernier,  48;  oft-set,  92;  on 
drawings  for  photography,  119;  for  lines  in 
perspective,  709. 

School-houses,  616-622 ;  isometrical  view  of,  702. 

Screw  pile,  427. 

Screw,  principle  of,  191 ;  the  differential,  194. 

Screw  propeller,  865. 

Screws,  shades  and  shadows  on,  157 ;  wood  and 
metal,  252 ;  drawing  of  triangular  and  square 
threaded,  327. 

Scroll  moulding,  681. 

Seasoning  of  timber,  168. 

Seats,  desks,  school  furniture,  616;  space  occupied 
by,  624. 

Sector,  drawing  instrument,  49 ;  area  of,  766. 

Sewers,  466 ;  of  vitrified  ware  or  cement,  467 ; 
Washington,  Brooklyn,  466. 

Shade  lines,  144. 

Shading  and  shadows,  manipulation  of,  and  meth- 
ods of  tinting,  159-166. 

Shadows,  perspective  projection  of,  721. 

Shafting,  diagram  of  strength  and  length  between 
bearings,  260. 

Shafts,  cold-rolled,  178 ;  wooden,  iron,  and  steel 
257 ;  cast-iron,  plan  and  sections,  259. 

Sheds  for  wood  or  coal,  594. 

Sheet-iron  arches  for  concrete  floors,  563. 

Sheet-piling,  417. 

Ship  construction,  wave-line,  isometrical  projec- 
tion of,  704. 

Shipping  measure,  770. 

Shoe  for  wooden  curb  of  well,  428. 

Silver,  properties  of,  182. 

Sine,  cosine,  versed  sine,  secant,  tangent,  21. 

Sink,  cast-iron,  650. 

Skeleton  construction  of  iron  and  steel,  565,  693, 
898. 

Skeleton  frame  of  working  beam,  354. 
Sketching  from  Nature,  745. 
Skew  bevels,  plan  of,  323. 


Skew  bridges,  520. 

Smith's  process  for  coating  pipes,  465. 

Sockets  for  wire  ropes,  336. 

Soil  or  house-sewer  pipe,  650 ;  extension  to  roof, 
652. 

Soldering  union,  nipple,  403. 

Solders,  composition  and  use  of,  810. 

Solids,  orthographic  projection  of,  122;  intersec- 
tions, 130. 

Spaces  occupied  by  check  valves,  table  of,  376 ; 
globe  valves,  378. 

Specials  for  water  mains,  463. 

Specifications  of  pipe  mains,  Brooklyn,  N.  Y.,  465. 

Specific  gravity  of  liquids,  earths,  808;  woods, 
metals,  and  gases,  809. 

Speed  of  belts,  291,  292. 

Sphere,  development  of  the  surface  of,  144 ;  shade 
on,  155. 

Spherical  bearing,  866. 

Spike  frames,  555. 

Spiral,  construction  of,  35. 
riveted  pipes,  776. 

Spire  finials,  673. 

Spires,  900,  901 ;  of  English  churches,  671. 

Splatter  work  in  drawing,  751. 

Split  pulleys,  283. 

Sponge,  means  of  correcting  errors  in  drawings, 
166. 

Springs,  driving,  equalizing  bar,  elliptic,  bolster,' 
873. 

Sprocket  wheels,  300. 

Spur  wheel,  drawing  of,  317;  oblique  projection 
of,  319. 

Spur  wheels,  parts  of,  302,  306. 

Square,  multiples  of,  27  ;  on  the  hypothenuse,  29  ; 
reduction  of  areas  of,  30. 

Squares,  cubes,  and  roots  of  numbers,  table  of,  820- 

827. 
divisions  into  triangles  and  octagons,  59. 

Stables,  barn,  carriage  house,  stable  proper,  floor 
of,  631. 

Stairs,  578;  treads  and  risers,  fliers  and  wind- 
ers, landing,  headway,  nosing,  strings,  car- 
riages, newel  post,  and  baluster,  579 ;  laying 
out,  framing  for,  581 ;  hand  rail,  582 ;  wrought- 
iron  strings  and  rails,  cast-iron  treads  and 
risers,  584. 

Stalls,  pitch  of  bottom  and  breadth  of,  631. 

Stamp  mill,  347. 

Standard  for  the  support  of  shafting,  265. 

Standard  I-beams,  channels,  A.  A.  S.  M.,  779. 

Standard  rails,  dimensions  of,  481. 

Stanhope  levers,  212. 

Stationary  boilers,  Philadelphia  Water- Works,  392. 

Stay  bolts,  proportions  of,  392. 

Steam  and  hot-water  circulation  as  a  means  of 
heating,  641. 

Steam  cylinders,  359. 

Steam  engine,  horizontal  frame,  356 ;  Corliss,  219, 
220,  869. 

Steam  heating,  arrangement  of  mains  and  returns 
for,  642. 


INDEX. 


921 


Steam,  its  application,  205. 

Steam  jacket,  346. 

Steam  piston  packing,  347. 

Steam  valve,  plan  and  section  of,  379. 

Steel,  homogeneous  metal,  178  ;  from  pure  wrought- 
iron,  179. 

Steelyard  and  platform  scales,  194. 

Step  for  an  upright  shaft,  269. 

Steps  for  stairs,  breadth  of,  treads  of,  and  height 
of  risers,  579. 

Stiffeners  for  the  webs  of  plate  girders,  247. 

Stipple  paper  or  clay  board,  751. 

Stirling  boiler,  867. 

Stirrup  irons  for  wooden  beams,  559. 

Stokers,  mechanical,  Wilkinson  and  Coxe,  866. 

Stones  and  masonry,  conventional  signs  of,  171. 

Stones,  granitic,  argillaceous,  sand,  lime,  charac- 
teristics of,  173. 

Stop  chamfering,  682. 

Stores  and  warehouses,  612,  614. 

Stoves,  open  and  close,  638. 

Straight  edges,  37. 

Strength  of  men  and  animals,  202. 

Stress,  tensile,  compressive,  shearing,  transverse, 
tortional,  230,  234. 

String  courses,  680. 

St.  Sophia,  roof  of,  667. 

Studs  for  house  framing,  556. 

Stuffing  boxes  and  glands,  packings  for,  369. 

Stylus,  tracing  point,  44. 

Suspension  bearings,  270. 

Suspension  bridges,  table  of  dimensions,  523'. 

Sulphur,  characteristics  of,  182. 

Summer  house,  887. 

Surfaces,  development  of,  cylinders  and  cones,  141. 
in  shade,  tinting,  160. 

Sweetwater  arched  masonry  dam,  877. 

Table  of  railway  curves,  103. 
co-ordinates  of  curvature  for  maps,  115. 
length  of  degree  of  longitude,  116. 
sliding  and  rolling  friction,  Morin,  198. 
safe  loads  of  cast-iron  columns,  231. 
safe  loads  of  Phoenix  columns,  232. 
safe  central  load  of  yellow-pine  beams,  239. 
strength  of  wrought-iron  I-beams,  243. 
strength  of  steel  beams,  244. 
strength  of  steel  box  girders,  245. 
dimensions  and  weights  of  Z-bars,  247. 
dimensions   of  bolts   and  nuts,  United   States 

standard,  256. 

proportions  of  sunk  keys,  260. 
distances  between  bearings  of  shafts,  261. 
horse  power  transmitted  by  shafts,  262. 
horse  power  transmitted  by  wire  ropes,  298. 
pitch,  diameters,  and  teeth  of  gears,  312. 
relation  of  diametral  to  circular  pitch,  313. 
radius  of  arcs  of  circles  for  gear  teeth,  Adcock, 

313-315. 

sizes  of  sheaves  and  blocks,  334. 
capacities  and  sizes  of  hooks.  337. 
dimensions  of  eyes  and  cranks,  339. 


Table  of  space  occupied  by  check  valves,  376. 

dimensions  of  globe  valves,  378. 

dimensions  of  single-riveted  lap  joints,  384. 

dimensions  of  double-riveted  lap  joints,  385. 

dimensions  of  treble-riveted  lap  joints,  386. 

number  of  tubes  in  horizontal  and  tubular  boil- 
ers, 390. 

proportions  of  stay  bolts  for  flat  surfaces,  392. 

dimensions  of  pipe  flanges  and  cast-iron  pipes, 
399. 

dimensions  of  wrought-iron  tubes  and  coup- 
lings, 401. 

diameters  and  thicknesses  of  cast-iron  pipes, 
with  lead  for  joints,  463. 

size  of  egg-shaped  sewer  and  circular  equiva- 
lents, 468. 

dimensions  of  standard  rails,  481. 

dimensions  of  parts  of  roofs,  489,  490. 

dimensions  of  a  wrought-iron  roof,  492. 

material  for  plate-girder  bridges,  503. 

material  for  lattice-girder  bridges,  505. 

arch  bridges,  dimensions  of,  521. 

suspension  bridges,  dimensions  of,  523. 

loads  for  floors,  559. 

theatres  and  their  dimensions,  630. 

polygons,  chords,  verticals,  and  areas,  766. 

lineal  measures  and  of  surfaces,  768. 

capacity,  liquid  and  dry  measure,  769. 

weights,  apothecaries',  Troy,  avoirdupois,  dy- 
namic, 770. 

cubic  or  solid  measure,  770. 

inches  and  sixteenths  in  decimals  of  a  foot,  770. 

fifth  powers,  772. 

weight  of  cast-iron  balls,  of  cast-iron  pipes,  772. 

weight  of  rolled  iron,  773. 

weight  of  wrought-iron  and  brass  plates,  774. 

wrought-iron  welded  tubes,  of  boiler  tubes,  775. 

weight  of  pipes  for  driven  wells,  spiral  pipe, 
light  pipe  for  leaders,  and  air  pipes,  776. 

weight  of  copper  and  brass  rods,  776. 

weight  of  rivets,  spikes,  777 ;  of  cut  nails,  ot 
iron  nails,  of  telegraph  wire,  778. 

weight  of  beams  and  channels  of  the  A.  ot 
A.  S.  M.,  779. 

weights  of  lead  pipe,  of  a  cubic  foot  of  water,  780. 

discharges  of  water  over  weirs,  782,  783. 

equalizing  the  diameter  of  pipes,  791. 

volume  and.  weight  of  dry  air,  794. 

saturated  steam,  798,  799. 

expansive  working  of  steam,  factors  of  evapora- 
tion, 800. 

mils  and  ohms,  807. 

specific  gravities  of  gases,  of  liquids,  of  earths, 
etc.,  808. 

woods  and  metals  and  properties  of,  809. 

circumferences,  diameters,  and  areas  of  circles, 
811-819. 

squares,  cubes,  and  roots  of  numbers,  820-827. 

reciprocals,  828,  829. 

latitudes  and  departures,  830-835. 

natural  sines  and  cosines,  836-844. 

logarithms  of  numbers,  845-859. 


922 


INDEX. 


Tanks,  lead-lined,  coated  with  asphalt    varnish, 
650. 

Taps  for  city  mains,  sizes  of,  649. 

Telegraph  and  telephone  lines,  table  of  sizes  of 
wire,  778. 

Teredo  and  Limnoria,  169. 

Terra  cotta,  175,  888. 

Thames-Ditton  pump,  365. 

Theatres,  dimensions  and  plans  of,  630. 

Thrust  bearings  for  screw-propeller  shafts,  272. 

Thumb-nut,  338. 

Timber   frames,  forms  and   dimensions  of  parts, 
555. 

Timber,  sections,  conventional  signs,  seasoning,  168. 

Tin,  properties  of,  182. 

Tinting  and  shading,  manipulation  of,  159;  pre- 
paring colours  for,  164. 

Tires  of  wagons,  201. 

Titles  of  maps  and  charts,  69. 

Toggle-joint,  195. 

Topographical  drawing,  conventional  signs  of,  95 

Topography,  coloured,  116;  conventional  colours 
of,  117. 

Torsional  stress,  234. 

Tower  for  water  tank  in  New  York  city,  674. 

Towers,  Eomanesque,  670. 

Traceries,  perpendicular,  leaf,  flamboyant,  Sara- 
cenic, and  Moorish,  676. 

Tracing  cloth,  52. 

Trains,  time-table  of,  74. 

Trammel,  ellipsograph,  31. 

Transverse  stress  of  beams,  235. 

Traps,  antisiphoning,  653 ;  for  sewer  pipes,  655. 

Trestle  bent  of  elevated  railroad,  498. 

Trestles  for  drawing-table,  37. 

Triangles  for  drawing,  37. 

Triangle  and  square,  use  of,  22. 

Triangles,  isosceles,  equilateral,  right-angled,  simi- 
lar, 26. 

Triple  compound  steam  engine,  210. 

Trundle  pins  or  wheels,  301. 

Truss    bridges,  effect  of  unequal    loading,  484: 
wooden,  Howe,  Pratt,  499. 

Trusses  for  roof  and  floor  of  a  gymnasium,  493. 

Trussing  of  a  beam  by  struts  and  tension  rods,  250. 

T-square,  38. 

Tubes,  weight  of  wrought-iron  welded,  table  of 
775. 

Tubs  set  for  washing,  651. 

Tudor  arched  doorway  with  hood  mouldings,  677. 

Tunnels  and  principles  of  timbering,  535. 

Turbine,  Fourneyron,  Boyden,  and  Jonval,  204. 

Turn-buckle  or  swivels,  255. 
Turn-table,  510. 
Tusk  tenons,  558. 

United  Electric  Light  and  Power  Station,  801. 

United  States  Survey,  ranges  of,  93. 

Unit  of  force  and  space,  201. 

Upright  boiler,  Shapley's,  396. 

Upset  of  bolts,  255. 

Urinals,  656. 


Valve  diagrams,  steam,  218. 
gear,  Corliss,  link,  Joy's,  Walschaert,  219-228. 
motion  of  St.  Louis  pumping  engine,  345. 
motion,  slide  valves,  216. 

Valves,  automatic,  double-beat,  372;  poppet,  disk, 
rubber,  flap,  ball,  air,  pump,  loaded  flap,  but- 
terfly, check,  377 ;  safety,  381 ;  controlled  by 
hand.  376;  cocks,  bibs,  plain,  hose,  compres- 
sion, air,  stop  and  plug  cocks,  globe,  straight, 
angle    and    cross,    damper,    380;    regulator, 
steam-hammer,  hydrant,  383. 
Variable  speed  gear,  333. 
Vaulting,  fan-tracery,  668. 
Vaults  and  domes,  667. 
Venetian  school  of  architecture,  678. 
Ventilation  and  warming,  634. 

by  compressed  air  in  French  exhibition,  368. 
Vessels  in  launching,  friction  of,  198. 
Vestibule  doors,  884. 
Villa,  Italian,  607. 

Wagon  tires,  473. 
Wall  girders,  position  of,  568. 
Walls,  dimensions  of,  New  York  city  laws,  569. 
Walls  in  masonry,  556 ;  concrete,  555. 
Walschaert  valve  gear,  226. 
Wash-basins,  sizes  of,  651. 
Wash  drawings,  749. 
Washers,  table  of,  256. 
Water-back,  650. 

Water-closets,  appliances  of,  652 ;  basins,  655 ;  cis- 
tern, isometrical  projection  of,  700. 

washout,  hopper,  pan,  flap,  siphon-jet,  652-654. 
Water,  diagram  of  path  and  velocity  in  flume,  72. 

flow  of,  781. 

jet  for  the  sinking  of  piles,  426. 

lines  of  a  ship,  546. 

mains,  dimensions,  and  weight  of,  462,  463. 

pipe  of  sheet  iron,  460. 

power  and  its  applications,  203. 

weight  of  a  cubic  foot  of,  at  different  tempera- 
tures, table  of,  780. 

wheels,  tub,  flutter,  breast,  overshot,  undershot, 

Scotch,  turbines,  Pelton,  203,  204. 
Wave-line  principle  of  ship  construction,  545. 
Waves  of  sound  in  halls  of  audience,  623. 
Weather-cocks,  673. 
Weaving-room,  location  of  looms,  531. 
Wedge  gearing,  332. 
Weight  of  gas  mains,  472. 
Weights,  apothecaries',  Troy,  avoirdupois,  769. 

of  material,  177. 

Weirs,  table  of  discharge  of,  782. 
Westinghouse  engines,  steepled  compound,  804. 
Weston-Capen  double-friction  clutch,  279. 
Wheel  and  axle,  principle  of,  189. 
Whitworth's  quick  return  motion,  213. 
Winch,  centreboard,  724. 
Windlass,  724. 

Window  frames,  sashes,  blinds,  573-578 ;  dimen- 
sions of,  577. 
Windows  and  doors,  examples  of,  889-897. 


INDEX. 


923 


Windows  and  doors,  Byzantine,  Romanesque,  Nor- 
man, Lancet,  traceried,  674. 
Wire  nails,  weight  of,  778. 

ropes,  sockets  for,  336. 
Wiring  computer,  Carl  Hering,  806. 
Wooden  plate  pulley,  285. 
shaft  in  plan  and  section,  258. 
steps  for  shafts,  271. 
packing  for  pump  pistons,  363. 
Woods,  characteristics  and  use  of,  169 ;  white  pine, 
Southern  pine,  Canadian   red,   Norway,   and 
silver  pines,  spruce,  hemlock,  ash,  chestnut, 
black  walnut,  butternut,  hickory,  beech,  live 
oak,  white  oak,   bass,    poplar,  white    wood, 
cedar,  locust,  elm,  maples,  170. 
Working  beam,  354. 
Working  strain  of  one-inch  rope,  296. 


World's  Fair  buildings,  908-910. 
Worm  and  worm  wheel,  330;  the  Albro,  3'28. 
Worthington  stearn  pump,  3.66. 
Wrought-iron  columns,  strength  of,  233. 

diagram  of,  234. 

rim  pulleys,  283. 

crank  connections  of  river-boat  engines,  354. 

pipe  connections,  400. 

tubes  and  couplings,  dimensions  of,  401. 

curb  pier  with  inside  piles,  431. 

trestles  for  bridges,  514. 

chimney  stack,  530. 

string  and  rail  for  stairs,  583. 

spikes,  table  of  weight  of,  777. 


Zinc,  properties  and  uses  of,  182. 


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animation,  the  brightness,  the  force,  and  the  charm  with  which  he  arrays  the  facts  before  us 
are  such  that  we  can  hardly  conceive  of  more  interesting  reading  for  an  American  citizen  who 
cares  to  know  the  nature  of  those  causes  which  have  made  not  only  him  but  his  environment 
and  the  opportunities  life  has  given  him  what  they  are." — New  York  Times. 

"  Those  who  can  read  between  the  lines  may  discover  in  these  pages  constant  evidences  of 
care  and  skill  and  faithful  labor,  of  which  the  old-time  superficial  essayists,  compiling  library 
notes  on  dates  and  striking  events,  had  no  conception  ;  but  to  the  general  reader  the  fluent 
narrative  gives  no  hint  of  the  conscientious  labors,  far-reaching,  world-wide,  vast  and  yet  micro- 
scopically minute,  that  give  the  strength  and  value  which  are  felt  rather  than  seen.  This  is  due 
to  the  art  of  presentation.  The  author's  position  as  a  scientific  workman  we  may  accept  on  the 
abundant  testimony  of  the  experts  who  know  the  solid  worth  of  his  work  ;  his  skill  as  a  literary 
artist  we  can  all  appreciate,  the  charm  of  his  style  being  self-evident." — Philadelphia  Telegraph. 

"  The  third  volume  contains  the  brilliantly  written  and  fascinating  story  of  the  progress  and 
doings  of  the  people  of  this  country  from  the  era  of  the  Louisiana  purchase  to  the  opening 
scenes  of  the  second  war  with  Great  Britain — say  a  period  of  ten  years.  In  every  page  of  the 
book  the  reader  finds  that  fascinating  flow  of  narrative,  that  clear  and  lucid  style,  and  that 
penetrating  power  of  thought  and  judgment  which  distinguished  the  previous  volumes." — 
Columbus  State  Journal. 

"  Prof.  McMaster  has  more  than  fulfilled  the  promises  made  in  his  first  volumes,  and  his 
work  is  constantly  growing  better  and  more  valuable  as  he  brings  it  nearer  to  our  own  time. 
His  style  is  clear,  simple,  and  idiomatic,  and  there  is  just  enough  of  the  critical  spirit  in  the 
narrative  to  guide  the  reader." — Boston  Herald. 

"Take  it  all  in  all,  the  History  promises  to  be  the  ideal  American  history.  Not  so  much 
given  to  dates  and  battles  and  great  events  as  in  the  fact  that  it  is  like  a  great  panorama  of  the 
people,  revealing  their  inner  life  and  action.  It  contains,  with  all  its  sober  facts,  the  spice  of 
personalities  and  incidents,  which  relieves  every  page  from  dullness." — Chicago  Inter-Ocean. 

"  In  his  first  two  volumes  Prof.  McMaster  achieved  a  distinct  success.  In  this  (third)  vol- 
ume the  reputation  thus  gained  is  fully  sustained.  The  same  brilliancy  of  style  which  charac- 
terizes his  previous  volumes  is  seen  here,  and  the  same  excellent  arrangement  and  thorough 
comprehension  of  causes  and  results  is  apparent." — Boston  Advertiser. 

"  History  written  in  this  picturesque  style  will  tempt  the  most  heedless  to  read.  Prof. 
McMaster  is  more  than  a  stylist ;  he  is  a  student,  and  his  History  abounds  in  evidences  of  re- 
search in  quarters  not  before  discovered  by  the  historian."—  Chicago  Tribune. 

"  A  History  sui  generis  which  has  made  and  will  keep  its  own  place  in  our  literature." — 
New  York  Evening  Post. 

"  His  style  is  vigorous  and  his  treatment  candid  and  impartial." — New  York  Tribune. 

New  York:   D.  APPLETON  &  CO.,  72  Fifth  Avenue. 


THE  UNITED  STATES  OF  AMERICA. 

A  Study  of  the  American  Commonwealth,  its 
Natural  Resources,  People,  Industries,  Manu- 
factures, Commerce,  and  its  Work  in  Litera- 
ture, Science,  Education,  and  Self-  Government. 

Edited  by  NATHANIEL  S.  SHALER,  S.  D., 

PROFESSOR   OF  GEOLOGY   IN    HARVARD    UNIVERSITY. 

In  two  volumes,  royal  8vo.     With  Maps,  and  150  fulUpage  Illustrations. 

Cloth,  $10.00. 


Every  subject  in  this  comprehensive  work  is  timely,  because  it  is  of  immediate  in- 
terest to  every  American.  Special  attention,  however,  may  be  called  to  the  account 
of  "  American  Productive  Industry,"  by  the  Hon.  Edward  Atkinson,  with  its  array 
of  immensely  informing  diagrams  and  tables  ;  and  also  to  "  Industry  and  Finance," 
a  succinct  and  logical  presentation  of  the  subject  by  Professor  F.  W.  Taussig,  of  Har- 
vard University.  Both  these  eminent  authorities  deal  with  questions  which  are  upper- 
most to-day. 

LIST  OF  CONTRIBUTORS. 

HON.  WILLIAM  L.  WILSON,  Chairman  of  the  Ways  and  Means  Committee,  Fifty  third 
Congress. 

HON.  J.   R.   SOLEY,  formerly  Assistant  Secretary  of  the  Navy. 

EDWARD   ATKINSON,   LL.  D.,  PH.  D. 

COL.  T.  A.  DODGE,  U.  S.  A. 

COL.  GEORGE    E.  WARING,  JR. 

J.  B.  McMASTER,  Professor  of  History  in  the  University  of  Pennsylvania. 

CHARLES   DUDLEY   WARNER,  LL.  D. 

MAJOR  J.  W.  POWELL,  Director  of  the  United  States  Geological  Survey  and  the  Bureau 
of  Ethnology. 

WILLIAM   T.    HARRIS,  LL.  D.,  United  States  Commissioner  of  Education. 

LYMAN   ABBOTT,  D.  D. 

H.  H.  BANCROFT,  author  of  "  Native  Races  of  the  Pacific  Coast. " 

HARRY    PRATT  JUDSON,  Head  Dean  of  the  Colleges,  University  of  Chicago. 

JUDGE  THOMAS  M.  COOLEY,  formerly  Chairman  of  the  Interstate  Commerce  Com- 
mission. 

CHARLES    FRANCIS   ADAMS. 

D.  A.  SARGENT,  M.  D.,   Director  of  the  Hemenway  Gymnasium,  Harvard  University. 

CHARLES    HORTON   COOLEY. 

A.  E.   KENNELLY,  Assistant  to  Thomas  A.  Edison. 

D.  C.  GILMAN,   LL.  D.,  President  of  Johns  Hopkins  University. 

H.  G.  PROUT,   Editor  of  the  Railroad  Gazette. 

F.  D.   MILLET,  formarly  Vice-President  of  the  National  Academy  of  Design. 

F."  W.  TAUSSIG,  Professor  of  Political  Economy  in  Harvard  University. 

HENRY   VAN    BRUNT. 

H.  P.  FAIRFIELD. 

SAMUEL  W.   ABBOTT,  M.  D.,  Secretary  of  the  State  Board  of  Health,  Massachusetts. 

N.  S.  SHALER. 

Sold  only  by  subscription.    Prospectus,  giving  detailed  chapter  titles  and  specimen 
illustrations,  mailed  free  on  request. 


New  York  :    D.  APPLETON   &   CO.,  72  Fifth  Avenue. 


The  Warfare  of  Science  with  Theology. 

A  History  of  the  Warfare  of  Science  with  Theology  in  Christendom. 
BY  ANDREW    D.  WHITE,  LL.  D., 

Late  President  and  Professor  of  History  at  Cornell  University. 

In  two  volumes.     8vo.     Cloth,  $5.00. 

"  The  story  of  the  struggle  of  searchers  after  truth  with  the  organized  forces  of  ignorance, 
bigotry,  and  superstition  is  the  most  inspiring  chapter  in  the  whole  history  of  mankind. 
That  story  has  never  been  better  told  than  by  the  ex-  President  of  Cornell  University  in  these 
two  volumes.  ...  A  wonderful  story  it  is  that  he  tells." — London  Daily  Chronicle. 

"The  two  noble  volumes,  packed  with  rare  historical  data  and  printed  and  clothed  in  the 
best  style  of  modern  typographical  art,  more  than  realize  the  promise  of  "the- earlier  essays. 
The  book  is  an  invaluable  record  of  the  difficulties  that  biblical  superstition  has  interposed  to 
the  advance  of  physical  knowledge  ;  a  treasury  of  information  concerning  the  progress  of 
modern  science,  gathered  with  the  most  assiduous  and  patient  research  during  a  quarter  of 
a  century  in  the  libraries  not  only  of  this  country,  but  of  Europe  also.  The  painstaking  in- 
vestigations and  rare  erudition  it  embodies,  the  broad  field  it  has  so  diligently  delved  and 
gleaned,  and  the  reverent  Christian  spirit  it  manifests,  make  it  a  monumental  work,  destined 
to  become  a  classic  authority  on  the  subjects  it  has  made  its  own  henceforth.  The  previous 
works  in  this  field,  such  as  Dr.  Draper's  '  Conflict  of  Religion  and  Science,'  and  Professor 
Shields's  '  Final  Philosophy,'  must  yield  pre-eminence  to  President  White's  admirable  history. 
The  new  book  is  far  fuller  and  more  accurate  in  its  narrative,  clearer  in  its  treatment,  and 
more  judicious  in  its  judgments." — The  New  World,  London. 

"  It  is  a  complete  survey  of  the  whole  field  of  battle.  .  .  .  The  chapters  are  full  of  striking 
interest.  The  author  of  these  volumes  shows  that  the  warfare  of  science  has  never  been  with 
religion  but  only  with  old  errors  that  were  confounded  with  it,  and  that  the  Eternal  Verities 
become  the  more  clear  and  sure  as  the  ancient  guesses  which  have  been  confounded  with 
them  are  cleared  finally  away." — London  Daily  News. 

"  Such  an  honest  and  thorough  treatment  of  the  subject  in  all  its  bearings  that  it  will  carry 
weight  and  be  accepted  as  an  authority  in  tracing  the  process  by  which  the  scientific  method 
has  come  to  be  supreme  in  modern  thought  and  life." — Boston  Herald. 

"  It  is  graphic,  lucid,  even-tempered — never  bitter  nor  vindictive.  No  student  of  human 
progress  should  fail  to  read  these  volumes.  While  they  have  about  them  the  fascination  of  a 
well-told  tale,  they  are  also  crowded  with  the  facts  of  history  that  have  had  a  tremendous 
bearing  upon  the  development  of  the  race. " — Brooklyn  Eagle. 

"  A  conscientious  summary  of  the  body  of  learning  to  which  it  relates,  accumulated  during 
long  years  of  research.  .  .  .  A  monument  of  industry." — New  York  Evening  Post. 

"  So  interesting  as  to  enchain  the  attention  at  once  and  keep  it  enchained.  Concise  as  a 
history  of  the  universe  could  be  made,  tabulated  so  that  instant  reference  to  a  particular  bit 
of  history,  theory,  or  biography  may  be  had,  it  will  be  valuable  as  a  lexicon  relating  to 
religious  controversy." — Chicago  Times- Herald. 

"  Dr.  White  knows  much  of  science  and  he  knows  much  of  theology.  But  his  point  of 
view  is  that  of  a  historian.  It  is  this  fact  which  gives  the  greatest  value  to  his  book.  We 
have  whole  libraries  of  controversial  works  dealing  with  the  relations  between  science  and 
theology,  but  they  have  been  written  either  by  scientists  or  theologians.  President  White 
occupies  the  impartial  position  of  the  historic  scholar,  who  has  no  prejudices  against  the 
truth  of  science  and  no  hostility  toward  the  truth  of  religion." — N.  Y.  Review  of  Reviews. 

' '  The  work  is  a  masterpiece  of  a  mind  as  devoid  of  wanton  iconoclasm  as  of  moral 
cowardice.  It  is  a  definite  statement  of  where  the  best  thinkers  of  the  world  now  stand  in 
the  religio-scientific  conflict.  It  is  clear,  honest,  brave,  and  must  be  given  a  place  among  the 
great  books  of  the  year." — Chicago  Tribune. 

"This  is  and  will  continue  to  be  one  of  the  great  books  of  the  world,  like  Thucydides's 
'  History  of  the  Peloponnesian  War.'  So  long  as  Science  and  Theology  retain  their  place  in 
human  interest,  this  history  of  the  conflict  of  ages  between  them  will  exert  its  attraction  and 
read  its  lesson.  It  is  a  great  book." — The  Outlook. 


NEW  YORK:    D.  APPLETON   &   CO.,  72  FIFTH  AVENUE. 


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